Question

A non-conducting hollow sphere of mass m and radius R having total charge 'q' is rotating with constant angular velocity ${}^{\prime }{\omega }^{\prime }$ about a vertical axis as shown in the figure. The sphere is then gently placed on the horizontal surface having a magnetic field applied in the horizontal direction as shown. If there is sufficient friction to prevent any slipping, then the friction force acting on the sphere at $t=0$ is $\frac{q\omega RB}{n}$. Find the value of n.

Answer 1

A non-conducting hollow sphere of mass $=m$

Radius $=r$

Total charge$=q$

Rotating with constant angular velocity$=\omega$

When $t=0$ the friction force acting on the sphere

$\frac{q\omega RB}{n}=K_e\frac{qa}{n^2}n=\frac{\omega }{K_e}$