(a) Show that a surface current density K(ϕ)=Icosϕ/2R flowing in the axial direction on a right circular cylindrical surface of radius R produces inside the cylinder a uniform magnetic induction B0=μ0I/4R in a direction perpendicular to the cylinder axis. Show that the field outside is that of a two-dimensional dipole.
(b) Calculate the total magnetostatic field energy per unit length. How is it divided inside and outside the cylinder?
(c) What is the inductance per unit length of the system, viewed as a long circuit with current flowing up one side of the cylinder and back the other?
Answer: L=πμ0/8.