A sphere of radius R, uniformly charged with the surface charge density σ , rotates around the axis passing through its centre at an angular velocity ω . Find the magnetic induction at the centre of the rotating sphere. Also find its magnetic moment.
Text Solution
Verified by ExpertsCHECK THE SOLUTION.
Sol. Charge on the differential circular strip is
dq = (2 π R sin θ )(R d θ ) σ
or dq = 2 πσ R 2 sin θ d θ
Then dI = 
= ωσ R 2 sin θ d θ
Magnetic field at the centre is
dB = 
= 
B = 
θ d θ = μ 0 ωσ R 
θ d θ
or 
= 
μ 0 ωσ R( 
)
Magnetic moment due to elementary ring, dµ = (dI) π r 2 ∴ µ = 
= ( ωσ R
2 sin θ ) σ R 2 sin 2 θ d θ
= 2 π R 4 ωσ R 2 
θ d θ = 
πσ R 4 ω
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