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 _______ .

Step-by-step solution

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 = 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