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

Current in loop- `i= (ev)/(2pi r)`
Magnetic field due to circular current at the centre - `B = (mu_(0))/(4pi) * (2pi i)/(r ) = (mu_(0))/(4pi) * (ev)/(r^(2))`
`therefore r = sqrt((mu_(0))/(4pi) * (ev)/(B)) implies r prop sqrt((v)/(B))`