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Re: Important Information
Yeah, but don't forget that no one has tried to mess up PC either.
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Hunchman801
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Re: Important Information
Because PC has always been fair towards its members 
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foultzboyz
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Re: Important Information
And that's what Pirate-Community was all about back in 2003--giving Rayman fans a fair board to come to, and it paid off.
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Hunchman801
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Re: Important Information
I tried my best, and I'm glad it worked 
Re: Important Information
It is very fair, and I have made very good friends here! 
I have only made one or two at Rz, that, is Abhi, Phoenixan, and Xenon (before he knew sumo_066 = neo).
I have only made one or two at Rz, that, is Abhi, Phoenixan, and Xenon (before he knew sumo_066 = neo).-
Hunchman801
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Re: Important Information
Almost no one feels ignored here, because all members are important 
Re: Important Information
The classical formulae for the energy and momentum of electromagnetic radiation can be re-expressed in terms of photon events. For example, the pressure of electromagnetic radiation on an object derives from the transfer of photon momentum per unit time and unit area to that object, since pressure is force per unit area and force is the change in momentum per unit time.
Re: Important Information
The Maxwell wave theory, however, does not account for all properties of light. The Maxwell theory predicts that the energy of a light wave depends only on its intensity, not on its frequency; nevertheless, several independent types of experiments show that the energy imparted by light to atoms depends only on the light's frequency, not on its intensity. For example, some chemical reactions can be provoked only by light of frequency higher than a certain threshold; light of lower frequency, no matter how intense, is incapable of exciting the reaction. Similarly, electrons can be ejected from a metal plate by shining light of sufficiently high frequency on it (the photoelectric effect); the energy of the ejected electron is related only to the light's frequency, not to its intensity.
Re: Important Information
The modern concept of the photon was developed gradually (1905–17) by Albert Einstein to explain experimental observations that did not fit the classical wave model of light. In particular, the photon model accounted for the frequency dependence of light's energy, and explained the ability of matter and radiation to be in thermal equilibrium. Other physicists sought to explain these anomalous observations by semiclassical models, in which light is still described by Maxwell's equations but the material objects that emit and absorb light are quantized. Although these semiclassical models contributed to the development of quantum mechanics, further experiments proved Einstein's hypothesis that light itself is quantized; the quanta of light are photons.
Re: Important Information
A key element of quantum mechanics is Heisenberg's uncertainty principle, which forbids the simultaneous measurement of the position and momentum of a particle along the same direction. Remarkably, the uncertainty principle for charged, material particles requires the quantization of light into photons, and even the frequency dependence of the photon's energy and momentum. An elegant illustration is Heisenberg's thought experiment for locating an electron with an ideal microscope.[31] The position of the electron can be determined to within the resolving power of the microscope, which is given by a formula from classical optics
Re: Important Information
Since the photon is massless, the photon moves at c \! (the speed of light in empty space) and its energy E \! and momentum \mathbf{p} are related by E = c \, p \!, where p \! is the magnitude of the momentum. For comparison, the corresponding equation for particles with an invariant mass m \! would be E^{2} = c^{2} p^{2} + m^{2} c^{4} \!, as shown in special relativity.
The energy and momentum of a photon depend only on its frequency \nu \! or, equivalently, its wavelength \lambda \!
E = \hbar\omega = h\nu = \frac{h c}{\lambda}
\mathbf{p} = \hbar\mathbf{k}
and consequently the magnitude of the momentum is
p = \hbar k = \frac{h}{\lambda} = \frac{h\nu}{c}
The energy and momentum of a photon depend only on its frequency \nu \! or, equivalently, its wavelength \lambda \!
E = \hbar\omega = h\nu = \frac{h c}{\lambda}
\mathbf{p} = \hbar\mathbf{k}
and consequently the magnitude of the momentum is
p = \hbar k = \frac{h}{\lambda} = \frac{h\nu}{c}
Re: Important Information
Photons must obey Bose–Einstein statistics if they are to allow the superposition principle of electromagnetic fields, the condition that Maxwell's equations are linear. All particles are divided into bosons and fermions, depending on whether they have integer or half-integer spin, respectively. The spin-statistics theorem shows that all bosons obey Bose–Einstein statistics, whereas all fermions obey Fermi-Dirac statistics or, equivalently, the Pauli exclusion principle, which states that at most one particle can occupy any given state. Thus, if the photon were a fermion, only one photon could move in a particular direction at a time. This is inconsistent with the experimental observation that lasers can produce coherent light of arbitrary intensity, that is, with many photons moving in the same direction. Hence, the photon must be a boson and obey Bose–Einstein statistics.
Re: Important Information
In physics, a magnetic field is that part of the electromagnetic field that exerts a force on a moving charge. A magnetic field can be caused either by another moving charge (i.e., by an electric current) or by a changing electric field. The magnetic field is a vector quantity, and has SI units of tesla, 1 T = 1 kg·s-1·C-1.
Re: Important Information
In physics, a magnetic field is that part of the electromagnetic field that exerts a force on a moving charge. A magnetic field can be caused either by another moving charge (i.e., by an electric current) or by a changing electric field. The magnetic field is a vector quantity, and has SI units of tesla, 1 T = 1 kg·s-1·C-1.
There are two quantities that physicists may refer to as the magnetic field, notated \mathbf{H} and \mathbf{B}. Although the term "magnetic field" was historically reserved for \mathbf{H}, with \mathbf{B} being termed the "magnetic induction," \mathbf{B} is now understood to be the more fundamental entity, and most modern writers refer to \mathbf{B} as the magnetic field, except when context fails to make it clear whether the quantity being discussed is \mathbf{H} or \mathbf{B}. See [1]
Contents
[hide]
* 1 Definition
* 2 The Difference between B and H
* 3 Magnetic field of current flow of charged particles
* 4 Lorentz force on wire segment
* 5 Symbols and terminology
* 6 Properties
o 6.1 Magnetic field lines
o 6.2 Pole labelling confusions
o 6.3 Field density
* 7 Historical Information
* 8 Rotating magnetic fields
* 9 Hall effect
* 10 Extension to the Theory of Relativity
* 11 See also
* 12 References
* 13 Notes
* 14 External links
[edit] Definition
The following term in Lorentz transformations of the electric field E of moving with the velocity v electric charge is called magnetic field B:
\mathbf{B} = \mathbf{v}\times \frac{1}{c^2}\mathbf{E}
where
\mathbf{v} \ is velocity of the electric charge, measured in metres per second
\times \ indicates a vector cross product
c is the speed of light in a vacuum measured in metres per second
\mathbf{E} is the electric field measured in newtons per coulomb or volts per metre
As seen from the definition, the unit of magnetic field is newton-second per coulomb-metre (or newton per ampere-metre) and is called the tesla. Like the electric field, the magnetic field exerts force on electric charge — but unlike an electric field, only on moving charge:
\mathbf{F} = q \mathbf{v} \times \mathbf{B}
where
\mathbf{F} is the force produced, measured in newtons
q \ is electric charge that the magnetic field is acting on, measured in coulombs
\mathbf{v} \ is velocity of the electric charge q \, measured in metres per second
Because magnetic field is the relativistic product of Lorentz transformations, the force it produces is called the Lorentz force.
The force due to the magnetic field is different in different frames — moving magnetic field (as well as changing magnetic field) transforms partially or fully back into electric field under Lorentz transformations. This results in Faraday's law of induction.
[edit] The Difference between B and H
The difference between the \mathbf{B} vector and the \mathbf{H} vector can be traced back to Maxwell's 1855 paper entitled 'On Faraday's Lines of Force'. It is later clarified in his concept of a sea of molecular vortices that appears in his 1861 paper On Physical Lines of Force - 1861. Within that context, \mathbf{H} represented pure vorticity (spin), whereas \mathbf{B} was a weighted vorticity that was weighted for the density of the vortex sea. Maxwell considered magnetic permeability µ to be a measure of the density of the vortex sea. Hence the relationship,
(1) Magnetic Induction Current
\mathbf{B} = \mu \mathbf{H}
was essentially a rotational analogy to the linear electric current relationship,
(2) Electric Convection Current
\mathbf{J} = \rho \mathbf{v}
where ρ is electric charge density. \mathbf{B} was seen as a kind of magnetic current of vortices aligned in their axial planes, with \mathbf{H} being the circumferential velocity of the vortices.
The electric current equation can be viewed as a convective current of electric charge that involves linear motion. By analogy, the magnetic equation is an inductive current involving spin. There is no linear motion in the inductive current along the direction of the \mathbf{B} vector. The magnetic inductive current represents lines of force. In particular, it represents lines of inverse square law force.
The extension of the above considerations confirms that where \mathbf{B} is to \mathbf{H}, and where \mathbf{J} is to ?, then it necessarily follows from Gauss's law and from the equation of continuity of charge that \mathbf{D} is to \mathbf{E}. Ie. \mathbf{B} parallels with \mathbf{D}, whereas \mathbf{H} parallels with \mathbf{E}.
[edit] Magnetic field of current flow of charged particles
Charged particle drifts in a homogenous magnetic field. (A) No disturbing force (B) With an electric field, E (C) With an independent force, F (eg. gravity) (D) In an inhomgeneous magnetic field, grad H
Charged particle drifts in a homogenous magnetic field. (A) No disturbing force (B) With an electric field, E (C) With an independent force, F (eg. gravity) (D) In an inhomgeneous magnetic field, grad H
Substituting into the definition of magnetic field
\mathbf{B} = \mathbf{v}\times \frac{1}{c^2}\mathbf{E}
the proper electric field of point-like charge (see Coulomb's law)
\mathbf{E} = { 1 \over 4 \pi \epsilon_0} {q \over r^2} \hat{r}= {10^{-7}}{c^2} {q \over \ {r}^2} \hat{r}
results in the equation of magnetic field of moving charge, which is usually called the Biot-Savart law:
\mathbf{B} = \mathbf{v}\times \frac{\mu_0}{4 \pi}\frac{q}{r^2}\hat{r}
where
q is electric charge, whose motion creates the magnetic field, measured in coulombs
\mathbf{v} is velocity of the electric charge q that is generating \mathbf{B}, measured in metres per second
\mathbf{B} is the magnetic field (measured in teslas)
[edit] Lorentz force on wire segment
Integrating the Lorentz force on an individual charged particle over a flow (current) of charged particles results in the Lorentz force on a stationary wire carrying electric current:
F = I B l \,
where
F = forces, measured in newtons
I = current in wire, measured in amperes
B = magnetic field, measured in teslas
l = length of wire, measured in metres
In the equation above, the current vector I is a vector with magnitude equal to the scalar current, I, and direction pointing along the wire in which the current is flowing.
Alternatively, instead of current, the wire segment l can be considered a vector.
The Lorentz force on a macroscopic current carrier is often referred to as the Laplace force.
[edit] Symbols and terminology
Magnetic field is usually denoted by the symbol \mathbf{B} \. Historically, \mathbf{B} \ was called the magnetic flux density or magnetic induction. A distinct quantity, \mathbf{H}, was called the magnetic field (strength), and this terminology is still often used to distinguish the two in the context of magnetic materials (non-trivial permeability µ). Otherwise, however, this distinction is often ignored, and both quantities are frequently referred to as "the magnetic field." (Some authors call \mathbf{H} the auxiliary field, instead.) In linear materials, such as air or free space, the two quantities are linearly related:
\mathbf{B} = \mu \mathbf{H} \
where
\ \mu is the magnetic permeability of the medium, measured in henries per metre.
In SI units, \mathbf{B} \ and \mathbf{H} \ are measured in teslas (T) and amperes per metre (A/m), respectively; or, in cgs units, in gauss (G) and oersteds (Oe), respectively. Two parallel wires carrying an electric current in the same direction will generate a magnetic field that will cause a force of attraction between them. This fact is used to define the value of an ampere of electric current. While like charges repel and unlike ones attract, the opposite holds for currents: if the current in one of the two parallel wires is reversed, the two will repel.
[edit] Properties
Maxwell did much to unify static electricity and magnetism, producing a set of four equations relating the two fields. However, under Maxwell's formulation, there were still two distinct fields describing different phenomena. It was Albert Einstein who showed, using special relativity, that electric and magnetic fields are two aspects of the same thing (a rank-2 tensor), and that one stationary observer may perceive a magnetic force where a moving observer perceives only an electrostatic force. Thus, using special relativity, magnetic forces are a manifestation of electrostatic forces of charges in motion and may be predicted from knowledge of the electrostatic forces and the velocity of movement (relative to some observer) of the charges.
A thought experiment one can do to show this is with two identical infinite and parallel lines of charge having no motion relative to each other but moving together relative to an observer. Another observer is moving alongside the two lines of charge (at the same velocity) and observes only electrostatic repulsive force and acceleration. The first or "stationary" observer seeing the two lines (and second observer) moving past with some known velocity also observes that the "moving" observer's clock is ticking more slowly (due to time dilation) and thus observes the repulsive acceleration of the lines more slowly than that which the "moving" observer sees. The reduction of repulsive acceleration can be thought of as an attractive force, in a classical physics context, that reduces the electrostatic repulsive force and also that is increasing with increasing velocity. This pseudo-force is precisely the same as the electromagnetic force in a classical context.
A changing magnetic field is mathematically the same as a moving magnetic field (see relativity of motion). Thus, according to Einstein's field transformation equations (that is, the Lorentz transformation of the field from a proper reference frame to a non-moving reference frame), part of it is manifested as an electric field component. This is known as Faraday's law of induction and is the principle behind electric generators and electric motors.
[edit] Magnetic field lines
Magnetic field lines shown by iron filings
Magnetic field lines shown by iron filings
The direction of the magnetic field vector follows from the definition above. It coincides with the direction of orientation of a magnetic dipole, such as a small magnet, a small loop of current in the magnetic field, or a cluster of small particles of ferromagnetic material (see figure).
[edit] Pole labelling confusions
See also Magnetic North Pole and Magnetic South Pole.
The end of a compass needle that points north was historically called the "north" magnetic pole of the needle. Since dipoles are vectors and align "head to tail" with each other, the magnetic pole located near the geographic North Pole is actually the "south" pole.
The "north" and "south" poles of a magnet or a magnetic dipole are labelled similarly to north and south poles of a compass needle. Near the north pole of a bar or a cylinder magnet, the magnetic field vector is directed out of the magnet; near the south pole, into the magnet. This magnetic field continues inside the magnet (so there are no actual "poles" anywhere inside or outside of a magnet where the field stops or starts). Breaking a magnet in half does not separate the poles but produces two magnets with two poles each.
Earth's magnetic field is probably produced by electric currents in its liquid core.
[edit] Field density
Magnetic field density, otherwise known as magnetic flux density, is essentially what the layman knows as a magnetic field — akin to a gravitational or electric field. It is a response of a medium to the presence of a magnetic field. The SI unit of magnetic flux density is the tesla. 1 tesla = 1 weber per square metre.
It can be more easily explained if one works backwards from the equation:
B=\frac {F} {I L} \,
where
B is the magnitude of flux density, measured in teslas
F is the force experienced by a wire, measured in Newtons
I is the current, measured in amperes
L is the length of the wire, measured in metres
Demonstration of Fleming's left hand rule
Demonstration of Fleming's left hand rule
For a magnetic flux density to equal 1 tesla, a force of 1 newton must act on a wire of length 1 metre carrying 1 ampere of current.
1 newton of force is not easily accomplished. For example: the most powerful superconducting electromagnets in the world have flux densities of 'only' 20 T. This is true obviously for both electromagnets and natural magnets, but a magnetic field can only act on moving charge — hence the current, I, in the equation.
The equation can be adjusted to incorporate moving single charges, ie protons, electrons, and so on via
F = BQv \,
where
Q is the charge in coulombs, and
v is the velocity of that charge in metres per second.
Fleming's left hand rule for motion, current and polarity can be used to determine the direction of any one of those from the other two, as seen in the example. It can also be remembered in the following way. The digits from the thumb to second finger indicate 'Force', 'B-field', and 'I(Current)' respectively, or F-B-I in short. For professional use, the right hand grip rule is used instead which originated from the definition of cross product in the right hand system of coordinates.
Other units of magnetic flux density are
1 gauss = 10-4 teslas = 100 microteslas (µT)
1 gamma = 10-9 teslas = 1 nanotesla (nT)
[edit] Historical Information
The difference between the B field and the H field can be historically traced back to Maxwell's concept of a sea of molecular vortices. See his original 1861 paper 'On Physical Lines of Force'.
Within that context, H represented pure vorticity (spin), whereas B was a weighted vorticity that was weighted for the density of the vortex sea. Maxwell considered magnetic permeability to be a measure of the density of the vortex sea. Hence the relationship,
(1) Magnetic Induction Current
\mathbf{B} \ = \ \mu \mathbf{H}
was essentially an angular analogy to the linear electric current relationship,
(2) Electric Convection Current
\mathbf{J} \ = \ \rho \mathbf{v}
B was seen as a kind of magnetic current of vortices aligned in their axial planes, with H being the circumferential velocity of the vortices.
The electric current equation can be viewed as a convective current of electric charge that involves motion. By analogy, the magnetic equation is an inductive current involving spin. There is no linear motion in the inductive current along the direction of the B vector. The magnetic inductive current represents lines of force. In particular, it represents lines of inverse square law force.
The extension of the above considerations confirms that where B is to H, and where J is to ?, then it necessary follows from Gauss's law and from the equation of continuity of charge that D is to E. Ie. B parallels with D, whereas H parallels with E.
[edit] Rotating magnetic fields
Main article: Alternator
The rotating magnetic field is a key principle in the operation of alternating-current motors. A permanent magnet in such a field will rotate so as to maintain its alignment with the external field. This effect was conceptualized by Nikola Tesla, and later utilised in his, and others, early AC (alternating-current) electric motors. A rotating magnetic field can be constructed using two orthogonal coils with 90 degrees phase difference in their AC currents. However, in practice such a system would be supplied through a three-wire arrangement with unequal currents. This inequality would cause serious problems in standardization of the conductor size and so, in order to overcome it, three-phase systems are used where the three currents are equal in magnitude and have 120 degrees phase difference. Three similar coils having mutual geometrical angles of 120 degrees will create the rotating magnetic field in this case. The ability of the three-phase system to create a rotating field, utilized in electric motors, is one of the main reasons why three-phase systems dominate the world's electrical power supply systems.
Because magnets degrade with time, synchronous motors and induction motors use short-circuited rotors (instead of a magnet) following the rotating magnetic field of a multicoiled stator. The short-circuited turns of the rotor develop eddy currents in the rotating field of the stator, and these currents in turn move the rotor by the Lorentz force.
In 1882, Nikola Tesla identified the concept of the rotating magnetic field. In 1885, Galileo Ferraris independently researched the concept. In 1888, Tesla gained U.S. Patent 381968 for his work. Also in 1888, Ferraris published his research in a paper to the Royal Academy of Sciences in Turin.
[edit] Hall effect
Main article: Hall effect
Because the Lorentz force is charge-sign-dependent (see above), it results in charge separation when a conductor with current is placed in a transverse magnetic field, with a buildup of opposite charges on two opposite sides of conductor in the direction normal to the magnetic field, and the potential difference between these sides can be measured.
The Hall effect is often used to measure the magnitude of a magnetic field as well as to find the sign of the dominant charge carriers in semiconductors (negative electrons or positive holes).
[edit] Extension to the Theory of Relativity
Einstein explained in 1905 that a magnetic field is the relativistic part of an electric field.[2] It arises as a mathematical by-product of Lorentz coordinate transformation of electric field from one reference frame to another (usually from co-moving with the moving charge reference frame to the reference frame of non-moving observer). When an electric charge is moving from the perspective of an observer, the electric field of this charge due to space contraction is no longer seen by the observer as spherically symmetric due to non-radial time dilation, and it must be computed using the Lorentz transformations. One of the products of these transformations is the part of the electric field which only acts on moving charges — and we call it the "magnetic field".
The quantum-mechanical motion of electrons in atoms produces the magnetic fields of permanent ferromagnets. Spinning charged particles also have magnetic moment. Some electrically neutral particles (like the neutron) with non-zero spin also have magnetic moment due to the charge distribution in their inner structure. Particles with zero spin never have magnetic moment which is the consequence that a magnetic field is the result of motion of electric field.
A magnetic field is a vector field: it associates with every point in space a (pseudo) vector that may vary through time. The direction of the field is the equilibrium direction of a magnetic dipole (like a compass needle) placed in the field.
The Lorentz transformation of a spherically-symmetric proper electric field E of a moving electric charge (for example, the electric field of an electron moving in a conducting wire) from the charge's reference frame to the reference frame of a non-moving observer results in the following term which we can define or label as "magnetic field". We use the symbol \mathbf{B} for the magnetic field and for the sake of mathematical simplicity (one symbol instead of seven). Intuitively \mathbf{B} can be seen as a vector whose direction gives the axis of the possible directions of the force on a charged particle due to the magnetic field; the possible directions being at right angles to the axis \mathbf{B}, and the exact direction being at right angles to both the velocity of the particle and \mathbf{B}. The magnitude of \mathbf{B} is the amount of force per unit of charge multiplied by the speed of the particle.
There are two quantities that physicists may refer to as the magnetic field, notated \mathbf{H} and \mathbf{B}. Although the term "magnetic field" was historically reserved for \mathbf{H}, with \mathbf{B} being termed the "magnetic induction," \mathbf{B} is now understood to be the more fundamental entity, and most modern writers refer to \mathbf{B} as the magnetic field, except when context fails to make it clear whether the quantity being discussed is \mathbf{H} or \mathbf{B}. See [1]
Contents
[hide]
* 1 Definition
* 2 The Difference between B and H
* 3 Magnetic field of current flow of charged particles
* 4 Lorentz force on wire segment
* 5 Symbols and terminology
* 6 Properties
o 6.1 Magnetic field lines
o 6.2 Pole labelling confusions
o 6.3 Field density
* 7 Historical Information
* 8 Rotating magnetic fields
* 9 Hall effect
* 10 Extension to the Theory of Relativity
* 11 See also
* 12 References
* 13 Notes
* 14 External links
[edit] Definition
The following term in Lorentz transformations of the electric field E of moving with the velocity v electric charge is called magnetic field B:
\mathbf{B} = \mathbf{v}\times \frac{1}{c^2}\mathbf{E}
where
\mathbf{v} \ is velocity of the electric charge, measured in metres per second
\times \ indicates a vector cross product
c is the speed of light in a vacuum measured in metres per second
\mathbf{E} is the electric field measured in newtons per coulomb or volts per metre
As seen from the definition, the unit of magnetic field is newton-second per coulomb-metre (or newton per ampere-metre) and is called the tesla. Like the electric field, the magnetic field exerts force on electric charge — but unlike an electric field, only on moving charge:
\mathbf{F} = q \mathbf{v} \times \mathbf{B}
where
\mathbf{F} is the force produced, measured in newtons
q \ is electric charge that the magnetic field is acting on, measured in coulombs
\mathbf{v} \ is velocity of the electric charge q \, measured in metres per second
Because magnetic field is the relativistic product of Lorentz transformations, the force it produces is called the Lorentz force.
The force due to the magnetic field is different in different frames — moving magnetic field (as well as changing magnetic field) transforms partially or fully back into electric field under Lorentz transformations. This results in Faraday's law of induction.
[edit] The Difference between B and H
The difference between the \mathbf{B} vector and the \mathbf{H} vector can be traced back to Maxwell's 1855 paper entitled 'On Faraday's Lines of Force'. It is later clarified in his concept of a sea of molecular vortices that appears in his 1861 paper On Physical Lines of Force - 1861. Within that context, \mathbf{H} represented pure vorticity (spin), whereas \mathbf{B} was a weighted vorticity that was weighted for the density of the vortex sea. Maxwell considered magnetic permeability µ to be a measure of the density of the vortex sea. Hence the relationship,
(1) Magnetic Induction Current
\mathbf{B} = \mu \mathbf{H}
was essentially a rotational analogy to the linear electric current relationship,
(2) Electric Convection Current
\mathbf{J} = \rho \mathbf{v}
where ρ is electric charge density. \mathbf{B} was seen as a kind of magnetic current of vortices aligned in their axial planes, with \mathbf{H} being the circumferential velocity of the vortices.
The electric current equation can be viewed as a convective current of electric charge that involves linear motion. By analogy, the magnetic equation is an inductive current involving spin. There is no linear motion in the inductive current along the direction of the \mathbf{B} vector. The magnetic inductive current represents lines of force. In particular, it represents lines of inverse square law force.
The extension of the above considerations confirms that where \mathbf{B} is to \mathbf{H}, and where \mathbf{J} is to ?, then it necessarily follows from Gauss's law and from the equation of continuity of charge that \mathbf{D} is to \mathbf{E}. Ie. \mathbf{B} parallels with \mathbf{D}, whereas \mathbf{H} parallels with \mathbf{E}.
[edit] Magnetic field of current flow of charged particles
Charged particle drifts in a homogenous magnetic field. (A) No disturbing force (B) With an electric field, E (C) With an independent force, F (eg. gravity) (D) In an inhomgeneous magnetic field, grad H
Charged particle drifts in a homogenous magnetic field. (A) No disturbing force (B) With an electric field, E (C) With an independent force, F (eg. gravity) (D) In an inhomgeneous magnetic field, grad H
Substituting into the definition of magnetic field
\mathbf{B} = \mathbf{v}\times \frac{1}{c^2}\mathbf{E}
the proper electric field of point-like charge (see Coulomb's law)
\mathbf{E} = { 1 \over 4 \pi \epsilon_0} {q \over r^2} \hat{r}= {10^{-7}}{c^2} {q \over \ {r}^2} \hat{r}
results in the equation of magnetic field of moving charge, which is usually called the Biot-Savart law:
\mathbf{B} = \mathbf{v}\times \frac{\mu_0}{4 \pi}\frac{q}{r^2}\hat{r}
where
q is electric charge, whose motion creates the magnetic field, measured in coulombs
\mathbf{v} is velocity of the electric charge q that is generating \mathbf{B}, measured in metres per second
\mathbf{B} is the magnetic field (measured in teslas)
[edit] Lorentz force on wire segment
Integrating the Lorentz force on an individual charged particle over a flow (current) of charged particles results in the Lorentz force on a stationary wire carrying electric current:
F = I B l \,
where
F = forces, measured in newtons
I = current in wire, measured in amperes
B = magnetic field, measured in teslas
l = length of wire, measured in metres
In the equation above, the current vector I is a vector with magnitude equal to the scalar current, I, and direction pointing along the wire in which the current is flowing.
Alternatively, instead of current, the wire segment l can be considered a vector.
The Lorentz force on a macroscopic current carrier is often referred to as the Laplace force.
[edit] Symbols and terminology
Magnetic field is usually denoted by the symbol \mathbf{B} \. Historically, \mathbf{B} \ was called the magnetic flux density or magnetic induction. A distinct quantity, \mathbf{H}, was called the magnetic field (strength), and this terminology is still often used to distinguish the two in the context of magnetic materials (non-trivial permeability µ). Otherwise, however, this distinction is often ignored, and both quantities are frequently referred to as "the magnetic field." (Some authors call \mathbf{H} the auxiliary field, instead.) In linear materials, such as air or free space, the two quantities are linearly related:
\mathbf{B} = \mu \mathbf{H} \
where
\ \mu is the magnetic permeability of the medium, measured in henries per metre.
In SI units, \mathbf{B} \ and \mathbf{H} \ are measured in teslas (T) and amperes per metre (A/m), respectively; or, in cgs units, in gauss (G) and oersteds (Oe), respectively. Two parallel wires carrying an electric current in the same direction will generate a magnetic field that will cause a force of attraction between them. This fact is used to define the value of an ampere of electric current. While like charges repel and unlike ones attract, the opposite holds for currents: if the current in one of the two parallel wires is reversed, the two will repel.
[edit] Properties
Maxwell did much to unify static electricity and magnetism, producing a set of four equations relating the two fields. However, under Maxwell's formulation, there were still two distinct fields describing different phenomena. It was Albert Einstein who showed, using special relativity, that electric and magnetic fields are two aspects of the same thing (a rank-2 tensor), and that one stationary observer may perceive a magnetic force where a moving observer perceives only an electrostatic force. Thus, using special relativity, magnetic forces are a manifestation of electrostatic forces of charges in motion and may be predicted from knowledge of the electrostatic forces and the velocity of movement (relative to some observer) of the charges.
A thought experiment one can do to show this is with two identical infinite and parallel lines of charge having no motion relative to each other but moving together relative to an observer. Another observer is moving alongside the two lines of charge (at the same velocity) and observes only electrostatic repulsive force and acceleration. The first or "stationary" observer seeing the two lines (and second observer) moving past with some known velocity also observes that the "moving" observer's clock is ticking more slowly (due to time dilation) and thus observes the repulsive acceleration of the lines more slowly than that which the "moving" observer sees. The reduction of repulsive acceleration can be thought of as an attractive force, in a classical physics context, that reduces the electrostatic repulsive force and also that is increasing with increasing velocity. This pseudo-force is precisely the same as the electromagnetic force in a classical context.
A changing magnetic field is mathematically the same as a moving magnetic field (see relativity of motion). Thus, according to Einstein's field transformation equations (that is, the Lorentz transformation of the field from a proper reference frame to a non-moving reference frame), part of it is manifested as an electric field component. This is known as Faraday's law of induction and is the principle behind electric generators and electric motors.
[edit] Magnetic field lines
Magnetic field lines shown by iron filings
Magnetic field lines shown by iron filings
The direction of the magnetic field vector follows from the definition above. It coincides with the direction of orientation of a magnetic dipole, such as a small magnet, a small loop of current in the magnetic field, or a cluster of small particles of ferromagnetic material (see figure).
[edit] Pole labelling confusions
See also Magnetic North Pole and Magnetic South Pole.
The end of a compass needle that points north was historically called the "north" magnetic pole of the needle. Since dipoles are vectors and align "head to tail" with each other, the magnetic pole located near the geographic North Pole is actually the "south" pole.
The "north" and "south" poles of a magnet or a magnetic dipole are labelled similarly to north and south poles of a compass needle. Near the north pole of a bar or a cylinder magnet, the magnetic field vector is directed out of the magnet; near the south pole, into the magnet. This magnetic field continues inside the magnet (so there are no actual "poles" anywhere inside or outside of a magnet where the field stops or starts). Breaking a magnet in half does not separate the poles but produces two magnets with two poles each.
Earth's magnetic field is probably produced by electric currents in its liquid core.
[edit] Field density
Magnetic field density, otherwise known as magnetic flux density, is essentially what the layman knows as a magnetic field — akin to a gravitational or electric field. It is a response of a medium to the presence of a magnetic field. The SI unit of magnetic flux density is the tesla. 1 tesla = 1 weber per square metre.
It can be more easily explained if one works backwards from the equation:
B=\frac {F} {I L} \,
where
B is the magnitude of flux density, measured in teslas
F is the force experienced by a wire, measured in Newtons
I is the current, measured in amperes
L is the length of the wire, measured in metres
Demonstration of Fleming's left hand rule
Demonstration of Fleming's left hand rule
For a magnetic flux density to equal 1 tesla, a force of 1 newton must act on a wire of length 1 metre carrying 1 ampere of current.
1 newton of force is not easily accomplished. For example: the most powerful superconducting electromagnets in the world have flux densities of 'only' 20 T. This is true obviously for both electromagnets and natural magnets, but a magnetic field can only act on moving charge — hence the current, I, in the equation.
The equation can be adjusted to incorporate moving single charges, ie protons, electrons, and so on via
F = BQv \,
where
Q is the charge in coulombs, and
v is the velocity of that charge in metres per second.
Fleming's left hand rule for motion, current and polarity can be used to determine the direction of any one of those from the other two, as seen in the example. It can also be remembered in the following way. The digits from the thumb to second finger indicate 'Force', 'B-field', and 'I(Current)' respectively, or F-B-I in short. For professional use, the right hand grip rule is used instead which originated from the definition of cross product in the right hand system of coordinates.
Other units of magnetic flux density are
1 gauss = 10-4 teslas = 100 microteslas (µT)
1 gamma = 10-9 teslas = 1 nanotesla (nT)
[edit] Historical Information
The difference between the B field and the H field can be historically traced back to Maxwell's concept of a sea of molecular vortices. See his original 1861 paper 'On Physical Lines of Force'.
Within that context, H represented pure vorticity (spin), whereas B was a weighted vorticity that was weighted for the density of the vortex sea. Maxwell considered magnetic permeability to be a measure of the density of the vortex sea. Hence the relationship,
(1) Magnetic Induction Current
\mathbf{B} \ = \ \mu \mathbf{H}
was essentially an angular analogy to the linear electric current relationship,
(2) Electric Convection Current
\mathbf{J} \ = \ \rho \mathbf{v}
B was seen as a kind of magnetic current of vortices aligned in their axial planes, with H being the circumferential velocity of the vortices.
The electric current equation can be viewed as a convective current of electric charge that involves motion. By analogy, the magnetic equation is an inductive current involving spin. There is no linear motion in the inductive current along the direction of the B vector. The magnetic inductive current represents lines of force. In particular, it represents lines of inverse square law force.
The extension of the above considerations confirms that where B is to H, and where J is to ?, then it necessary follows from Gauss's law and from the equation of continuity of charge that D is to E. Ie. B parallels with D, whereas H parallels with E.
[edit] Rotating magnetic fields
Main article: Alternator
The rotating magnetic field is a key principle in the operation of alternating-current motors. A permanent magnet in such a field will rotate so as to maintain its alignment with the external field. This effect was conceptualized by Nikola Tesla, and later utilised in his, and others, early AC (alternating-current) electric motors. A rotating magnetic field can be constructed using two orthogonal coils with 90 degrees phase difference in their AC currents. However, in practice such a system would be supplied through a three-wire arrangement with unequal currents. This inequality would cause serious problems in standardization of the conductor size and so, in order to overcome it, three-phase systems are used where the three currents are equal in magnitude and have 120 degrees phase difference. Three similar coils having mutual geometrical angles of 120 degrees will create the rotating magnetic field in this case. The ability of the three-phase system to create a rotating field, utilized in electric motors, is one of the main reasons why three-phase systems dominate the world's electrical power supply systems.
Because magnets degrade with time, synchronous motors and induction motors use short-circuited rotors (instead of a magnet) following the rotating magnetic field of a multicoiled stator. The short-circuited turns of the rotor develop eddy currents in the rotating field of the stator, and these currents in turn move the rotor by the Lorentz force.
In 1882, Nikola Tesla identified the concept of the rotating magnetic field. In 1885, Galileo Ferraris independently researched the concept. In 1888, Tesla gained U.S. Patent 381968 for his work. Also in 1888, Ferraris published his research in a paper to the Royal Academy of Sciences in Turin.
[edit] Hall effect
Main article: Hall effect
Because the Lorentz force is charge-sign-dependent (see above), it results in charge separation when a conductor with current is placed in a transverse magnetic field, with a buildup of opposite charges on two opposite sides of conductor in the direction normal to the magnetic field, and the potential difference between these sides can be measured.
The Hall effect is often used to measure the magnitude of a magnetic field as well as to find the sign of the dominant charge carriers in semiconductors (negative electrons or positive holes).
[edit] Extension to the Theory of Relativity
Einstein explained in 1905 that a magnetic field is the relativistic part of an electric field.[2] It arises as a mathematical by-product of Lorentz coordinate transformation of electric field from one reference frame to another (usually from co-moving with the moving charge reference frame to the reference frame of non-moving observer). When an electric charge is moving from the perspective of an observer, the electric field of this charge due to space contraction is no longer seen by the observer as spherically symmetric due to non-radial time dilation, and it must be computed using the Lorentz transformations. One of the products of these transformations is the part of the electric field which only acts on moving charges — and we call it the "magnetic field".
The quantum-mechanical motion of electrons in atoms produces the magnetic fields of permanent ferromagnets. Spinning charged particles also have magnetic moment. Some electrically neutral particles (like the neutron) with non-zero spin also have magnetic moment due to the charge distribution in their inner structure. Particles with zero spin never have magnetic moment which is the consequence that a magnetic field is the result of motion of electric field.
A magnetic field is a vector field: it associates with every point in space a (pseudo) vector that may vary through time. The direction of the field is the equilibrium direction of a magnetic dipole (like a compass needle) placed in the field.
The Lorentz transformation of a spherically-symmetric proper electric field E of a moving electric charge (for example, the electric field of an electron moving in a conducting wire) from the charge's reference frame to the reference frame of a non-moving observer results in the following term which we can define or label as "magnetic field". We use the symbol \mathbf{B} for the magnetic field and for the sake of mathematical simplicity (one symbol instead of seven). Intuitively \mathbf{B} can be seen as a vector whose direction gives the axis of the possible directions of the force on a charged particle due to the magnetic field; the possible directions being at right angles to the axis \mathbf{B}, and the exact direction being at right angles to both the velocity of the particle and \mathbf{B}. The magnitude of \mathbf{B} is the amount of force per unit of charge multiplied by the speed of the particle.
Re: Important Information
In physics, the space surrounding an electric charge has a property called an electric field. This electric field exerts a force on other charged objects. The concept of electric field was introduced by Michael Faraday.
The electric field is a vector with SI units of newtons per coulomb (N C-1) or, equivalently, volts per meter (V m-1). The direction of the field at a point is defined by the direction of the electric force exerted on a positive test charge placed at that point. The strength of the field is defined by the ratio of the electric force on a charge at a point to the magnitude of the charge placed at that point. Electric fields contain electrical energy with energy density proportional to the square of the field intensity. The electric field is to charge as acceleration is to mass and force density is to volume.
A moving charge has not just an electric field but also a magnetic field, and in general the electric and magnetic fields are not completely separate phenomena; what one observer perceives as an electric field, another observer in a different frame of reference perceives as a mixture of electric and magnetic fields. For this reason, one speaks of "electromagnetism" or "electromagnetic fields." In quantum mechanics, disturbances in the electromagnetic fields are called photons, and the energy of photons is quantized.
Contents
[hide]
* 1 Definition (for electrostatics)
* 2 Coulomb's law
* 3 Properties (in electrostatics)
* 4 Energy in the electric field
* 5 Parallels between electrostatics and gravity
* 6 Time-varying fields
* 7 See also
* 8 External links
[edit] Definition (for electrostatics)
Electric field is defined as the electric force per unit charge. The direction of the field is taken to be the direction of the force it would exert on a positive test charge. The electric field is radially outward from a positive charge and radially in toward a negative point charge.
The electric field is defined as the proportionality constant between charge and force (in other words, the force per unit of test charge):
\vec{E} = \frac{\vec{F}}{q}
where
\vec{F} is the electric force given by Coulomb's law,
q is the charge of a "test charge",
However, note that this equation is only true in the case of electrostatics, that is to say, when there is nothing moving. The more general case of moving charges causes this equation to become the Lorentz force equation.
[edit] Coulomb's law
The electric field surrounding a point charge is given by Coulomb's law:
\vec{E} =\frac{1}{4 \pi \epsilon_0}\frac{Q}{r^2}\hat{r}
where
Q is the charge of the particle creating the electric field,
r is the distance from the particle with charge Q to the E-field evaluation point,
\hat{r} is the Unit vector pointing from the particle with charge Q to the E-field evaluation point,
ε0 is the Permittivity of free space.
Coulomb's law is actually a special case of Gauss's Law, a more fundamental description of the relationship between the distribution of electric charge in space and the resulting electric field. Gauss's law is one of Maxwell's equations, a set of four laws governing electromagnetics.
[edit] Properties (in electrostatics)
Illustration of the electric field surrounding a positive (red) and a negative (green) charge (larger image).
Illustration of the electric field surrounding a positive (red) and a negative (green) charge (larger image).
According to Equation (1) above, electric field is dependent on position. The electric field due to any single charge falls off as the square of the distance from that charge.
Electric fields follow the superposition principle. If more than one charge is present, the total electric field at any point is equal to the vector sum of the respective electric fields that each object would create in the absence of the others.
\vec{E}_{\rm total} = \sum_i \vec{E}_i = \vec{E}_1 + \vec{E}_2 + \vec{E}_3 \ldots \,\!
If this principle is extended to an infinite number of infinitesimally small elements of charge, the following formula results:
\vec{E} = \frac{1}{4\pi\epsilon_0} \int\frac{\rho}{r^2} \hat{r}\,\mathrm{d}V
where
ρ is the charge density, or the amount of charge per unit volume.
The electric field at a point is equal to the negative gradient of the electric potential there. In symbols,
\vec{E} = -\vec{\nabla}\phi
where
φ(x,y,z) is the scalar field representing the electric potential at a given point.
If several spatially distributed charges generate such an electric potential, e.g. in a solid, an electric field gradient may also be defined.
Considering the permittivity \varepsilon of a material, which may differ from the permittivity of free space \varepsilon_{0}, the electric displacement field is:
\vec{D} = \varepsilon \vec{E}
[edit] Energy in the electric field
Main article: Electrical energy
The electric field stores energy. The energy density of the electric field is given by
u = \frac{1}{2} \epsilon |\vec{E}|^2
where
ε is the permittivity of the medium in which the field exists
\vec{E} is the electric field vector.
The total energy stored in the electric field in a given volume V is therefore
\int_{V} \frac{1}{2} \epsilon |\vec{E}|^2 \, \mathrm{d}V
where
dV is the differential volume element.
[edit] Parallels between electrostatics and gravity
Coulomb's law, which describes the interaction of electric charges:
\vec{F} = \frac{1}{4 \pi \epsilon_0}\frac{Qq}{r^2}\hat{r} = q\vec{E}
is similar to the Newtonian gravitation law:
\vec{F} = G\frac{Mm}{r^2}\hat{r} = m\vec{g}
This suggests similarities between the electric field E and the gravitational field g, so sometimes mass is called "gravitational charge".
Similarities between electrostatic and gravitational forces:
1. Both act in a vacuum.
2. Both are central and conservative.
3. Both obey an inverse-square law (both are inversely proprotional to square of r).
4. Both propagate with finite speed c.
Differences between electrostatic and gravitational forces:
1. Electrostatic forces are much greater than gravitational forces (by about 1036 times).
2. Gravitational forces are always attractive in nature, whereas electrostatic forces may be either attractive or repulsive.
3. Gravitational forces are independent of the medium whereas electrostatic forces depend on the medium. This is due to the fact that a medium contains charges; the fast motion of these charges, in response to an external electromagnetic field, produces a large secondary electromagnetic field which should be accounted for. While slow motion of ordinary masses in response to changing gravitational field produces extremely weak secondary "gravimagnetic field" which may be neglected in most cases (except, of course, when mass moves with relativistic speeds).
[edit] Time-varying fields
Charges do not only produce electric fields. As they move, they generate magnetic fields, and if the magnetic field changes, it generates electric fields. This "secondary" electric field can be computed using Faraday's law of induction,
\vec{\nabla} \times \vec{E} = -\frac{\partial \vec{B}} {\partial t}
where
\vec{\nabla} \times \vec{E} indicates the curl of the electric field,
-\frac{\partial \vec{B}} {\partial t} represents the vector rate of decrease of magnetic flux density with time.
This means that a magnetic field changing in time produces a curled electric field, possibly also changing in time. The situation in which electric or magnetic fields change in time is no longer electrostatics, but rather electrodynamics or electromagnetics.
The electric field is a vector with SI units of newtons per coulomb (N C-1) or, equivalently, volts per meter (V m-1). The direction of the field at a point is defined by the direction of the electric force exerted on a positive test charge placed at that point. The strength of the field is defined by the ratio of the electric force on a charge at a point to the magnitude of the charge placed at that point. Electric fields contain electrical energy with energy density proportional to the square of the field intensity. The electric field is to charge as acceleration is to mass and force density is to volume.
A moving charge has not just an electric field but also a magnetic field, and in general the electric and magnetic fields are not completely separate phenomena; what one observer perceives as an electric field, another observer in a different frame of reference perceives as a mixture of electric and magnetic fields. For this reason, one speaks of "electromagnetism" or "electromagnetic fields." In quantum mechanics, disturbances in the electromagnetic fields are called photons, and the energy of photons is quantized.
Contents
[hide]
* 1 Definition (for electrostatics)
* 2 Coulomb's law
* 3 Properties (in electrostatics)
* 4 Energy in the electric field
* 5 Parallels between electrostatics and gravity
* 6 Time-varying fields
* 7 See also
* 8 External links
[edit] Definition (for electrostatics)
Electric field is defined as the electric force per unit charge. The direction of the field is taken to be the direction of the force it would exert on a positive test charge. The electric field is radially outward from a positive charge and radially in toward a negative point charge.
The electric field is defined as the proportionality constant between charge and force (in other words, the force per unit of test charge):
\vec{E} = \frac{\vec{F}}{q}
where
\vec{F} is the electric force given by Coulomb's law,
q is the charge of a "test charge",
However, note that this equation is only true in the case of electrostatics, that is to say, when there is nothing moving. The more general case of moving charges causes this equation to become the Lorentz force equation.
[edit] Coulomb's law
The electric field surrounding a point charge is given by Coulomb's law:
\vec{E} =\frac{1}{4 \pi \epsilon_0}\frac{Q}{r^2}\hat{r}
where
Q is the charge of the particle creating the electric field,
r is the distance from the particle with charge Q to the E-field evaluation point,
\hat{r} is the Unit vector pointing from the particle with charge Q to the E-field evaluation point,
ε0 is the Permittivity of free space.
Coulomb's law is actually a special case of Gauss's Law, a more fundamental description of the relationship between the distribution of electric charge in space and the resulting electric field. Gauss's law is one of Maxwell's equations, a set of four laws governing electromagnetics.
[edit] Properties (in electrostatics)
Illustration of the electric field surrounding a positive (red) and a negative (green) charge (larger image).
Illustration of the electric field surrounding a positive (red) and a negative (green) charge (larger image).
According to Equation (1) above, electric field is dependent on position. The electric field due to any single charge falls off as the square of the distance from that charge.
Electric fields follow the superposition principle. If more than one charge is present, the total electric field at any point is equal to the vector sum of the respective electric fields that each object would create in the absence of the others.
\vec{E}_{\rm total} = \sum_i \vec{E}_i = \vec{E}_1 + \vec{E}_2 + \vec{E}_3 \ldots \,\!
If this principle is extended to an infinite number of infinitesimally small elements of charge, the following formula results:
\vec{E} = \frac{1}{4\pi\epsilon_0} \int\frac{\rho}{r^2} \hat{r}\,\mathrm{d}V
where
ρ is the charge density, or the amount of charge per unit volume.
The electric field at a point is equal to the negative gradient of the electric potential there. In symbols,
\vec{E} = -\vec{\nabla}\phi
where
φ(x,y,z) is the scalar field representing the electric potential at a given point.
If several spatially distributed charges generate such an electric potential, e.g. in a solid, an electric field gradient may also be defined.
Considering the permittivity \varepsilon of a material, which may differ from the permittivity of free space \varepsilon_{0}, the electric displacement field is:
\vec{D} = \varepsilon \vec{E}
[edit] Energy in the electric field
Main article: Electrical energy
The electric field stores energy. The energy density of the electric field is given by
u = \frac{1}{2} \epsilon |\vec{E}|^2
where
ε is the permittivity of the medium in which the field exists
\vec{E} is the electric field vector.
The total energy stored in the electric field in a given volume V is therefore
\int_{V} \frac{1}{2} \epsilon |\vec{E}|^2 \, \mathrm{d}V
where
dV is the differential volume element.
[edit] Parallels between electrostatics and gravity
Coulomb's law, which describes the interaction of electric charges:
\vec{F} = \frac{1}{4 \pi \epsilon_0}\frac{Qq}{r^2}\hat{r} = q\vec{E}
is similar to the Newtonian gravitation law:
\vec{F} = G\frac{Mm}{r^2}\hat{r} = m\vec{g}
This suggests similarities between the electric field E and the gravitational field g, so sometimes mass is called "gravitational charge".
Similarities between electrostatic and gravitational forces:
1. Both act in a vacuum.
2. Both are central and conservative.
3. Both obey an inverse-square law (both are inversely proprotional to square of r).
4. Both propagate with finite speed c.
Differences between electrostatic and gravitational forces:
1. Electrostatic forces are much greater than gravitational forces (by about 1036 times).
2. Gravitational forces are always attractive in nature, whereas electrostatic forces may be either attractive or repulsive.
3. Gravitational forces are independent of the medium whereas electrostatic forces depend on the medium. This is due to the fact that a medium contains charges; the fast motion of these charges, in response to an external electromagnetic field, produces a large secondary electromagnetic field which should be accounted for. While slow motion of ordinary masses in response to changing gravitational field produces extremely weak secondary "gravimagnetic field" which may be neglected in most cases (except, of course, when mass moves with relativistic speeds).
[edit] Time-varying fields
Charges do not only produce electric fields. As they move, they generate magnetic fields, and if the magnetic field changes, it generates electric fields. This "secondary" electric field can be computed using Faraday's law of induction,
\vec{\nabla} \times \vec{E} = -\frac{\partial \vec{B}} {\partial t}
where
\vec{\nabla} \times \vec{E} indicates the curl of the electric field,
-\frac{\partial \vec{B}} {\partial t} represents the vector rate of decrease of magnetic flux density with time.
This means that a magnetic field changing in time produces a curled electric field, possibly also changing in time. The situation in which electric or magnetic fields change in time is no longer electrostatics, but rather electrodynamics or electromagnetics.
Re: Important Information
Suggested reading
* Wilczek, Frank ; Quantum Field Theory, Review of Modern Physics 71 (1999) S85-S95. Review article written by a master of Q.C.D., Nobel laureate 2003. Full text available at : hep-th/9803075
* Ryder, Lewis H. ; Quantum Field Theory (Cambridge University Press, 1985), [ISBN 0-521-33859-X]. Introduction to relativistic Q.F.T. for particle physics.
* Zee, Anthony ; Quantum Field Theory in a Nutshell, Princeton University Press (2003) [ISBN 0-691-01019-6].
* Peskin, M and Schroeder, D. ;An Introduction to Quantum Field Theory (Westview Press, 1995) [ISBN 0-201-50397-2]
* Weinberg, Steven ; The Quantum Theory of Fields (3 volumes) Cambridge University Press (1995). A monumental treatise on Q.F.T. written by a leading expert, Nobel laureate 1979.
* Loudon, Rodney ; The Quantum Theory of Light (Oxford University Press, 1983), [ISBN 0-19-851155-8]
* D.A. Bromley (2000). Gauge Theory of Weak Interactions. Springer. ISBN 3-540-67672-4.
* Gordon L. Kane (1987). Modern Elementary Particle Physics. Perseus Books. ISBN 0-201-11749-5.
* Wilczek, Frank ; Quantum Field Theory, Review of Modern Physics 71 (1999) S85-S95. Review article written by a master of Q.C.D., Nobel laureate 2003. Full text available at : hep-th/9803075
* Ryder, Lewis H. ; Quantum Field Theory (Cambridge University Press, 1985), [ISBN 0-521-33859-X]. Introduction to relativistic Q.F.T. for particle physics.
* Zee, Anthony ; Quantum Field Theory in a Nutshell, Princeton University Press (2003) [ISBN 0-691-01019-6].
* Peskin, M and Schroeder, D. ;An Introduction to Quantum Field Theory (Westview Press, 1995) [ISBN 0-201-50397-2]
* Weinberg, Steven ; The Quantum Theory of Fields (3 volumes) Cambridge University Press (1995). A monumental treatise on Q.F.T. written by a leading expert, Nobel laureate 1979.
* Loudon, Rodney ; The Quantum Theory of Light (Oxford University Press, 1983), [ISBN 0-19-851155-8]
* D.A. Bromley (2000). Gauge Theory of Weak Interactions. Springer. ISBN 3-540-67672-4.
* Gordon L. Kane (1987). Modern Elementary Particle Physics. Perseus Books. ISBN 0-201-11749-5.
Re: Important Information
Superconductivity is a phenomenon occurring in certain materials at extremely low temperatures, characterized by exactly zero electrical resistance and the exclusion of the interior magnetic field (the Meissner effect).
The electrical resistivity of a metallic conductor decreases gradually as the temperature is lowered. However, in ordinary conductors such as copper and silver, impurities and other defects impose a lower limit. Even near absolute zero a real sample of copper shows a non-zero resistance. The resistance of a superconductor, on the other hand, drops abruptly to zero when the material is cooled below its "critical temperature", typically 20 kelvins or less. An electrical current flowing in a loop of superconducting wire can persist indefinitely with no power source. Like ferromagnetism and atomic spectral lines, superconductivity is a quantum mechanical phenomenon. It cannot be understood simply as the idealization of "perfect conductivity" in classical physics.
Superconductivity occurs in a wide variety of materials, including simple elements like tin and aluminum, various metallic alloys and some heavily-doped semiconductors. Superconductivity does not occur in noble metals like gold and silver, nor in most ferromagnetic metals.
In 1986 the discovery of a family of cuprate-perovskite ceramic materials known as high-temperature superconductors, with critical temperatures in excess of 90 kelvins, spurred renewed interest and research in superconductivity for several reasons. As a topic of pure research, these materials represented a new phenomenon not explained by the current theory. And, because the superconducting state persists up to more manageable temperatures, more commercial applications are feasible, especially if materials with even higher critical temperatures could be discovered.
Contents
[hide]
* 1 Elementary properties of superconductors
o 1.1 Zero electrical "dc" resistance
o 1.2 Superconducting phase transition
o 1.3 Meissner effect
* 2 Theories of superconductivity
* 3 History of superconductivity
* 4 Applications
* 5 Superconductors in popular culture
* 6 See also
* 7 References
o 7.1 Books
o 7.2 Journal articles
* 8 External links
o 8.1 News
* 9 Media
[edit] Elementary properties of superconductors
Most of the physical properties of superconductors vary from material to material, such as the heat capacity and the critical temperature at which superconductivity is destroyed. On the other hand, there is a class of properties that are independent of the underlying material. For instance, all superconductors have exactly zero resistivity to low applied currents when there is no magnetic field present. The existence of these "universal" properties implies that superconductivity is a thermodynamic phase, and thus possess certain distinguishing properties which are largely independent of microscopic details.
[edit] Zero electrical "dc" resistance
Electric cables for accelerators at CERN: top, regular cables for LEP; bottom, superconducting cables for the LHC.
Electric cables for accelerators at CERN: top, regular cables for LEP; bottom, superconducting cables for the LHC.
The simplest method to measure the electrical resistance of a sample of some material is to place it in an electrical circuit in series with a current source I and measure the resulting voltage U across the sample. The resistance of the sample is given by Ohm's law as R = \frac{U}{I}. If the voltage is zero, this means that the resistance is zero and that the sample is in the superconducting state.
Superconductors are also able to maintain a current with no applied voltage whatsoever, a property exploited in superconducting electromagnets such as those found in MRI machines. Experiments have demonstrated that currents in superconducting coils can persist for years without any measurable degradation. Experimental evidence points to a current lifetime of at least 100,000 years, and theoretical estimates for the lifetime of persistent current exceed the lifetime of the universe.
In a normal conductor, an electrical current may be visualized as a fluid of electrons moving across a heavy ionic lattice. The electrons are constantly colliding with the ions in the lattice, and during each collision some of the energy carried by the current is absorbed by the lattice and converted into heat (which is essentially the vibrational kinetic energy of the lattice ions.) As a result, the energy carried by the current is constantly being dissipated. This is the phenomenon of electrical resistance.
The situation is different in a superconductor. In a conventional superconductor, the electronic fluid cannot be resolved into individual electrons. Instead, it consists of bound pairs of electrons known as Cooper pairs. This pairing is caused by an attractive force between electrons from the exchange of phonons. Due to quantum mechanics, the energy spectrum of this Cooper pair fluid possesses an energy gap, meaning there is a minimum amount of energy ΔE that must be supplied in order to excite the fluid. Therefore, if ΔE is larger than the thermal energy of the lattice (given by kT, where k is Boltzmann's constant and T is the temperature), the fluid will not be scattered by the lattice. The Cooper pair fluid is thus a superfluid, meaning it can flow without energy dissipation.
In a class of superconductors known as type II superconductors (including all known high-temperature superconductors), an extremely small amount of resistivity appears at temperatures not too far below the nominal superconducting transition when an electrical current is applied in conjunction with a strong magnetic field (which may be caused by the electrical current). This is due to the motion of vortices in the electronic superfluid, which dissipates some of the energy carried by the current. If the current is sufficiently small, the vortices are stationary, and the resistivity vanishes. The resistance due to this effect is tiny compared with that of non-superconducting materials, but must be taken into account in sensitive experiments. However, as the temperature decreases far enough below the nominal superconducting transition, these vortices can become frozen into a disordered but stationary phase known as a "vortex glass". Below this vortex glass transition temperature, the resistance of the material becomes truly zero.
[edit] Superconducting phase transition
Behavior of heat capacity (cv) and resistivity (ρ) at the superconducting phase transition
Behavior of heat capacity (cv) and resistivity (ρ) at the superconducting phase transition
In superconducting materials, the characteristics of superconductivity appear when the temperature T is lowered below a critical temperature Tc. The value of this critical temperature varies from material to material. Conventional superconductors usually have critical temperatures ranging from less than 1 K to around 20 K. Solid mercury, for example, has a critical temperature of 4.2 K. As of 2001, the highest critical temperature found for a conventional superconductor is 39 K for magnesium diboride (MgB2), although this material displays enough exotic properties that there is doubt about classifying it as a "conventional" superconductor. Cuprate superconductors can have much higher critical temperatures: YBa2Cu3O7, one of the first cuprate superconductors to be discovered, has a critical temperature of 92 K, and mercury-based cuprates have been found with critical temperatures in excess of 130 K. The explanation for these high critical temperatures remains unknown. (Electron pairing due to phonon exchanges explains superconductivity in conventional superconductors, but it does not explain superconductivity in the newer superconductors that have a very high Tc.)
The onset of superconductivity is accompanied by abrupt changes in various physical properties, which is the hallmark of a phase transition. For example, the electronic heat capacity is proportional to the temperature in the normal (non-superconducting) regime. At the superconducting transition, it suffers a discontinuous jump and thereafter ceases to be linear. At low temperatures, it varies instead as e−α /T for some constant α. (This exponential behavior is one of the pieces of evidence for the existence of the energy gap.)
The order of the superconducting phase transition was long a matter of debate. Experiments indicate that the transition is second-order, meaning there is no latent heat. In the seventies calculations suggested that it may actually be weakly first-order due to the effect of long-range fluctuations in the electromagnetic field. Only recently it was shown theoretically with the help of a disorder field theory, in which the vortex lines of the superconductor play a major role, that the transition is of second order within the type II regime and of first order (i.e., latent heat) within the type I regime, and that the two regions are separated by a tricritical point.
[edit] Meissner effect
When a superconductor is placed in a weak external magnetic field H, the field penetrates the superconductor for only a short distance λ, called the penetration depth, after which it decays rapidly to zero. This is called the Meissner effect, and is a defining characteristic of superconductivity. For most superconductors, the penetration depth is on the order of 100 nm.
The Meissner effect is sometimes confused with the kind of diamagnetism one would expect in a perfect electrical conductor: according to Lenz's law, when a changing magnetic field is applied to a conductor, it will induce an electrical current in the conductor that creates an opposing magnetic field. In a perfect conductor, an arbitrarily large current can be induced, and the resulting magnetic field exactly cancels the applied field.
The Meissner effect is distinct from this because a superconductor expels all magnetic fields, not just those that are changing. Suppose we have a material in its normal state, containing a constant internal magnetic field. When the material is cooled below the critical temperature, we would observe the abrupt expulsion of the internal magnetic field, which we would not expect based on Lenz's law.
The Meissner effect was explained by London and London, who showed that the electromagnetic free energy in a superconductor is minimized provided
\nabla^2\mathbf{H} = \lambda^{-2} \mathbf{H}\,
where H is the magnetic field and λ is the penetration depth.
This equation, which is known as the London equation, predicts that the magnetic field in a superconductor decays exponentially from whatever value it possesses at the surface.
The Meissner effect breaks down when the applied magnetic field is too large. Superconductors can be divided into two classes according to how this breakdown occurs. In Type I superconductors, superconductivity is abruptly destroyed when the strength of the applied field rises above a critical value Hc. Depending on the geometry of the sample, one may obtain an intermediate state consisting of regions of normal material carrying a magnetic field mixed with regions of superconducting material containing no field. In Type II superconductors, raising the applied field past a critical value Hc1 leads to a mixed state in which an increasing amount of magnetic flux penetrates the material, but there remains no resistance to the flow of electrical current as long as the current is not too large. At a second critical field strength Hc2, superconductivity is destroyed. The mixed state is actually caused by vortices in the electronic superfluid, sometimes called fluxons because the flux carried by these vortices is quantized. Most pure elemental superconductors (except niobium, technetium, vanadium and carbon nanotubes) are Type I, while almost all impure and compound superconductors are Type II.
[edit] Theories of superconductivity
Since the discovery of superconductivity, great efforts have been devoted to finding out how and why it works. During the 1950s, theoretical condensed matter physicists arrived at a solid understanding of "conventional" superconductivity, through a pair of remarkable and important theories: the phenomenological Ginzburg-Landau theory (1950) and the microscopic BCS theory (1957). Generalizations of these theories form the basis for understanding the closely related phenomenon of superfluidity (because they fall into the Lambda transition universality class), but the extent to which similar generalizations can be applied to unconventional superconductors as well is still controversial.
[edit] History of superconductivity
Main article: History of superconductivity
Superconductivity was discovered in 1911 by Heike Kamerlingh Onnes, who was studying the resistance of solid mercury at cryogenic temperatures using the recently-discovered liquid helium as a refrigerant. At the temperature of 4.2 K, he observed that the resistance abruptly disappeared. For this discovery, he was awarded the Nobel Prize in Physics in 1913.
In subsequent decades, superconductivity was found in several other materials. In 1913, lead was found to superconduct at 7 K, and in 1941 niobium nitride was found to superconduct at 16 K.
The next important step in understanding superconductivity occurred in 1933, when Meissner and Ochsenfeld discovered that superconductors expelled applied magnetic fields, a phenomenon which has come to be known as the Meissner effect. In 1935, F. and H. London showed that the Meissner effect was a consequence of the minimization of the electromagnetic free energy carried by superconducting current.
In 1950, the phenomenological Ginzburg-Landau theory of superconductivity was devised by Landau and Ginzburg. This theory, which combined Landau's theory of second-order phase transitions with a Schrödinger-like wave equation, had great success in explaining the macroscopic properties of superconductors. In particular, Abrikosov showed that Ginzburg-Landau theory predicts the division of superconductors into the two categories now referred to as Type I and Type II. Abrikosov and Ginzburg were awarded the 2003 Nobel Prize for their work (Landau having died in 1968.)
Also in 1950, Maxwell and Reynolds et al. found that the critical temperature of a superconductor depends on the isotopic mass of the constituent element. This important discovery pointed to the electron-phonon interaction as the microscopic mechanism responsible for superconductivity.
The complete microscopic theory of superconductivity was finally proposed in 1957 by Bardeen, Cooper, and Schrieffer. Independently superconductivity phenomenon was explained by Nikolay Bogolyubov. This BCS theory explained the superconducting current as a superfluid of Cooper pairs, pairs of electrons interacting through the exchange of phonons. For this work, the authors were awarded the Nobel Prize in 1972.
The BCS theory was set on a firmer footing in 1958, when Bogoliubov showed that the BCS wavefunction, which had originally been derived from a variational argument, could be obtained using a canonical transformation of the electronic Hamiltonian. In 1959, Gor'kov showed that the BCS theory reduced to the Ginzburg-Landau theory close to the critical temperature.
In 1962, the first commercial superconducting wire, a niobium-titanium alloy, was developed by researchers at Westinghouse. In the same year, Josephson made the important theoretical prediction that a supercurrent can flow between two pieces of superconductor separated by a thin layer of insulator. This phenomenon, now called the Josephson effect, is exploited by superconducting devices such as SQUIDs. It is used in the most accurate available measurements of the magnetic flux quantum h/e, and thus (coupled with the quantum Hall resistivity) for Planck's constant h. Josephson was awarded the Nobel Prize for this work in 1973.
A quench of the superconducting state in a superconducting magnet will result in the boiling away of potentially thousands of dollars worth of liquid helium, as seen in the above image of such an event at the ATRAP experiment at CERN.
A quench of the superconducting state in a superconducting magnet will result in the boiling away of potentially thousands of dollars worth of liquid helium, as seen in the above image of such an event at the ATRAP experiment at CERN.
Until 1986, physicists had believed that BCS theory forbade superconductivity at temperatures above about 30 K. In that year, Bednorz and Müller discovered superconductivity in a lanthanum-based cuprate perovskite material, which had a transition temperature of 35 K (Nobel Prize in Physics, 1987). It was shortly found by Paul C. W. Chu of the University of Houston and M.K. Wu at the University of Alabama in Huntsville [1] that replacing the lanthanum with yttrium, i.e. making YBCO, raised the critical temperature to 92 K, which was important because liquid nitrogen could then be used as a refrigerant (at atmospheric pressure, the boiling point of nitrogen is 77 K.) This is important commercially because liquid nitrogen can be produced cheaply on-site with no raw materials, and is not prone to some of the problems (solid air plugs, etc) of helium in piping. Many other cuprate superconductors have since been discovered, and the theory of superconductivity in these materials is one of the major outstanding challenges of theoretical condensed matter physics.
[edit] Applications
Main article: Technological applications of superconductivity
Superconductors are used to make some of the most powerful electromagnets known to man, including those used in MRI machines and the beam-steering magnets used in particle accelerators. They can also be used for magnetic separation, where weakly magnetic particles are extracted from a background of less or non-magnetic particles, as in the pigment industries.
Superconductors have also been used to make digital circuits (e.g. based on the Rapid Single Flux Quantum technology) and microwave filters for mobile phone base stations.
Superconductors are used to build Josephson junctions which are the building blocks of SQUIDs (superconducting quantum interference devices), the most sensitive magnetometers known. Series of Josephson devices are used to define the SI volt. Depending on the particular mode of operation, a Josephson junction can be used as photon detector or as mixer. The large resistance change at the transition from the normal- to the superconducting state is used to build thermometers in cryogenic micro-calorimeter photon detectors.
Other early markets are arising where the relative efficiency, size and weight advantages of devices based on HTS outweigh the additional costs involved.
Promising future applications include high-performance transformers, power storage devices, electric power transmission, electric motors (e.g. for vehicle propulsion, as in vactrains or maglev trains), magnetic levitation devices, and Fault Current Limiters. However superconductivity is sensitive to moving magnetic fields so applications that use alternating current (e.g. transformers) will be more difficult to develop than those that rely upon direct current.
[edit] Superconductors in popular culture
Superconductivity has long been a staple of science fiction. One of the first mentions of the phenomenon occurred in Robert A. Heinlein's novel Beyond This Horizon (1942). Notably, the use of a fictional room temperature superconductor was a major plot point in the Ringworld novels by Larry Niven, first published in 1970. Organic superconductors were featured in a science fiction novel by physicist Robert L. Forward.
Superconductivity is a popular device in science fiction due to the simplicity of the underlying concept - zero electrical resistance - and the rich technological possibilities. For example, superconducting magnets could be used to generate the powerful magnetic fields used by Bussard ramjets, a type of spacecraft commonly encountered in science fiction. The most troublesome property of real superconductors, the need for cryogenic cooling, is often circumvented by postulating the existence of room temperature superconductors. Many stories attribute additional properties to their fictional superconductors, ranging from infinite heat conductivity (ie thermal superconductivity) in Niven's novels (real superconductors conduct heat poorly, though superfluid helium has immense but finite heat conductivity) to providing power to an interstellar travel device in the Stargate movie and TV series.
In the movie Terminator 2: Judgment Day, the CPU of the T-800 destroyed in Terminator 1 is found to be superconductive at room temperature.
Superconductors are a technology required in the Civilization series (computer game) in order to build the spaceship to Alpha Centauri hence achieving a space victory. Superconductors are also an early technology in another of Sid Meier's games, Alpha Centauri (game)
In the movie "Strangers with Candy", students in a science class build a superconductor made of soup cans.
In the movie "Joe versus the Volcano", an industrialist needs a mineral called bubaru to make superconductors.
The electrical resistivity of a metallic conductor decreases gradually as the temperature is lowered. However, in ordinary conductors such as copper and silver, impurities and other defects impose a lower limit. Even near absolute zero a real sample of copper shows a non-zero resistance. The resistance of a superconductor, on the other hand, drops abruptly to zero when the material is cooled below its "critical temperature", typically 20 kelvins or less. An electrical current flowing in a loop of superconducting wire can persist indefinitely with no power source. Like ferromagnetism and atomic spectral lines, superconductivity is a quantum mechanical phenomenon. It cannot be understood simply as the idealization of "perfect conductivity" in classical physics.
Superconductivity occurs in a wide variety of materials, including simple elements like tin and aluminum, various metallic alloys and some heavily-doped semiconductors. Superconductivity does not occur in noble metals like gold and silver, nor in most ferromagnetic metals.
In 1986 the discovery of a family of cuprate-perovskite ceramic materials known as high-temperature superconductors, with critical temperatures in excess of 90 kelvins, spurred renewed interest and research in superconductivity for several reasons. As a topic of pure research, these materials represented a new phenomenon not explained by the current theory. And, because the superconducting state persists up to more manageable temperatures, more commercial applications are feasible, especially if materials with even higher critical temperatures could be discovered.
Contents
[hide]
* 1 Elementary properties of superconductors
o 1.1 Zero electrical "dc" resistance
o 1.2 Superconducting phase transition
o 1.3 Meissner effect
* 2 Theories of superconductivity
* 3 History of superconductivity
* 4 Applications
* 5 Superconductors in popular culture
* 6 See also
* 7 References
o 7.1 Books
o 7.2 Journal articles
* 8 External links
o 8.1 News
* 9 Media
[edit] Elementary properties of superconductors
Most of the physical properties of superconductors vary from material to material, such as the heat capacity and the critical temperature at which superconductivity is destroyed. On the other hand, there is a class of properties that are independent of the underlying material. For instance, all superconductors have exactly zero resistivity to low applied currents when there is no magnetic field present. The existence of these "universal" properties implies that superconductivity is a thermodynamic phase, and thus possess certain distinguishing properties which are largely independent of microscopic details.
[edit] Zero electrical "dc" resistance
Electric cables for accelerators at CERN: top, regular cables for LEP; bottom, superconducting cables for the LHC.
Electric cables for accelerators at CERN: top, regular cables for LEP; bottom, superconducting cables for the LHC.
The simplest method to measure the electrical resistance of a sample of some material is to place it in an electrical circuit in series with a current source I and measure the resulting voltage U across the sample. The resistance of the sample is given by Ohm's law as R = \frac{U}{I}. If the voltage is zero, this means that the resistance is zero and that the sample is in the superconducting state.
Superconductors are also able to maintain a current with no applied voltage whatsoever, a property exploited in superconducting electromagnets such as those found in MRI machines. Experiments have demonstrated that currents in superconducting coils can persist for years without any measurable degradation. Experimental evidence points to a current lifetime of at least 100,000 years, and theoretical estimates for the lifetime of persistent current exceed the lifetime of the universe.
In a normal conductor, an electrical current may be visualized as a fluid of electrons moving across a heavy ionic lattice. The electrons are constantly colliding with the ions in the lattice, and during each collision some of the energy carried by the current is absorbed by the lattice and converted into heat (which is essentially the vibrational kinetic energy of the lattice ions.) As a result, the energy carried by the current is constantly being dissipated. This is the phenomenon of electrical resistance.
The situation is different in a superconductor. In a conventional superconductor, the electronic fluid cannot be resolved into individual electrons. Instead, it consists of bound pairs of electrons known as Cooper pairs. This pairing is caused by an attractive force between electrons from the exchange of phonons. Due to quantum mechanics, the energy spectrum of this Cooper pair fluid possesses an energy gap, meaning there is a minimum amount of energy ΔE that must be supplied in order to excite the fluid. Therefore, if ΔE is larger than the thermal energy of the lattice (given by kT, where k is Boltzmann's constant and T is the temperature), the fluid will not be scattered by the lattice. The Cooper pair fluid is thus a superfluid, meaning it can flow without energy dissipation.
In a class of superconductors known as type II superconductors (including all known high-temperature superconductors), an extremely small amount of resistivity appears at temperatures not too far below the nominal superconducting transition when an electrical current is applied in conjunction with a strong magnetic field (which may be caused by the electrical current). This is due to the motion of vortices in the electronic superfluid, which dissipates some of the energy carried by the current. If the current is sufficiently small, the vortices are stationary, and the resistivity vanishes. The resistance due to this effect is tiny compared with that of non-superconducting materials, but must be taken into account in sensitive experiments. However, as the temperature decreases far enough below the nominal superconducting transition, these vortices can become frozen into a disordered but stationary phase known as a "vortex glass". Below this vortex glass transition temperature, the resistance of the material becomes truly zero.
[edit] Superconducting phase transition
Behavior of heat capacity (cv) and resistivity (ρ) at the superconducting phase transition
Behavior of heat capacity (cv) and resistivity (ρ) at the superconducting phase transition
In superconducting materials, the characteristics of superconductivity appear when the temperature T is lowered below a critical temperature Tc. The value of this critical temperature varies from material to material. Conventional superconductors usually have critical temperatures ranging from less than 1 K to around 20 K. Solid mercury, for example, has a critical temperature of 4.2 K. As of 2001, the highest critical temperature found for a conventional superconductor is 39 K for magnesium diboride (MgB2), although this material displays enough exotic properties that there is doubt about classifying it as a "conventional" superconductor. Cuprate superconductors can have much higher critical temperatures: YBa2Cu3O7, one of the first cuprate superconductors to be discovered, has a critical temperature of 92 K, and mercury-based cuprates have been found with critical temperatures in excess of 130 K. The explanation for these high critical temperatures remains unknown. (Electron pairing due to phonon exchanges explains superconductivity in conventional superconductors, but it does not explain superconductivity in the newer superconductors that have a very high Tc.)
The onset of superconductivity is accompanied by abrupt changes in various physical properties, which is the hallmark of a phase transition. For example, the electronic heat capacity is proportional to the temperature in the normal (non-superconducting) regime. At the superconducting transition, it suffers a discontinuous jump and thereafter ceases to be linear. At low temperatures, it varies instead as e−α /T for some constant α. (This exponential behavior is one of the pieces of evidence for the existence of the energy gap.)
The order of the superconducting phase transition was long a matter of debate. Experiments indicate that the transition is second-order, meaning there is no latent heat. In the seventies calculations suggested that it may actually be weakly first-order due to the effect of long-range fluctuations in the electromagnetic field. Only recently it was shown theoretically with the help of a disorder field theory, in which the vortex lines of the superconductor play a major role, that the transition is of second order within the type II regime and of first order (i.e., latent heat) within the type I regime, and that the two regions are separated by a tricritical point.
[edit] Meissner effect
When a superconductor is placed in a weak external magnetic field H, the field penetrates the superconductor for only a short distance λ, called the penetration depth, after which it decays rapidly to zero. This is called the Meissner effect, and is a defining characteristic of superconductivity. For most superconductors, the penetration depth is on the order of 100 nm.
The Meissner effect is sometimes confused with the kind of diamagnetism one would expect in a perfect electrical conductor: according to Lenz's law, when a changing magnetic field is applied to a conductor, it will induce an electrical current in the conductor that creates an opposing magnetic field. In a perfect conductor, an arbitrarily large current can be induced, and the resulting magnetic field exactly cancels the applied field.
The Meissner effect is distinct from this because a superconductor expels all magnetic fields, not just those that are changing. Suppose we have a material in its normal state, containing a constant internal magnetic field. When the material is cooled below the critical temperature, we would observe the abrupt expulsion of the internal magnetic field, which we would not expect based on Lenz's law.
The Meissner effect was explained by London and London, who showed that the electromagnetic free energy in a superconductor is minimized provided
\nabla^2\mathbf{H} = \lambda^{-2} \mathbf{H}\,
where H is the magnetic field and λ is the penetration depth.
This equation, which is known as the London equation, predicts that the magnetic field in a superconductor decays exponentially from whatever value it possesses at the surface.
The Meissner effect breaks down when the applied magnetic field is too large. Superconductors can be divided into two classes according to how this breakdown occurs. In Type I superconductors, superconductivity is abruptly destroyed when the strength of the applied field rises above a critical value Hc. Depending on the geometry of the sample, one may obtain an intermediate state consisting of regions of normal material carrying a magnetic field mixed with regions of superconducting material containing no field. In Type II superconductors, raising the applied field past a critical value Hc1 leads to a mixed state in which an increasing amount of magnetic flux penetrates the material, but there remains no resistance to the flow of electrical current as long as the current is not too large. At a second critical field strength Hc2, superconductivity is destroyed. The mixed state is actually caused by vortices in the electronic superfluid, sometimes called fluxons because the flux carried by these vortices is quantized. Most pure elemental superconductors (except niobium, technetium, vanadium and carbon nanotubes) are Type I, while almost all impure and compound superconductors are Type II.
[edit] Theories of superconductivity
Since the discovery of superconductivity, great efforts have been devoted to finding out how and why it works. During the 1950s, theoretical condensed matter physicists arrived at a solid understanding of "conventional" superconductivity, through a pair of remarkable and important theories: the phenomenological Ginzburg-Landau theory (1950) and the microscopic BCS theory (1957). Generalizations of these theories form the basis for understanding the closely related phenomenon of superfluidity (because they fall into the Lambda transition universality class), but the extent to which similar generalizations can be applied to unconventional superconductors as well is still controversial.
[edit] History of superconductivity
Main article: History of superconductivity
Superconductivity was discovered in 1911 by Heike Kamerlingh Onnes, who was studying the resistance of solid mercury at cryogenic temperatures using the recently-discovered liquid helium as a refrigerant. At the temperature of 4.2 K, he observed that the resistance abruptly disappeared. For this discovery, he was awarded the Nobel Prize in Physics in 1913.
In subsequent decades, superconductivity was found in several other materials. In 1913, lead was found to superconduct at 7 K, and in 1941 niobium nitride was found to superconduct at 16 K.
The next important step in understanding superconductivity occurred in 1933, when Meissner and Ochsenfeld discovered that superconductors expelled applied magnetic fields, a phenomenon which has come to be known as the Meissner effect. In 1935, F. and H. London showed that the Meissner effect was a consequence of the minimization of the electromagnetic free energy carried by superconducting current.
In 1950, the phenomenological Ginzburg-Landau theory of superconductivity was devised by Landau and Ginzburg. This theory, which combined Landau's theory of second-order phase transitions with a Schrödinger-like wave equation, had great success in explaining the macroscopic properties of superconductors. In particular, Abrikosov showed that Ginzburg-Landau theory predicts the division of superconductors into the two categories now referred to as Type I and Type II. Abrikosov and Ginzburg were awarded the 2003 Nobel Prize for their work (Landau having died in 1968.)
Also in 1950, Maxwell and Reynolds et al. found that the critical temperature of a superconductor depends on the isotopic mass of the constituent element. This important discovery pointed to the electron-phonon interaction as the microscopic mechanism responsible for superconductivity.
The complete microscopic theory of superconductivity was finally proposed in 1957 by Bardeen, Cooper, and Schrieffer. Independently superconductivity phenomenon was explained by Nikolay Bogolyubov. This BCS theory explained the superconducting current as a superfluid of Cooper pairs, pairs of electrons interacting through the exchange of phonons. For this work, the authors were awarded the Nobel Prize in 1972.
The BCS theory was set on a firmer footing in 1958, when Bogoliubov showed that the BCS wavefunction, which had originally been derived from a variational argument, could be obtained using a canonical transformation of the electronic Hamiltonian. In 1959, Gor'kov showed that the BCS theory reduced to the Ginzburg-Landau theory close to the critical temperature.
In 1962, the first commercial superconducting wire, a niobium-titanium alloy, was developed by researchers at Westinghouse. In the same year, Josephson made the important theoretical prediction that a supercurrent can flow between two pieces of superconductor separated by a thin layer of insulator. This phenomenon, now called the Josephson effect, is exploited by superconducting devices such as SQUIDs. It is used in the most accurate available measurements of the magnetic flux quantum h/e, and thus (coupled with the quantum Hall resistivity) for Planck's constant h. Josephson was awarded the Nobel Prize for this work in 1973.
A quench of the superconducting state in a superconducting magnet will result in the boiling away of potentially thousands of dollars worth of liquid helium, as seen in the above image of such an event at the ATRAP experiment at CERN.
A quench of the superconducting state in a superconducting magnet will result in the boiling away of potentially thousands of dollars worth of liquid helium, as seen in the above image of such an event at the ATRAP experiment at CERN.
Until 1986, physicists had believed that BCS theory forbade superconductivity at temperatures above about 30 K. In that year, Bednorz and Müller discovered superconductivity in a lanthanum-based cuprate perovskite material, which had a transition temperature of 35 K (Nobel Prize in Physics, 1987). It was shortly found by Paul C. W. Chu of the University of Houston and M.K. Wu at the University of Alabama in Huntsville [1] that replacing the lanthanum with yttrium, i.e. making YBCO, raised the critical temperature to 92 K, which was important because liquid nitrogen could then be used as a refrigerant (at atmospheric pressure, the boiling point of nitrogen is 77 K.) This is important commercially because liquid nitrogen can be produced cheaply on-site with no raw materials, and is not prone to some of the problems (solid air plugs, etc) of helium in piping. Many other cuprate superconductors have since been discovered, and the theory of superconductivity in these materials is one of the major outstanding challenges of theoretical condensed matter physics.
[edit] Applications
Main article: Technological applications of superconductivity
Superconductors are used to make some of the most powerful electromagnets known to man, including those used in MRI machines and the beam-steering magnets used in particle accelerators. They can also be used for magnetic separation, where weakly magnetic particles are extracted from a background of less or non-magnetic particles, as in the pigment industries.
Superconductors have also been used to make digital circuits (e.g. based on the Rapid Single Flux Quantum technology) and microwave filters for mobile phone base stations.
Superconductors are used to build Josephson junctions which are the building blocks of SQUIDs (superconducting quantum interference devices), the most sensitive magnetometers known. Series of Josephson devices are used to define the SI volt. Depending on the particular mode of operation, a Josephson junction can be used as photon detector or as mixer. The large resistance change at the transition from the normal- to the superconducting state is used to build thermometers in cryogenic micro-calorimeter photon detectors.
Other early markets are arising where the relative efficiency, size and weight advantages of devices based on HTS outweigh the additional costs involved.
Promising future applications include high-performance transformers, power storage devices, electric power transmission, electric motors (e.g. for vehicle propulsion, as in vactrains or maglev trains), magnetic levitation devices, and Fault Current Limiters. However superconductivity is sensitive to moving magnetic fields so applications that use alternating current (e.g. transformers) will be more difficult to develop than those that rely upon direct current.
[edit] Superconductors in popular culture
Superconductivity has long been a staple of science fiction. One of the first mentions of the phenomenon occurred in Robert A. Heinlein's novel Beyond This Horizon (1942). Notably, the use of a fictional room temperature superconductor was a major plot point in the Ringworld novels by Larry Niven, first published in 1970. Organic superconductors were featured in a science fiction novel by physicist Robert L. Forward.
Superconductivity is a popular device in science fiction due to the simplicity of the underlying concept - zero electrical resistance - and the rich technological possibilities. For example, superconducting magnets could be used to generate the powerful magnetic fields used by Bussard ramjets, a type of spacecraft commonly encountered in science fiction. The most troublesome property of real superconductors, the need for cryogenic cooling, is often circumvented by postulating the existence of room temperature superconductors. Many stories attribute additional properties to their fictional superconductors, ranging from infinite heat conductivity (ie thermal superconductivity) in Niven's novels (real superconductors conduct heat poorly, though superfluid helium has immense but finite heat conductivity) to providing power to an interstellar travel device in the Stargate movie and TV series.
In the movie Terminator 2: Judgment Day, the CPU of the T-800 destroyed in Terminator 1 is found to be superconductive at room temperature.
Superconductors are a technology required in the Civilization series (computer game) in order to build the spaceship to Alpha Centauri hence achieving a space victory. Superconductors are also an early technology in another of Sid Meier's games, Alpha Centauri (game)
In the movie "Strangers with Candy", students in a science class build a superconductor made of soup cans.
In the movie "Joe versus the Volcano", an industrialist needs a mineral called bubaru to make superconductors.
Re: Important Information
Organic chemistry is a specific discipline within chemistry which involves the scientific study of the structure, properties, composition, reactions, and preparation (by synthesis or by other means) of chemical compounds consisting of primarily carbon and hydrogen, which may contain any number of other elements, including nitrogen, oxygen, halogens as well as phosphorus, silicon and sulfur. [1] [2]
The original definition of organic chemistry came from the misperception that these compounds were always related to life processes, but it has been shown that this is not the case (See Historic highlights). Moreover, it is known that life also depends heavily on inorganic chemistry; for example, many enzymes rely on transition metals such as iron and copper; and materials such as shells, teeth and bones are part organic, part inorganic in composition. These are to be added to the metals mentioned above, HCl solution used in the digestion of food and the water, the main constituent of all living creatures, which are all subjects also of inorganic chemistry. Apart from elemental carbon, inorganic chemistry deals only with simple carbon compounds, with molecular structures which do not contain carbon to carbon connections (its oxides, acids, salts, carbides, and minerals). This does not mean that single-carbon organic compounds do not exist (viz. methane and its simple derivatives). Compounds that are related to life processes are dealt with in the branch of chemistry which is called biochemistry.
Because of their unique properties, multi-carbon compounds exhibit extremely large variety and the range of application of organic compounds is enormous. They form the basis of, or are important constituents of many products (paints, plastics, food, explosives, drugs, petrochemicals, and many others) and of course (apart from a very few exceptions) they form the basis of all life processes.
The different shapes and chemical reactivities of organic molecules provide an astonishing variety of functions, like those of enzyme catalysts in biochemical reactions of live systems. The autopropagating nature of these organic chemicals is what life is all about.
Because of the special properties of carbon, it is likely that life in other star systems would be carbon-based, in spite of speculations about the possibility of substituting silicon, which lies just below carbon in the periodic table.
Trends in organic chemistry include chiral synthesis, green chemistry, microwave chemistry, fullerenes and microwave spectroscopy.
Contents
[hide]
* 1 Historic highlights
* 2 Classification of organic substances
o 2.1 Description and nomenclature
o 2.2 Classification
+ 2.2.1 Hydrocarbons and functional groups
+ 2.2.2 Aliphatic compounds
+ 2.2.3 Aromatic and alicyclic compounds
+ 2.2.4 Polymers
+ 2.2.5 Biomolecules
+ 2.2.6 Others
* 3 Characteristics of organic substances
* 4 Molecular structure elucidation
* 5 Organic reactions
* 6 See also
* 7 References
* 8 External links
[edit] Historic highlights
Friedrich Wöhler
Friedrich Wöhler
Towards the beginning of the nineteenth century, chemists generally thought that compounds from living organisms were too complicated in structure and that these compounds, through a 'vital force' or vitalism, were unique in that they could self-propagate. They named these compounds 'organic' and proceeded to ignore them.
Organic chemistry received a boost when it was realized that these compounds could be treated in ways similar to inorganic compounds and could be manufactured by means other than 'vital force'. Around 1816 Michel Chevreuil started a study of soaps made from various fats and alkali. He separated the different acids that, in combination with the alkali, produced the soap. Since these were all individual compounds, he demonstrated that it was possible to make a chemical change in various fats (which traditionally come from organic sources), producing new compounds, without 'vital force'.
The real event that has completely destroyed the myth of 'vitalism' occurred, however, when in 1828 Friedrich Wöhler first manufactured the organic chemical urea (carbamide), a constituent of the liquid waste matter urine from the inorganic ammonium cyanate NH4OCN, in what is now called the Wöhler synthesis.
A great next step was when in 1856 William Henry Perkin, while trying to manufacture quinine, again accidentally came to manufacture the organic dye now called Perkin's mauve, which by generating a huge amount of money greatly increased interest in organic chemistry. Another step was the laboratory preparation of DDT by Othmer Zeidler in 1874, but the insecticide properties of this compound were not discovered until much later.
The history of organic chemistry continues with the discovery of petroleum and its separation into fractions according to boiling ranges. The conversion of different compound types or individual compounds by various chemical processes created the petroleum chemistry leading to the birth of the petrochemical industry, which successfully manufactured artificial rubbers, the various organic adhesives, the property-modifying petroleum additives, and plastics.
The pharmaceutical industry began in the last decade of the 19th century when acetylsalicylic acid (aspirin) manufacture was started in Germany by Bayer.
Biochemistry, the chemistry of living organisms, their structure and interactions in vitro and inside living systems, has only started in the 20th century, opening up a brand new chapter of organic chemistry with enormous scope.
[edit] Classification of organic substances
[edit] Description and nomenclature
Classification is not possible without having a full description of the individual compounds. In contrast with inorganic chemistry, in which describing a chemical compound could be achieved by simply enumerating the chemical symbols of the elements present in the compound together with the number of these elements in the molecule, in organic chemistry the relative arrangement of the atoms within a molecule has to be added for a full description.
One way of describing the molecule is by drawing its structural formula. Because of the complexity this method has changed, becoming simplified over the years. The latest version is the line formula, which achieves simplicity without introducing ambiguity, while representing carbon and hydrogen by implication. The disadvantages which arise both from the fact that structural formulae cannot be described by words and that they are not easily printable does not arise when the structure is described by the organic nomenclature .
Because of the difficulty arising from the very large number and variety of organic compounds, chemists realized early on that the establishment of an internationally accepted system of naming organic compounds was of paramount importance. The Geneva Nomenclature was born in 1892 as a result of a number of international meetings on the subject.
It was also realized that as the family of organic compounds grew, the system would have to be expanded and modified. This task was ultimately taken on by the International Union on Pure and Applied Chemistry (IUPAC). Recognizing the fact that in the branch of biochemistry, the complexity of organic structures increases, the IUPAC organisation joined forces with the International Union of Biochemistry and Molecular Biology, IUBMB, to produce a list of joint recommendations on nomenclature.
Further on, as number and complexity grew, new recommendations were made within IUPAC for simplification. The first such recommendation was presented in 1951 when a cyclic benzene structure was named a cyclophane. Later recommendations extended the method to the simplification of other complex cyclic structures, including for instance heterocyclics as well, and named such structures phanes.
For ordinary communication, to spare a tedious description, the official IUPAC naming recommendations are not always followed in practice except when it is necessary to give a concise definition to a compound, or when the IUPAC name is simpler (viz. ethanol against ethyl alcohol). Otherwise the common or trivial name may be used, often derived from the source of the compound.
[edit] Classification
In summary: organic substances are classified by their molecular structural arrangement and by what other atoms are present with the chief (carbon) constituent in their makeup, whilst in a structural formula, hydrogen is implicitly assumed to occupy all free valences of an appropriate carbon atom, which remain after accounting for branching, other element(s) and/or multiple bonding.
[edit] Hydrocarbons and functional groups
Acetic acid contains a carboxyl (-COOH) functional group
Acetic acid contains a carboxyl (-COOH) functional group
Classification normally starts with the hydrocarbons: compounds which contain only carbon and hydrogen. For sub-classes see below. Other elements present themselves in atomic configurations called functional groups which have decisive influence on the chemical and physical characteristics of the compound; thus those containing the same atomic formations have similar characteristics, which may be miscibility with water, acidity/ alkalinity, chemical reactivity, oxidation resistance, or others. Some functional groups are also radicals, similar to those in inorganic chemistry, defined as polar atomic configurations which pass during chemical reactions from one chemical compound into another without change.
Some of the elements of the functional groups (O, S, N, halogens) may stand alone and the group name is not strictly appropriate, but because of their decisive effect on the way they modify the characteristics of the hydrocarbons in which they are present they are classed with the functional groups, and their specific effect on the properties lends excellent means for characterisation and classification.
Referring to the hydrocarbon types below, many, if not all of the functional groups which are typically present within aliphatic compounds are also represented within the aromatic and alicyclic group of compounds, unless they are dehydrated, which would lead to non-reacting co-optional groups.
Reference is made here again to the organic nomenclature, which shows an extensive (if not comprehensive) number of classes of compounds according to the presence of various functional groups, based on the IUPAC recommendations, but also some based on trivial names. Putting compounds in sub-classes becomes more difficult when more than one functional group is present.
Two overarching chain type categories exist: Open Chain aliphatic compounds and Closed Chain cyclic compounds. Those in which both open chain and cyclic parts are present are normally classed with the latter.
[edit] Aliphatic compounds
The aliphatic hydrocarbons are subdivided into three groups, homologous series according to their state of saturation: paraffins alkanes without any double or triple bonds, olefins alkenes with double bonds, which can be mono-olefins with a single double bond, di-olefins, or di-enes with two, or poly-olefins with more. The third group with a triple bond is named after the name of the shortest member of the homologue series as the acetylenes alkynes. The rest of the group is classed according to the functional groups present.
From another aspect aliphatics can be straight chain or branched chain compounds, and the degree of branching also affects characteristics, like octane number or cetane number in petroleum chemistry.
[edit] Aromatic and alicyclic compounds
Benzene is one of the best-known aromatic compounds
Benzene is one of the best-known aromatic compounds
Cyclic compounds can, again, be saturated or unsaturated. Because of the bonding angle of carbon, the most stable configurations contain six carbon atoms, but while rings with five carbon atoms are also frequent, others are rarer. The cyclic hydrocarbons divide into alicyclics and aromatics (also called arenes).
Of the alicyclic compounds the cycloalkanes do not contain multiple bonds, whilst the cycloalkenes and the cycloalkynes do. Typically this latter type only exists in the form of large rings, called macrocycles. The simplest member of the cycloalkane family is the three-membered cyclopropane.
Aromatic hydrocarbons contain conjugated double bonds. One of the simplest examples of these is benzene, the structure of which was formulated by Kekulé who first proposed the delocalization or resonance principle for explaining its structure. For "conventional" cyclic compounds, aromaticity is conferred by the presence of 4n + 2 delocalized pi electrons, where n is an integer. Particular instability (antiaromaticity) is conferred by the presence of 4n conjugated pi electrons.
The characteristics of the cyclic hydrocarbons are again altered if heteroatoms are present, which can exist as either substituents attached externally to the ring (exocyclic) or as a member of the ring itself (endocyclic). In the case of the latter, the ring is termed a heterocycle. Pyridine and furan are examples of aromatic heterocycles while piperidine and tetrahydrofuran are the corresponding alicyclic heterocycles. The heteroatom of heterocyclic molecules is generally oxygen, sulfur, or nitrogen, with the latter being particularly common in biochemical systems.
Rings can fuse with other rings on an edge to give polycyclic compounds. The purine nucleoside bases are notable polycyclic aromatic heterocycles. Rings can also fuse on a "corner" such that one atom (almost always carbon) has two bonds going to one ring and two to another. Such compounds are termed spiro and are important in a number of natural products.
[edit] Polymers
This swimming board is made of polystyrene, an example of a polymer
This swimming board is made of polystyrene, an example of a polymer
One important property of carbon in organic chemistry is that it can form certain compounds, the individual molecules of which are capable of attaching themselves to one another, thereby forming a chain or a network. The process is called polymerization and the chains or networks polymers, whilst the source compound is a monomer. Two main groups of polymers exist: those artificially manufactured are referred to as industrial polymers [3] or synthetic polymers and those naturally occurring as biopolymers.
Since the invention of the first artificial polymer, bakelite, the family has quickly grown with the invention of others. Common synthetic organic polymers are polyethylene or polythene, polypropylene, nylon, teflon or PTFE, polystyrene, polyesters, polymethylmethacrylate (commonly known as perspex or plexiglas) polyvinylchloride or PVC, and polyisobutylene important artificial or synthetic rubber also the polymerised butadiene, a rubber component.
The examples are generic terms, and many varieties of each of these may exist, with their physical characteristics fine tuned for a specific use. Changing the conditions of polymerisation changes the chemical composition of the product by altering chain length, or branching, or the tacticity. With a single monomer as a start the product is a homopolymer. Further, secondary component(s) may be added to create a heteropolymer (co-polymer) and the degree of clustering of the different components can also be controlled. Physical characteristics, such as hardness, density, mechanical or tensile strength, abrasion resistance, heat resistance, transparency, colour, etc. will depend on the final composition.
The only other element that can produce polymers is silicon. The silicones, however, show one major difference from carbon based polymers, inasmuch as unlike the direct C-C bonds of those based on carbon in silicones the Si atoms are joined indirectly through oxygen links.
[edit] Biomolecules
Biomolecular chemistry is a major category within organic chemistry. Many complex multi-functional group molecules are important in living organisms. Some are long-chain biopolymers. The main classes are carbohydrates, amino acids and proteins, polysaccharides, lipids, and nucleic acids.
[edit] Others
Organic compounds containing bonds of carbon to nitrogen, oxygen and the halogens are not normally grouped separately. Others are sometimes put into major groups within organic chemistry and discussed under titles such as organosulfur chemistry, organometallic chemistry, organophosphorus chemistry and organosilicon chemistry.
[edit] Characteristics of organic substances
Most bonds in organic compounds are covalent, as in the C-H bonds in methane here
Most bonds in organic compounds are covalent, as in the C-H bonds in methane here
Organic compounds are generally covalently bonded. This allows for unique structures such as long carbon chains and rings. The reason carbon is excellent at forming unique structures and that there are so many carbon compounds is that carbon atoms form very stable covalent bonds with one another (catenation). In contrast to inorganic materials, organic compounds typically melt, boil, sublimate, or decompose below 300 °C. Neutral organic compounds tend to be less soluble in water compared to many inorganic salts, with the exception of certain compounds such as ionic organic compounds and low molecular weight alcohols and carboxylic acids where hydrogen bonding occurs.
Organic compounds tend rather to dissolve in organic solvents which are either pure substances like ether or ethyl alcohol, or mixtures, such as the paraffinic solvents such as the various petroleum ethers and white spirits, or the range of pure or mixed aromatic solvents obtained from petroleum or tar fractions by physical separation or by chemical conversion. Solubility in the different solvents depends upon the solvent type and on the functional groups if present. Solutions are studied by the science of physical chemistry. Like inorganic salts, organic compounds may also form crystals. A unique property of carbon in organic compounds is that its valency does not always have to be taken up by atoms of other elements, and when it is not, a condition termed unsaturation results. In such cases we talk about carbon carbon double bonds or triple bonds. Double bonds alternating with single in a chain are called conjugated double bonds. An aromatic structure is a special case in which the conjugated chain is a closed ring.
[edit] Molecular structure elucidation
Molecular models of caffeine
Molecular models of caffeine
Organic compounds consist of carbon atoms, hydrogen atoms, and functional groups. The valence of carbon is 4, and hydrogen is 1, functional groups are generally 1. From the number of carbon atoms and hydrogen atoms in a molecule the degree of unsaturation can be obtained. Many, but not all structures can be envisioned by the simple valence rule that there will be one bond for each valence number. The knowledge of the chemical formula for an organic compound is not sufficient information because many isomers can exist. Organic compounds often exist as mixtures. Because many organic compounds have relatively low boiling points and/or dissolve easily in organic solvents there exist many methods for separating mixtures into pure constituents that are specific to organic chemistry such as distillation, crystallization and chromatography techniques. There exist several methods for deducing the structure an organic compound. In general usage are (in alphabetical order):
* Crystallography: This is the most precise method for determining molecular geometry; however, it is very difficult to grow crystals of sufficient size and high quality to get a clear picture, so it remains a secondary form of analysis. Crystallography has seen especially extensive use in biochemistry (for protein structure determination) and in the characterization of organometallic catalysts, which often possess significant symmetry.
* Elemental analysis: A destructive method used to determine the elemental composition of a molecule. See also mass spectrometry, below.
* Infrared spectroscopy: Chiefly used to determine the presence (or absence) of certain functional groups.
* Mass spectrometry: Used to determine the molecular weight of a compound and from the fragmentation pattern its structure. High resolution mass spectrometry can often identify the precise formula of a compound through knowledge of isotopic masses and abundances; it is thus sometimes used in lieu of elemental analysis.
* Nuclear magnetic resonance (NMR) spectrometry identifies different nuclei based on their chemical environment. This is the most important and commonly used spectroscopic technique for organic chemists, often permitting complete assignment of atom connectivity and even stereochemistry given the proper set of spectroscopy experiments (e.g. correlation spectroscopy).
* Optical rotation: Distinguishes between two enantiomers of a chiral compound based on the sign of rotation of plane polarized light. If the specific rotation of an enantiomer is known, the magnitude of rotation also gives the ratio of enantiomers in a mixed sample, though HPLC with a chiral column also can supply this information.
* UV/VIS spectroscopy: Used to determine degree of conjugation in the system. While still sometimes used to characterize molecules, UV/VIS is more commonly used to quantitate how much of a known compound is present in a (typically liquid) sample.
Additional methods are provided by analytical chemistry.
[edit] Organic reactions
Organic reactions are chemical reactions involving organic compounds. While pure hydrocarbons undergo certain limited classes of reactions, many more reactions which organic compounds undergo are largely determined by functional groups. The general theory of these reactions involves careful analysis of such properties as the electron affinity of key atoms, bond strengths and steric hindrance. These issues can determine the relative stability of short-lived reactive intermediates, which usually directly determine the path of the reaction. An example of a common reaction is a substitution reaction written as:
Nu− + C-X → C-Nu + X−
where X is some functional group and Nu is a nucleophile.
There are many important aspects of a specific reaction. Whether it will occur spontaneously or not is determined by the Gibbs free energy change of the reaction. The heat that is either produced or needed by the reaction is found from the total enthalpy change. Other concerns include whether side reactions occur from the same reaction conditions. Any side reactions which occur typically produce undesired compounds which may be anywhere from very easy or very difficult to separate from the desired compound.
The original definition of organic chemistry came from the misperception that these compounds were always related to life processes, but it has been shown that this is not the case (See Historic highlights). Moreover, it is known that life also depends heavily on inorganic chemistry; for example, many enzymes rely on transition metals such as iron and copper; and materials such as shells, teeth and bones are part organic, part inorganic in composition. These are to be added to the metals mentioned above, HCl solution used in the digestion of food and the water, the main constituent of all living creatures, which are all subjects also of inorganic chemistry. Apart from elemental carbon, inorganic chemistry deals only with simple carbon compounds, with molecular structures which do not contain carbon to carbon connections (its oxides, acids, salts, carbides, and minerals). This does not mean that single-carbon organic compounds do not exist (viz. methane and its simple derivatives). Compounds that are related to life processes are dealt with in the branch of chemistry which is called biochemistry.
Because of their unique properties, multi-carbon compounds exhibit extremely large variety and the range of application of organic compounds is enormous. They form the basis of, or are important constituents of many products (paints, plastics, food, explosives, drugs, petrochemicals, and many others) and of course (apart from a very few exceptions) they form the basis of all life processes.
The different shapes and chemical reactivities of organic molecules provide an astonishing variety of functions, like those of enzyme catalysts in biochemical reactions of live systems. The autopropagating nature of these organic chemicals is what life is all about.
Because of the special properties of carbon, it is likely that life in other star systems would be carbon-based, in spite of speculations about the possibility of substituting silicon, which lies just below carbon in the periodic table.
Trends in organic chemistry include chiral synthesis, green chemistry, microwave chemistry, fullerenes and microwave spectroscopy.
Contents
[hide]
* 1 Historic highlights
* 2 Classification of organic substances
o 2.1 Description and nomenclature
o 2.2 Classification
+ 2.2.1 Hydrocarbons and functional groups
+ 2.2.2 Aliphatic compounds
+ 2.2.3 Aromatic and alicyclic compounds
+ 2.2.4 Polymers
+ 2.2.5 Biomolecules
+ 2.2.6 Others
* 3 Characteristics of organic substances
* 4 Molecular structure elucidation
* 5 Organic reactions
* 6 See also
* 7 References
* 8 External links
[edit] Historic highlights
Friedrich Wöhler
Friedrich Wöhler
Towards the beginning of the nineteenth century, chemists generally thought that compounds from living organisms were too complicated in structure and that these compounds, through a 'vital force' or vitalism, were unique in that they could self-propagate. They named these compounds 'organic' and proceeded to ignore them.
Organic chemistry received a boost when it was realized that these compounds could be treated in ways similar to inorganic compounds and could be manufactured by means other than 'vital force'. Around 1816 Michel Chevreuil started a study of soaps made from various fats and alkali. He separated the different acids that, in combination with the alkali, produced the soap. Since these were all individual compounds, he demonstrated that it was possible to make a chemical change in various fats (which traditionally come from organic sources), producing new compounds, without 'vital force'.
The real event that has completely destroyed the myth of 'vitalism' occurred, however, when in 1828 Friedrich Wöhler first manufactured the organic chemical urea (carbamide), a constituent of the liquid waste matter urine from the inorganic ammonium cyanate NH4OCN, in what is now called the Wöhler synthesis.
A great next step was when in 1856 William Henry Perkin, while trying to manufacture quinine, again accidentally came to manufacture the organic dye now called Perkin's mauve, which by generating a huge amount of money greatly increased interest in organic chemistry. Another step was the laboratory preparation of DDT by Othmer Zeidler in 1874, but the insecticide properties of this compound were not discovered until much later.
The history of organic chemistry continues with the discovery of petroleum and its separation into fractions according to boiling ranges. The conversion of different compound types or individual compounds by various chemical processes created the petroleum chemistry leading to the birth of the petrochemical industry, which successfully manufactured artificial rubbers, the various organic adhesives, the property-modifying petroleum additives, and plastics.
The pharmaceutical industry began in the last decade of the 19th century when acetylsalicylic acid (aspirin) manufacture was started in Germany by Bayer.
Biochemistry, the chemistry of living organisms, their structure and interactions in vitro and inside living systems, has only started in the 20th century, opening up a brand new chapter of organic chemistry with enormous scope.
[edit] Classification of organic substances
[edit] Description and nomenclature
Classification is not possible without having a full description of the individual compounds. In contrast with inorganic chemistry, in which describing a chemical compound could be achieved by simply enumerating the chemical symbols of the elements present in the compound together with the number of these elements in the molecule, in organic chemistry the relative arrangement of the atoms within a molecule has to be added for a full description.
One way of describing the molecule is by drawing its structural formula. Because of the complexity this method has changed, becoming simplified over the years. The latest version is the line formula, which achieves simplicity without introducing ambiguity, while representing carbon and hydrogen by implication. The disadvantages which arise both from the fact that structural formulae cannot be described by words and that they are not easily printable does not arise when the structure is described by the organic nomenclature .
Because of the difficulty arising from the very large number and variety of organic compounds, chemists realized early on that the establishment of an internationally accepted system of naming organic compounds was of paramount importance. The Geneva Nomenclature was born in 1892 as a result of a number of international meetings on the subject.
It was also realized that as the family of organic compounds grew, the system would have to be expanded and modified. This task was ultimately taken on by the International Union on Pure and Applied Chemistry (IUPAC). Recognizing the fact that in the branch of biochemistry, the complexity of organic structures increases, the IUPAC organisation joined forces with the International Union of Biochemistry and Molecular Biology, IUBMB, to produce a list of joint recommendations on nomenclature.
Further on, as number and complexity grew, new recommendations were made within IUPAC for simplification. The first such recommendation was presented in 1951 when a cyclic benzene structure was named a cyclophane. Later recommendations extended the method to the simplification of other complex cyclic structures, including for instance heterocyclics as well, and named such structures phanes.
For ordinary communication, to spare a tedious description, the official IUPAC naming recommendations are not always followed in practice except when it is necessary to give a concise definition to a compound, or when the IUPAC name is simpler (viz. ethanol against ethyl alcohol). Otherwise the common or trivial name may be used, often derived from the source of the compound.
[edit] Classification
In summary: organic substances are classified by their molecular structural arrangement and by what other atoms are present with the chief (carbon) constituent in their makeup, whilst in a structural formula, hydrogen is implicitly assumed to occupy all free valences of an appropriate carbon atom, which remain after accounting for branching, other element(s) and/or multiple bonding.
[edit] Hydrocarbons and functional groups
Acetic acid contains a carboxyl (-COOH) functional group
Acetic acid contains a carboxyl (-COOH) functional group
Classification normally starts with the hydrocarbons: compounds which contain only carbon and hydrogen. For sub-classes see below. Other elements present themselves in atomic configurations called functional groups which have decisive influence on the chemical and physical characteristics of the compound; thus those containing the same atomic formations have similar characteristics, which may be miscibility with water, acidity/ alkalinity, chemical reactivity, oxidation resistance, or others. Some functional groups are also radicals, similar to those in inorganic chemistry, defined as polar atomic configurations which pass during chemical reactions from one chemical compound into another without change.
Some of the elements of the functional groups (O, S, N, halogens) may stand alone and the group name is not strictly appropriate, but because of their decisive effect on the way they modify the characteristics of the hydrocarbons in which they are present they are classed with the functional groups, and their specific effect on the properties lends excellent means for characterisation and classification.
Referring to the hydrocarbon types below, many, if not all of the functional groups which are typically present within aliphatic compounds are also represented within the aromatic and alicyclic group of compounds, unless they are dehydrated, which would lead to non-reacting co-optional groups.
Reference is made here again to the organic nomenclature, which shows an extensive (if not comprehensive) number of classes of compounds according to the presence of various functional groups, based on the IUPAC recommendations, but also some based on trivial names. Putting compounds in sub-classes becomes more difficult when more than one functional group is present.
Two overarching chain type categories exist: Open Chain aliphatic compounds and Closed Chain cyclic compounds. Those in which both open chain and cyclic parts are present are normally classed with the latter.
[edit] Aliphatic compounds
The aliphatic hydrocarbons are subdivided into three groups, homologous series according to their state of saturation: paraffins alkanes without any double or triple bonds, olefins alkenes with double bonds, which can be mono-olefins with a single double bond, di-olefins, or di-enes with two, or poly-olefins with more. The third group with a triple bond is named after the name of the shortest member of the homologue series as the acetylenes alkynes. The rest of the group is classed according to the functional groups present.
From another aspect aliphatics can be straight chain or branched chain compounds, and the degree of branching also affects characteristics, like octane number or cetane number in petroleum chemistry.
[edit] Aromatic and alicyclic compounds
Benzene is one of the best-known aromatic compounds
Benzene is one of the best-known aromatic compounds
Cyclic compounds can, again, be saturated or unsaturated. Because of the bonding angle of carbon, the most stable configurations contain six carbon atoms, but while rings with five carbon atoms are also frequent, others are rarer. The cyclic hydrocarbons divide into alicyclics and aromatics (also called arenes).
Of the alicyclic compounds the cycloalkanes do not contain multiple bonds, whilst the cycloalkenes and the cycloalkynes do. Typically this latter type only exists in the form of large rings, called macrocycles. The simplest member of the cycloalkane family is the three-membered cyclopropane.
Aromatic hydrocarbons contain conjugated double bonds. One of the simplest examples of these is benzene, the structure of which was formulated by Kekulé who first proposed the delocalization or resonance principle for explaining its structure. For "conventional" cyclic compounds, aromaticity is conferred by the presence of 4n + 2 delocalized pi electrons, where n is an integer. Particular instability (antiaromaticity) is conferred by the presence of 4n conjugated pi electrons.
The characteristics of the cyclic hydrocarbons are again altered if heteroatoms are present, which can exist as either substituents attached externally to the ring (exocyclic) or as a member of the ring itself (endocyclic). In the case of the latter, the ring is termed a heterocycle. Pyridine and furan are examples of aromatic heterocycles while piperidine and tetrahydrofuran are the corresponding alicyclic heterocycles. The heteroatom of heterocyclic molecules is generally oxygen, sulfur, or nitrogen, with the latter being particularly common in biochemical systems.
Rings can fuse with other rings on an edge to give polycyclic compounds. The purine nucleoside bases are notable polycyclic aromatic heterocycles. Rings can also fuse on a "corner" such that one atom (almost always carbon) has two bonds going to one ring and two to another. Such compounds are termed spiro and are important in a number of natural products.
[edit] Polymers
This swimming board is made of polystyrene, an example of a polymer
This swimming board is made of polystyrene, an example of a polymer
One important property of carbon in organic chemistry is that it can form certain compounds, the individual molecules of which are capable of attaching themselves to one another, thereby forming a chain or a network. The process is called polymerization and the chains or networks polymers, whilst the source compound is a monomer. Two main groups of polymers exist: those artificially manufactured are referred to as industrial polymers [3] or synthetic polymers and those naturally occurring as biopolymers.
Since the invention of the first artificial polymer, bakelite, the family has quickly grown with the invention of others. Common synthetic organic polymers are polyethylene or polythene, polypropylene, nylon, teflon or PTFE, polystyrene, polyesters, polymethylmethacrylate (commonly known as perspex or plexiglas) polyvinylchloride or PVC, and polyisobutylene important artificial or synthetic rubber also the polymerised butadiene, a rubber component.
The examples are generic terms, and many varieties of each of these may exist, with their physical characteristics fine tuned for a specific use. Changing the conditions of polymerisation changes the chemical composition of the product by altering chain length, or branching, or the tacticity. With a single monomer as a start the product is a homopolymer. Further, secondary component(s) may be added to create a heteropolymer (co-polymer) and the degree of clustering of the different components can also be controlled. Physical characteristics, such as hardness, density, mechanical or tensile strength, abrasion resistance, heat resistance, transparency, colour, etc. will depend on the final composition.
The only other element that can produce polymers is silicon. The silicones, however, show one major difference from carbon based polymers, inasmuch as unlike the direct C-C bonds of those based on carbon in silicones the Si atoms are joined indirectly through oxygen links.
[edit] Biomolecules
Biomolecular chemistry is a major category within organic chemistry. Many complex multi-functional group molecules are important in living organisms. Some are long-chain biopolymers. The main classes are carbohydrates, amino acids and proteins, polysaccharides, lipids, and nucleic acids.
[edit] Others
Organic compounds containing bonds of carbon to nitrogen, oxygen and the halogens are not normally grouped separately. Others are sometimes put into major groups within organic chemistry and discussed under titles such as organosulfur chemistry, organometallic chemistry, organophosphorus chemistry and organosilicon chemistry.
[edit] Characteristics of organic substances
Most bonds in organic compounds are covalent, as in the C-H bonds in methane here
Most bonds in organic compounds are covalent, as in the C-H bonds in methane here
Organic compounds are generally covalently bonded. This allows for unique structures such as long carbon chains and rings. The reason carbon is excellent at forming unique structures and that there are so many carbon compounds is that carbon atoms form very stable covalent bonds with one another (catenation). In contrast to inorganic materials, organic compounds typically melt, boil, sublimate, or decompose below 300 °C. Neutral organic compounds tend to be less soluble in water compared to many inorganic salts, with the exception of certain compounds such as ionic organic compounds and low molecular weight alcohols and carboxylic acids where hydrogen bonding occurs.
Organic compounds tend rather to dissolve in organic solvents which are either pure substances like ether or ethyl alcohol, or mixtures, such as the paraffinic solvents such as the various petroleum ethers and white spirits, or the range of pure or mixed aromatic solvents obtained from petroleum or tar fractions by physical separation or by chemical conversion. Solubility in the different solvents depends upon the solvent type and on the functional groups if present. Solutions are studied by the science of physical chemistry. Like inorganic salts, organic compounds may also form crystals. A unique property of carbon in organic compounds is that its valency does not always have to be taken up by atoms of other elements, and when it is not, a condition termed unsaturation results. In such cases we talk about carbon carbon double bonds or triple bonds. Double bonds alternating with single in a chain are called conjugated double bonds. An aromatic structure is a special case in which the conjugated chain is a closed ring.
[edit] Molecular structure elucidation
Molecular models of caffeine
Molecular models of caffeine
Organic compounds consist of carbon atoms, hydrogen atoms, and functional groups. The valence of carbon is 4, and hydrogen is 1, functional groups are generally 1. From the number of carbon atoms and hydrogen atoms in a molecule the degree of unsaturation can be obtained. Many, but not all structures can be envisioned by the simple valence rule that there will be one bond for each valence number. The knowledge of the chemical formula for an organic compound is not sufficient information because many isomers can exist. Organic compounds often exist as mixtures. Because many organic compounds have relatively low boiling points and/or dissolve easily in organic solvents there exist many methods for separating mixtures into pure constituents that are specific to organic chemistry such as distillation, crystallization and chromatography techniques. There exist several methods for deducing the structure an organic compound. In general usage are (in alphabetical order):
* Crystallography: This is the most precise method for determining molecular geometry; however, it is very difficult to grow crystals of sufficient size and high quality to get a clear picture, so it remains a secondary form of analysis. Crystallography has seen especially extensive use in biochemistry (for protein structure determination) and in the characterization of organometallic catalysts, which often possess significant symmetry.
* Elemental analysis: A destructive method used to determine the elemental composition of a molecule. See also mass spectrometry, below.
* Infrared spectroscopy: Chiefly used to determine the presence (or absence) of certain functional groups.
* Mass spectrometry: Used to determine the molecular weight of a compound and from the fragmentation pattern its structure. High resolution mass spectrometry can often identify the precise formula of a compound through knowledge of isotopic masses and abundances; it is thus sometimes used in lieu of elemental analysis.
* Nuclear magnetic resonance (NMR) spectrometry identifies different nuclei based on their chemical environment. This is the most important and commonly used spectroscopic technique for organic chemists, often permitting complete assignment of atom connectivity and even stereochemistry given the proper set of spectroscopy experiments (e.g. correlation spectroscopy).
* Optical rotation: Distinguishes between two enantiomers of a chiral compound based on the sign of rotation of plane polarized light. If the specific rotation of an enantiomer is known, the magnitude of rotation also gives the ratio of enantiomers in a mixed sample, though HPLC with a chiral column also can supply this information.
* UV/VIS spectroscopy: Used to determine degree of conjugation in the system. While still sometimes used to characterize molecules, UV/VIS is more commonly used to quantitate how much of a known compound is present in a (typically liquid) sample.
Additional methods are provided by analytical chemistry.
[edit] Organic reactions
Organic reactions are chemical reactions involving organic compounds. While pure hydrocarbons undergo certain limited classes of reactions, many more reactions which organic compounds undergo are largely determined by functional groups. The general theory of these reactions involves careful analysis of such properties as the electron affinity of key atoms, bond strengths and steric hindrance. These issues can determine the relative stability of short-lived reactive intermediates, which usually directly determine the path of the reaction. An example of a common reaction is a substitution reaction written as:
Nu− + C-X → C-Nu + X−
where X is some functional group and Nu is a nucleophile.
There are many important aspects of a specific reaction. Whether it will occur spontaneously or not is determined by the Gibbs free energy change of the reaction. The heat that is either produced or needed by the reaction is found from the total enthalpy change. Other concerns include whether side reactions occur from the same reaction conditions. Any side reactions which occur typically produce undesired compounds which may be anywhere from very easy or very difficult to separate from the desired compound.
Re: Important Information
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Re: Important Information
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