# Can a Superconductor have an electric field inside it.?

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 .?

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 $$\frac{\partial {\bf J}}{\partial t}= \rho_s \frac{e^2}{m}{\bf E}.$$
• Are you trying to say that this electric field would become $0$ soon enough, because of the current response, as the superconductor goes into the steady-state? If that is the case, what creates this electric field to appear in the first place, since we are not applying a field from the outside. All that we did, is put a constant magnetic field outside, and observe the meissner effect. Is this electric field some intrinsic property of the superconductor ? Commented Jun 8, 2022 at 18:48
• In one of your other answers, you mentioned how the Meissner effect guarantees that the magnetic field would be $0$ inside a superconductor at all times. Are you saying that while $E$ can be non-zero when the superconductor is not in a steady state, the magnetic field inside would always be $0$ irrespective of whether we have a steady-state or not. Is that why in the derivation of the london equations, we assume force is related to electric field, and not the magnetic field ? Commented Jun 8, 2022 at 19:10
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.