IIT JEE , AIEEE Forum - Physics , Magnetism

cvramana

The kinetic energy remains constant because the magnetic force cannot change the speed of the charged particle. It can only change the direction of the charge motion.

Let us divide the shell into rings of radius x whose distance from the center of the sphere is given by y and the thickness dy. Let the charge on the ring be dq, where dq is given by

dq = s 2p x dy. The current in this part of the ring is given by di = dq w / 2p. The torque acting on the ring will be dt = di ( p x² B). Therefore the total torque acting on the ring will be

t = ò di ( p x² B) = ò s 2p x w p x² B dy / 2p = ò s x w p x² B dy = ò s w p x³ B dy

Now for the relation between x and y.

R² = x² + y² , from this eliminating x and integrating y between -r and +r we get the resultant torque.

But this torque will produce new rotation of the sphere and the therefore the torque value will change in such a way that the kinetic energy will remain constant always.

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