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. `sqrt((v)/(B))`
D. `sqrt((B)/(v))`

Answer

C

Explanation

The time taken by the electron to complete one revolution in the circular orbit is `T = (2pir)/(v)`
and the moving electron is equivalent to a current,
`I =(dq)/(dt) =e/T =(e)/((2pir)/(v))=(ev)/(2pir)`
The magnetic field at the centre of the curcle, due to the current is given by
`B = (mu_(0))/(4pi )((2pi n I)/(r))` In this case, `n=1`
`B = (mu_(0))/(4pi). (2pi)/(r )xx (ev)/(2pir)=(mu_(0)ev)/(4pi r ^(2))`
`therefore r ^(2) =(mu _(0)ev)/(4piB)` but `mu_(0),` e and ` 4 pi` are constant
`therefore r ^(2) prop v /B or r =sqrt((v)/(B))`