Consider a solid sphere of radius r and mass m which has a charge q distributed uniformly over its volume. The sphere is rotated about a diameter with an angular speed ω. Show that the magnetic moment μ and the angular momentum ℓ of the sphere are related as
Given
radius of solid sphere = r
mass of sphere = m
charge on the sphere =q
angular speed of the sphere = ω
magnetic moment and the angular momentum ℓ of the sphere are related –
Lets consider a differential strip of width dx at a distance x from the centre of the sphere.
Area of the strip is given as,
now, current i is given by-
Angular speed,
Now frequency f
current i becomes
Magnetic moment is given by-
where,
A= area of cross section
i=current flowing through it
n = number of turns
for number of turns n = 1
Integrating over the sphere-