Field and Wave Electromagnetics 2nd Edition by David Cheng

Exercise 79

In certain experiments it is desirable to have a region of constant magnetic flux density. This can be created in an off-center cylindrical cavity that is cut in a very long cylindrical conductor carrying a uniform current density. Refer to the cross section in Figure. The uniform axial current density is J = a z J. Find the magnitude and direction of B in the cylindrical cavity whose axis is displaced from that of the conducting part by a distance d. (Hint: Use principle of superposition and consider B in the cavity as that due to two long cylindrical conductors with radii b and a and current densities J and - J , respectively.)