Recently I have been reading the book called "Superconductivity, Superfluids and Condensates" from James F. Annett. I was confused by the expression that
zero electric field at all points inside a superconductor. In this way the current, $j$, can be finite.
Why the current density $j$ inside a superconductor has to be finite? And what happens when $j$ is infinite?
In a conventional conductor, the current density and the electric field obey Ohm's Law, $\vec{J} = \sigma \vec{E}$. A perfect conductor, such as a superconductor, is the $\sigma \to \infty$ limit of this equation; this implies that in this limit, we must have $\vec{E} \to 0$ in order to have $\vec{J}$ approach a finite limit.
Why the current density j inside a superconductor has to be finite?
Once the current density exceeds a certain critical current density the material stops superconducting. This critical current density is an important material property for many applications such as MRI. It dictates the amount of superconducting wire that is needed to achieve the desired field.
