8. Consider a perfectly conducting material, that is, a material for which the con- ductivity is infinite. Show that the magnetic field is time-independent inside a perfect conductor. Assume that in this perfectly conducting material, Ohm's law is replaced by the relation J: = 1 2 VB where J is the current density, is a constant that has dimension of length, and A is the vector potential, with the further constraint that VA = 0. From these relations, show that the magnetic field obeys the equation A, = 1 12B. From this, deduce that inside a perfect conductor of size d the magnetic field tends to zero, apart from a surface layer of thickness of the order of X. Now consider an infinite slab of this material of thickness 2d (with d < z