Question

A conducting disc of radius $R$ is placed in a uniform and constant magnetic field $B$ parallel to the axis of the disc. With what angular speed should the disc be rotated about its axis such that no electric field develops in the disc.
(the electronic charge and mass are $e$ and $m$)

• A. $\frac{eB}{2m}$
• B. $\frac{eB}{m}$
• C. $\frac{2\pi m}{eB}$
• D. $\frac{\pi m}{eB}$

Answer 1

The correct option is B $\frac{eB}{m}$

Consider a free electron in the disc at point P at a distance x from centre of disc.
The magnetic force on free electron is $=evB=e\omega xB$ (towards left)

Centrifugal force = $m{\omega }^{2}x$. (towards right)
For net force on the electron at P to be zero
i.e., e$\omega xB$ = m${\omega }^{2}x$
or $\omega =\frac{eB}{m}$
There shall be no flow of free electrons radially outwards and hence no electric field
shall develop within the disc
Ans. $\frac{eB}{m}$