An electron moves in a circular orbit with a uniform speed v. It produces a magnetic field B at the centre of the circle. The radius of the circle is proportional to

Options

A. `B/v`
B. `v/R`
C. `sqrt(v/B)`
D. `sqrt(B/v)`

Answer

C

Explanation

Equivalent current due to motion of electron in a circular orbit of radius R is `I = (ev)/(2 pi R)` and magnetic field B at the centre of the circular orbit `B = (mu_0 I)/(2R) = (mu_0)/(2R) cdot (ev)/(2 pi R) = (mu_0 ev)/(4pi R^2)`
`:. R = sqrt((mu_0 ev)/(4 pi B)) " or " R prop sqrt((v)/(B))`