Can a Superconductor have an electric field inside it.?

Question

I have been reading that an ideal supercondcutor can't have electric field inside it as its Resistance is zero. If you connect a superconductor with a voltage source will it not produce electric field inside .?

Answer 1

You can have an electric field in a superconductor, but not in a steady state. An electric field will cause a steadily growing current in accordance with the Josephson relations $$ {\bf J}= \rho_s e \frac{\hbar}{m}\nabla \theta $$ and $$ \hbar \frac{\partial\theta}{\partial t}= -eV(x). $$ Taking the gradient of the second equation and using the first gives us $$ \frac{\partial {\bf J}}{\partial t}= \rho_s \frac{e^2}{m}{\bf E}. $$

Answer 2

Yes, it will not produce electric field inside - if you look at Ohm rule: $\rho.J=E$. If $\rho$ is $0$, then with any voltage you will not have electric field inside.

Answer 3

I believe they do produce an electric field, because people design electromagnets with superconductors, and an electric field is necessary for an electromagnet.