Summary

Analyzing Permittivity
The permittivity response is the key aspect of the model and it describes the electrical
resistance response and why it vanishes at the material’s critical temperature. The model also
explains the behavior of magnetic fields and why they cannot exist inside superconducting
materials. II superconductors. This model is also able to explain why superconductors behave
differently than perfect conductors.
As a result, examining the permittivity response and understanding electromagnetic field

theory provides insight into the major aspects associated with superconducting materials.
UPERCONDUCTIVITY is a phenomenon in which a material’s electrical properties or

characteristics change when the temperature reaches a sufficiently low temperature. At this
temperature, known as the critical temperature, a superconductor’s electrical resistance reduces
to zero and the magnetic field inside the material becomes zero - . Since elevated electrical
resistance negatively affects energy and information transmission, superconductivity research is
especially important. Electrical resistivity is a material property that produces electrical
resistance in a material.
This resistivity is a function of temperature and typically as a material’s temperature

decreases, its electrical resistivity decreases .
Fred Lacy is with the Electrical Engineering Department, Southern
Through that material unimpeded and thus current can flow indefinitely . The Meissner effect is
the phenomenon that leads to the vanishing magnetic field in superconductors . This effect leads
to the wellknown levitating magnet above a superconducting material due to repulsive forces.
For small magnetic fields, regardless of whether the magnetic field is present before or after the
material is cooled to its critical temperature and regardless of whether the material is a type I or
type II superconductor, that magnetic field will be expelled from the interior of the
superconductor.
For larger magnetic fields, type II superconductors will exhibit a mixed state in which magnetic
fields can penetrate the interior of the material - . In order to understand this phenomenon of
superconductivity and to advance superconductivity research, comprehensive and accurate
models must be developed. Because the model from this prior research only addressed or
developed concepts associated with electrical resistivity of superconductors, the research
presented herein will explain why superconducting materials have their magnetic properties.
This will be accomplished by analyzing conduction electron interactions with atoms and then
using electromagnetic field theory.
Atomic analysis will be used to demonstrate that when the permittivity has certain properties,
electrons will move through a material unobstructed . Then electromagnetic theory will be used
to explain the response of superconducting materials to external magnetic fields. Finally, the
theory and model are used to explain why perfect conductors respond differently than
superconductors.
A model that describes the electrical resistance for conductors as a

function of temperature has been developed
Resistance R1 has the same general form for superconducting and non-superconducting
materials, however R2 will be different depending upon whether the material is superconducting
or not.
Results show that using these resistance equations will yield results that are consistent with
experimental results for superconductors and non-superconductors .
Each resistance can be modeled for specific materials by using the

equations in Tables I and II with specified values for
We consider the lattice shown in Fig. The electrical resistance of the system can be understood
after applying the Schrödinger wave equation to the conduction electrons in the periodic atomic
lattice. This analysis and subsequent analysis will reveal why the superconducting and non-
superconducting effects occur. Where V represents the potential energy that a traveling electron
will encounter at some instant in time.
Under general conditions, the potential energy can be determined, and the Schrödinger equation
can be solved.
Schrödinger wave equation reduces to
The potential will become zero when the permittivity becomes infinitely large.
The permittivity is the key parameter to understand the electromagnetic properties of

superconductors . When the permittivity becomes infinitely large, this will lead to the electrical
and magnetic characteristics of superconducting materials. Based on the permittivity, the
following sections will demonstrate and/or explain why these characteristics occur for
superconductors as well as why superconductors are different than perfect conductors. In
general, the electrical resistivity for materials is temperature dependent and will linearly
decrease with temperature.
Schrödinger wave equation, the conduction electrons become free particles and will experience
zero electrical resistance. Non-superconducting material and a type I superconducting material, .
When the temperature reaches the critical value, the atoms become ‘invisible’ and the
resistance drops to zero. This confirms that the electrical resistance R2 should be modeled as
zero resistance as given in Table II.
In addition to describing the electrical resistance of type I superconductors, this model can also
be used to describe the electrical resistance for type II or high-temperature superconductors. A
general graph of the electrical resistance for type II superconductors that is found
experimentally is shown in Fig. The difference between type I and type II materials is that the
permittivity of the atoms will not sharply approach infinity for type II superconductors as it does
or type I superconductors. So, instead of producing a permittivity with a sharp response as the
temperature approaches the critical temperature, the response will produce a permittivity that
gradually approaches infinity near the critical temperature.
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Analyzing Permittivity

As a result, examining the permittivity response and understanding electromagnetic field

UPERCONDUCTIVITY is a phenomenon in which a material’s electrical properties or

This resistivity is a function of temperature and typically as a material’s temperature

Fred Lacy is with the Electrical Engineering Department, Southern

A model that describes the electrical resistance for conductors as a

Each resistance can be modeled for specific materials by using the

Schrödinger wave equation reduces to

The permittivity is the key parameter to understand the electromagnetic properties of

Powered by TCPDF (www.tcpdf.org)

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