For a perfect conductor, \(E=0\) everywhere inside, and all the charge resides on the surface even when charge carriers are flowing.

(a) Use Maxwell's equations to show that the magnetic field inside a conductor is constant.

(b) Use Maxwell's equations to show that the magnetic flux through a perfect conducting loop is constant.

(c) A superconductor is more than just a perfect conductor. It also has the property that \(B=0\) inside the superconductor. Use Maxwell's equations to show why the current in a superconductor is confined to the surface.