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/B`
C. `sqrtB/v`
D. `sqrtv/B`

Answer

D

Explanation

A moving electron is equivilent to a current.`therefore I=(d_q)/(d_t)=e/T` The time taken by the electron to describe a circular path of radius r is `T=(2pir)/v therefore I=e/T=(e/(2pir))/v=(ev)/(2pir)therefore` The magnetic field at the center `B=(mu_0)/(4pi)((2piI)/r)therefore B=(mu_0)/(4pi).2pi.(ev)/(2pir)x1/r=(mu_0ev)/(4pir^(2))=K(v/r^(2))`where `K=(mu_0re)/(4pi)` is a constant `therefore r^(2)=(Kv)/B therefore r proptosqrtv/B`.