If a classical system does not have a constant charge-to-mass ratio throughout the system, the magnetic moment can be written

where Q is the total charge, M is the total mass, and g ≠ 1. 

(a) Show that g = 2 for a solid cylinder (I = 1/2 MR²) that spins about its axis and has a uniform charge on its cylindrical surface. 

(b) Show that g = 2.5 for a solid sphere (I = 2 MR²/5) that has a ring of charge on the surface at the equator, as shown in Figure 7-33.

Q 2M = g L