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Is there a formula for the effective speed of electron currents inside superconductors?

The formula for normal conductors is:

$$ V = \frac{I}{nAq}$$

I wonder if there are any changes to this formula for superconductors.

Is there any regime for existing superconductors where the electrons will be flowing at speeds near light speed? Or more precisely, is it possible to have carrier currents that produce drift velocities that are relativistic, while maintaining the superconducting phase?

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1 Answer 1

This formula is derived using conservation of charge principle and so it's valid for the superconductors as well. There's a critical magnetic field that above which a superconductor becomes normal conductor and it's a function of temperature.

If a large current is to pass through a superconductor, a magnetic field will be produced that disrupts superconductivity when exceeds this critical magnetic field, so you can't have arbitrarily large currents and drift speeds will be well below relativistic speeds.

This is an approximate formula for dependence of this critical magnetic field on temperature: $H_c(T) = H_0[1-({T \over T_c})^2]$

In which $T_c$ is the critical temperature at zero field and $H_0$ is the critical field at zero temperature. Typical values for $\mu H_0$ is in range of 0.01-0.1 Tesla.

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