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 ExpertsSol. 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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