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 period of electron moving in a circular orbit
`T=("circumference of circu lar path")/("speed")=(2pir)/(upsilon)`
Electric current corresponds to the revolution of electron is `I=e/T=e/((2pir//upsilon))=(ev)/(2pir)`
Magnetic field at centre of circular `B=(mu_(0)I)/(2r)=(mu_(0)eupsilon)/(4pir^(2))`
Hence `r=sqrt((mu_(0))/(4pi).(ev)/(B)) implies r prop sqrt((upsilon)/(B))`