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In this study the electromagnetic theory and quantum mechanics are utilized to find the resistivity in terms of electric and magnetic susceptibility in which the electron is considered as a wave. Critical temperature of the wire at which the resistance vanishes is found. In this case the resistance being imaginary which leads the real part of the resistance to real zero at critical temperature and the material becomes super conductor in this case. If one considers the motion of electron in the presence of inner magnetic field and resistance force, a new formula for the conductivity is to be found; this formula states that the material under investigation becomes a superconductor at critical temperature and depends on the strength of the magnetic field and friction resistance, and the substance conductivity is found to be super at all temperatures beyond the critical temperature.

In superconductors, the resistance is zero at temperatures less than the critical temperature [

When the temperature of a conductor approach to the absolute zero, the friction resistance can be ignored [

Including the position variable

Then

According to the definition of the potential

From Equation (3)

Then

While

Using Equation (6) and substituting the value of

Then the resistance

On other hand

Considering the electron as a wave, its velocity becomes [

Accordingly the resistivity is given by

If a magnetic field with a flux density

force

where

where

when the outer magnetic field vanishes, then the radial velocity becomes

And

where

And when an outer magnetic field

where

The equation of motion in the presence of the outer magnetic field is given in the form [

where

when

where

Dividing both sides by

The current for one atom with

where

The magnetic torque for one atom is given by

where

And from

But

So the magnetic torque for one atom

If the number of atoms per unit volume is assumed to be

According to the definition of susceptibility

Comparing Equations (26) and (27) the susceptibility being

Then the resistivity in Equation (11) becomes

where

The resistivity

or

Accordingly the critical temperature becomes

Assuming that the charges in the conductor are acted by a resistance force

The previous forces are given by the formulas

where

The equation of motion takes the formula

When the electron moves with a uniform constant velocity, the Equation (33) becomes

And the conductivity is given by

where

And the conductivity approaches to infinity when

According to the Maxwell-Boltzmann statistics the density of the atoms in the medium takes the formula [

Then

Equation (38) represents the critical temperature in which the conductivity becomes very huge, and when

The conductivity also becomes very high, and then

And finally the critical temperature is found to be

The classical rules of the electron motion in Equation (1) are used to find the classical formula of the resistivity given in Equation (11), and the electron is considered to be a wave according to the quantum principles and this clarified that the resistivity is a function of the electric and magnetic susceptibility.

The interpretation of Equation (28)―in which we derived the magnetic susceptibility from the electron equation of motion, that depend on the friction force within the friction coefficient

When we considered the electron motion due to the impact of an inner magnetic field, and a friction resistance, the conductivity was found to be as shown in Equation (36).

The mathematical analysis interprets that the conductivity becomes very high at temperatures less than the critical temperature, which depends on the friction resistance and the inner magnetic field as shown in Equations (41)-(42).

The model in which the resistance depends on the electric and magnetic susceptibility, clarifies that the resistance vanishes, and the metal becomes a superconductor at the critical temperature and the temperatures less than it; this relation is not clear in the famous models of the superconductivity.