“Hidden” Momentum in a Coaxial Cable

Calculate the electromagnetic momentum and identify the “hidden” mechanical momentum in a coaxial cable of length L, inner radius a, outer radius b, when a battery of voltage V is connected to one end and a load resistor R0 is connected to the other. The current may be taken as uniformly distributed over the inner conductor, which has resistivity ρ. The outer conductor has negligible resistivity, and the current flows on it in a thin sheet at radius b. The battery has negligible internal resistance. Deduce the charge per unit length on the outer surface of the inner conductor. Then, suppose the battery can be turned off in such a way that the current in the cable falls to zero with some time dependence I(t). Calculate the impulse on the charge on the surface of the inner conductor due to the electric field induced by the transient current. This problem is based on sec. 17 of [1], and on prob. 7.57, ex. 8.3 and ex. 12.12 of [2].