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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 .?

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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 $$ \frac{\partial {\bf J}}{\partial t}= \rho_s \frac{e^2}{m}{\bf E}. $$

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  • $\begingroup$ 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 ? $\endgroup$ Commented Jun 8, 2022 at 18:48
  • $\begingroup$ 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 ? $\endgroup$ Commented Jun 8, 2022 at 19:10
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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.

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

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    $\begingroup$ An electric field is not necessary for an electromagnet. A current OR an electric field can induce a magnetic field, hence why Ampere's Law has two terms. $\endgroup$ Commented Feb 1, 2018 at 2:43

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