Q. 615.0( 2 Votes )

Consider a solid sphere of radius r and mass m which has a charge q distributed uniformly over its volume. The sphere is rotated about a diameter with an angular speed ω. Show that the magnetic moment μ and the angular momentum ℓ of the sphere are related as

Answer :

Given


radius of solid sphere = r


mass of sphere = m


charge on the sphere =q


angular speed of the sphere = ω


magnetic moment and the angular momentum ℓ of the sphere are related –



Lets consider a differential strip of width dx at a distance x from the centre of the sphere.



Area of the strip is given as,




now, current i is given by-



Angular speed,




Now frequency f





current i becomes



Magnetic moment is given by-


where,


A= area of cross section


i=current flowing through it


n = number of turns


for number of turns n = 1



Integrating over the sphere-









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