# Perfect conductor

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A perfect conductor or perfect electric conductor (PEC) is an idealized material exhibiting infinite electrical conductivity or, equivalently, zero resistivity (cf. perfect dielectric). While perfect electrical conductors do not exist in nature, the concept is a useful model when electrical resistance is negligible compared to other effects. One example is ideal magnetohydrodynamics, the study of perfectly conductive fluids. Another example is electrical circuit diagrams, which carry the implicit assumption that the wires connecting the components have no resistance. Yet another example is in computational electromagnetics, where PEC can be simulated faster, since the parts of equations that take finite conductivity into account can be neglected.

The abbreviation cf. is used in writing to refer the reader to other material to make a comparison with the topic being discussed. It is used to form a contrast, for example: "Abbott (2010) found supportive results in her memory experiment, unlike those of previous work ." It is recommended that "cf." be used only to suggest a comparison, and the word "see" be used to point to a source of information. In physics and electrical engineering, a conductor is an object or type of material that allows the flow of charge in one or more directions. Materials made of metal are common electrical conductors. Electrical current is generated by the flow of negatively charged electrons, positively charged holes, and positive or negative ions in some cases. A circuit diagram is a graphical representation of an electrical circuit. A pictorial circuit diagram uses simple images of components, while a schematic diagram shows the components and interconnections of the circuit using standardized symbolic representations. The presentation of the interconnections between circuit components in the schematic diagram does not necessarily correspond to the physical arrangements in the finished device.

## Properties of perfect conductors

Perfect conductors:

• have exactly zero electrical resistance - a steady current within a perfect conductor will flow without losing energy to resistance. Resistance is what causes heating in conductors, thus a perfect conductor will generate no heat. Since energy is not being lost to heat, the current will not dissipate; it will flow indefinitely within the perfect conductor until there exists no potential difference.
• require a constant magnetic flux - the magnetic flux within the perfect conductor must be constant with time. Any external field applied to a perfect conductor will have no effect on its internal field configuration. In physics, specifically electromagnetism, the magnetic flux through a surface is the surface integral of the normal component of the magnetic field B passing through that surface. The SI unit of magnetic flux is the weber (Wb), and the CGS unit is the maxwell. Magnetic flux is usually measured with a fluxmeter, which contains measuring coils and electronics, that evaluates the change of voltage in the measuring coils to calculate the magnetic flux.

## Distinction between a perfect conductor and a superconductor

Superconductors, in addition to having no electrical resistance, exhibit quantum effects such as the Meissner effect and quantization of magnetic flux. Superconductivity is a phenomenon of exactly zero electrical resistance and expulsion of magnetic flux fields occurring in certain materials, called superconductors, when cooled below a characteristic critical temperature. It was discovered by Dutch physicist Heike Kamerlingh Onnes on April 8, 1911, in Leiden. Like ferromagnetism and atomic spectral lines, superconductivity is a quantum mechanical phenomenon. It is characterized by the Meissner effect, the complete ejection of magnetic field lines from the interior of the superconductor during its transitions into the superconducting state. The occurrence of the Meissner effect indicates that superconductivity cannot be understood simply as the idealization of perfect conductivity in classical physics. The Meissner effect is the expulsion of a magnetic field from a superconductor during its transition to the superconducting state. The German physicists Walther Meissner and Robert Ochsenfeld discovered this phenomenon in 1933 by measuring the magnetic field distribution outside superconducting tin and lead samples. The samples, in the presence of an applied magnetic field, were cooled below their superconducting transition temperature, whereupon the samples cancelled nearly all interior magnetic fields. They detected this effect only indirectly because the magnetic flux is conserved by a superconductor: when the interior field decreases, the exterior field increases. The experiment demonstrated for the first time that superconductors were more than just perfect conductors and provided a uniquely defining property of the superconductor state. The ability for the expulsion effect is determined by the nature of equilibrium formed by the neutralization within the unit cell of a superconductor. In physics, quantization is the process of transition from a classical understanding of physical phenomena to a newer understanding known as quantum mechanics. This is a generalization of the procedure for building quantum mechanics from classical mechanics. One also speaks of field quantization, as in the "quantization of the electromagnetic field", where one refers to photons as field "quanta". This procedure is basic to theories of particle physics, nuclear physics, condensed matter physics, and quantum optics.

In perfect conductors, the interior magnetic field must remain fixed but can have a zero or nonzero value.  In real superconductors, all magnetic flux is expelled during the phase transition to superconductivity (the Meissner effect), and the magnetic field is always zero within the bulk of the superconductor.

## Related Research Articles

The quantum Hall effect is a quantum-mechanical version of the Hall effect, observed in two-dimensional electron systems subjected to low temperatures and strong magnetic fields, in which the Hall conductance σ undergoes quantum Hall transitions to take on the quantized values The electrical resistance of an object is a measure of its opposition to the flow of electric current. The inverse quantity is electrical conductance, and is the ease with which an electric current passes. Electrical resistance shares some conceptual parallels with the notion of mechanical friction. The SI unit of electrical resistance is the ohm (Ω), while electrical conductance is measured in siemens (S).

The magnetic flux, represented by the symbol Φ, threading some contour or loop is defined as the magnetic field B multiplied by the loop area S, i.e. Φ = BS. Both B and S can be arbitrary and so is Φ. However, if one deals with the superconducting loop or a hole in a bulk superconductor, it turns out that the magnetic flux threading such a hole/loop is quantized. The (superconducting) magnetic flux quantumΦ0 = h/(2e)2.067833831(13)×10−15 Wb is a combination of fundamental physical constants: the Planck constant h and the electron charge e. Its value is, therefore, the same for any superconductor. The phenomenon of flux quantization was discovered experimentally by B. S. Deaver and W. M. Fairbank and, independently, by R. Doll and M. Näbauer, in 1961. The quantization of magnetic flux is closely related to the Little–Parks effect, but was predicted earlier by Fritz London in 1948 using a phenomenological model. The Josephson effect is the phenomenon of supercurrent, a current that flows indefinitely long without any voltage applied, across a device known as a Josephson junction (JJ), which consists of two or more superconductors coupled by a weak link. The weak link can consist of a thin insulating barrier, a short section of non-superconducting metal (S-N-S), or a physical constriction that weakens the superconductivity at the point of contact (S-s-S).

Eddy currents are loops of electrical current induced within conductors by a changing magnetic field in the conductor according to Faraday's law of induction. Eddy currents flow in closed loops within conductors, in planes perpendicular to the magnetic field. They can be induced within nearby stationary conductors by a time-varying magnetic field created by an AC electromagnet or transformer, for example, or by relative motion between a magnet and a nearby conductor. The magnitude of the current in a given loop is proportional to the strength of the magnetic field, the area of the loop, and the rate of change of flux, and inversely proportional to the resistivity of the material. When graphed, these circular currents within a piece of metal look vaguely like eddies or whirlpools in a liquid.

The Little–Parks effect was discovered in 1962 by William A. Little and Roland D. Parks in experiments with empty and thin-walled superconducting cylinders subjected to a parallel magnetic field. It was one of the first experiments that indicate the importance of Cooper-pairing principle in BCS theory. In physics and chemistry, the Nernst effect is a thermoelectric phenomenon observed when a sample allowing electrical conduction is subjected to a magnetic field and a temperature gradient normal (perpendicular) to each other. An electric field will be induced normal to both.

Superconductivity is the phenomenon of certain materials exhibiting zero electrical resistance and the expulsion of magnetic fields below a characteristic temperature. The history of superconductivity began with Dutch physicist Heike Kamerlingh Onnes's discovery of superconductivity in mercury in 1911. Since then, many other superconducting materials have been discovered and the theory of superconductivity has been developed. These subjects remain active areas of study in the field of condensed matter physics. Superdiamagnetism is a phenomenon occurring in certain materials at low temperatures, characterised by the complete absence of magnetic permeability and the exclusion of the interior magnetic field.

The thermal Hall effect is the thermal analog of the Hall effect. Here, a thermal gradient is produced across a solid instead of an electric field. When a magnetic field is applied, an orthogonal temperature gradient develops. In physics, a quantum vortex represents a quantized flux circulation of some physical quantity. In most cases quantum vortices are a type of topological defect exhibited in superfluids and superconductors. The existence of quantum vortices was predicted by Lars Onsager in 1947 in connection with superfluid helium. Onsager also pointed out that quantum vortices describe the circulation of superfluid and conjectured that their excitations are responsible for superfluid phase transitions. These ideas of Onsager were further developed by Richard Feynman in 1955 and in 1957 were applied to describe the magnetic phase diagram of type-II superconductors by Alexei Alexeyevich Abrikosov. In 1935 Fritz London published a very closely related work on magnetic flux quantization in superconductors. London's fluxoid can also be viewed as a quantum vortex.

The cryogenic current comparator (CCC) is used in the electrical precision measurements to compare electric currents with highest accuracy. This device exceeds the accuracy of other current comparators around several orders of magnitude and is used in electrical metrology for highly precise comparative measurements of electric resistances or for the amplification and measurement of extremely small electric currents.

A charge density wave (CDW) is an ordered quantum fluid of electrons in a linear chain compound or layered crystal. The electrons within a CDW form a standing wave pattern and sometimes collectively carry an electric current. The electrons in such a CDW, like those in a superconductor, can flow through a linear chain compound en masse, in a highly correlated fashion. Unlike a superconductor, however, the electric CDW current often flows in a jerky fashion, much like water dripping from a faucet due to its electrostatic properties. In a CDW, the combined effects of pinning and electrostatic interactions likely play critical roles in the CDW current's jerky behavior, as discussed in sections 4 & 5 below.

Superconductivity is characterized both by perfect conductivity and by the expulsion of magnetic fields. Changes in either temperature or magnetic field can cause the phase transition between normal and superconducting states. For a given temperature, the highest magnetic field under which a material remains superconducting is known as the critical field. The highest temperature under which the superconducting state is seen is known as the critical temperature. At that temperature even the smallest external magnetic field will destroy the superconducting state, so the critical field is zero. As temperature decreases, the critical field increases generally to a maximum at absolute zero.

Flux pumping is a method for magnetising superconductors to fields in excess of 15 teslas. The method can be applied to any type II superconductor and exploits a fundamental property of superconductors. That is their ability to support and maintain currents on the length scale of the superconductor. Conventional magnetic materials are magnetised on a molecular scale which means that superconductors can maintain a flux density orders of magnitude bigger than conventional materials. Flux pumping is especially significant when one bears in mind that all other methods of magnetising superconductors require application of a magnetic flux density at least as high as the final required field. This is not true of flux pumping.

Persistent current is a perpetual electric current, not requiring an external power source. Bean's critical state model, introduced by C. P. Bean in 1962, gives a macroscopic explanation of the irreversible magnetization behavior (hysteresis) of hard Type-II superconductors.

Macroscopic quantum phenomena refer to processes showing quantum behavior at the macroscopic scale, rather than at the atomic scale where quantum effects are prevalent. The best-known examples of macroscopic quantum phenomena are superfluidity and superconductivity; other examples include the quantum Hall effect. Since 2000 there has been extensive experimental work on quantum gases, particularly Bose–Einstein Condensates.

1. Henyey, Frank S. (1982). "Distinction between a Perfect Conductor and a Superconductor". Phys. Rev. Lett. 49 (6): 416. Bibcode:1982PhRvL..49..416H. doi:10.1103/PhysRevLett.49.416.