‘Q’ charge is uniformly distributed over the same surface of a right circular cone of semi-vertical angle θ and height h. The cone is uniformly rotated about its axis at angular velocity ω . Calculate the associated magnetic dipole moment.
Text Solution
Verified by ExpertsCHECK THE SOLUTION.
Sol. A ring radius r with charge q rotating with angular velocity ω is equivalent to a dipole of dipole moment
µ = NIA = qfA = q 
A
where f frequency of rotation (Hz), ω angle frequency of rotation.
Dipole moment of differential ring,
d μ = 
2 π r 
. 
π r 2 From similar triangles (see Fig.) we have
= 
d μ = 
ωπ 
⇒ μ = 
dx
= 
. 
= 
= 
= 
h
2 tan 2 θ
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