A conducting solid sphere of radius R and mass M carries charge Q and rotates with angular speed ω about a diameter. The ratio of magnetic dipole moment to angular momentum is αQ/(2M). Find α.

Question

G1 Physics · Accepted Answer

For a uniformly charged rotating spherical surface,

μ = QωR²/3.

For a solid sphere, L = Iω = (2/5)MR²ω.

Thus μ/L = [QωR²/3]/[(2/5)MR²ω] = 5Q/(6M).

Given μ/L = αQ/(2M),

α/2 = 5/6 ⇒ α = 5/3 ≈ 1.6667.