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 . The ratio of the magnitudes of the magnetic dipole moment to the angular momentum about the same axis is given as Q 2 M . The value of is _______ .
A. A
aligned & d M=d I A \\ & A= r^2= (R )^2 \\ & d I= d a T = (2 r)(R d ) 2 \\ & d I= 2 R^2 d 2 aligned dI = R ^2 ~d Magnetic dipole moment : M= d M= _0^ R^2 R^2 ^3 d M= R^4 _0^ ^3 d ( _0^ ^3 d = 4 3 ) M = ( Q 4 R ^2 ) R ^4 ( 4 3 ) Magnetic dipole moment M = QR ^2 3 Angular momentum L = ( 2 5 MR ^2 ) M ~L = QR ^2 3 2 5 MR ^2 = Q 2 M ( 5 3 ) = 5 3 =1.67
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