Question

Consider a solid sphere of radius r and mass m that has a charge q distributed uniformly over its volume. The sphere is rotated about its diameter with an angular speed ω. Show that the magnetic moment µ and the angular momentum l of the sphere are related as `mu = q/(2m) l`

Answer 1

Considering the strip of width dx at a distance x from the centre of the sphere.
Small area of the strip is given as,
da = 4π x dx
`i = (dq)/(dt) = (qw)/(2pi)`
`mu= ia = (qw)/(2pi)4pi` \[\int\limits\] `x dx`
`= q.wr^2 = q/ml`