Question

A uniformly charged non-conducting sphere of mass m0, radius R and charge Q is rotated with angular speed ω about an axis passing through its diameter. Its magnetic dipole moment will be

Answer 1

We know, a very important formula,
$\bold{\frac{M}{L}=\frac{Q}{2m}}$
Where M is magnetic moment , L is angular momentum of body , Q is the charge on body and m is the mass of body .

Now, L = Iω
Where I is moment of inertia and ω is angular velocity
for non-conducting solid sphere moment of inertia about it diameter = $\bold{I=\frac{2}{5}mr^2}$ where r is the radius of circle
So, I = 2/5 m₀R²
⇒ L = Iω = 2/5m₀R²ω , use it above formula

M/L = Q/2m₀
M = Q/2m₀ × L = Q/2m₀ × 2/5m₀R²ω = 1/5QωR²

Hence, magnetic moment = 1/5QωR²