A conducting solid sphere of radius R and mass M carries a charge Q . The sphere is rotating about an axis passing through its center with a uniform angular speed ω . The ratio of the magnitudes of th

Question

A conducting solid sphere of radius R and mass M carries a charge Q . The sphere is rotating about an axis passing through its center with a uniform angular speed ω . The ratio of the magnitudes of the magnetic dipole moment to the angular momentum about the same axis is given as α 2 M Q ​ . The value of α is _______ .

TestHub · Accepted Answer

​ d M = d I A A = π r 2 = π ( R sin θ ) 2 d I = T d a ​ = 2 π σ ( 2 π r ) ( R d θ ) ω ​ d I = 2 π σ 2 π R 2 ω sin θ d θ ​ ​ dI = σ R 2 ω sin θ d θ Magnetic dipole moment : M = ∫ d M = ∫ 0 π ​ σ R 2 ωπ R 2 sin 3 θ d θ M = σ R 4 ωπ ∫ 0 π ​ sin 3 θ d θ ( ∵ ∫ 0 π ​ sin 3 θ d θ = 3 4 ​ ) M = ( 4 π R 2 Q ​ ) R 4 ωπ ( 3 4 ​ ) Magnetic dipole moment M = 3 QR 2 ω ​ Angular momentum L = ( 5 2 ​ MR 2 ) ω L M ​ = 3 × 5 2 ​ MR 2 ω QR 2 ω ​ = 2 M Q ​ ( 3 5 ​ ) α = 3 5 ​ = 1.67

Physics - Magnetism Question with Solution | TestHub

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