General Solution of the Hollow Cylinder and Concentric DC Surface Current

We provide a general solution to the problem of an infinitely long, hollow cylinder of uniform, linear permeability in the presence of any continuous dc current distribution residing on a concentric cylindrical surface. The solution is expressed in terms of the spatial Fourier components of the applied surface current. Applications of this study include the design of dc magnetic shields and shield-coupled coils, as well as a benchmark for finite-element analysis. Examples involving canonical current structures-loops, solenoids, and saddle-shaped coils-are presented.