Time-dependent behavior of magnetic fields confined by conducting walls

An equation is derived which describes the total current flowing in a moving conducting surface surrounding a magnetic field, where diffusion of the field into the conductor is taken into account. Analytic and numerical solutions of the current equation are obtained for the cases of exponential and linear compression of the magnetic field with time, respectively. It is assumed that the electrical conductivity is constant, that the conducting surfaces are axially symmetric, and that the thickness and radius of curvature of the conducting walls is large compared with the effective depth of penetration of the field