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 electric charge and mass are `e` and `m`)

Options

A. `(eB)/(2m)`
B. `(eB)/m`
C. `(2pim)/(eB)`
D. `(pim)/(eB)`

Answer

B

Explanation

Consider a free electron in the disc at point `P` distant `x` from centre of disc.The magnetic force on free electron is =`evB=eomegaxB`(towards left) Centrifugal force=`momega^(2)x`(towards right) For net force on the electron at `P` at be zero
i.e. `eomegax B=momega^(2)x`
or `omega=(eB)/m`
There shall be no flow of free electrons radially outwards and hence no electric field shall develop