Under the influence of a unifrom magnetic field a charged particle is moving on a circle of radius `R` with Constnant speed `v`. The time period of the motion

Options

A. depends on v and not on R
B. depends on both R and v
C. is independent of both R and v
D. depends on R and not on v

Answer

C

Explanation

When magnetic field is perpendicular to motion of charged particle, then
Centripetal force = Magnetic force
i.e. ` ( mv ^ 2 ) /( R) Bqv or R = ( mv ) /( Bq ) `
Further, time period of the motion
` T = ( 2pi R ) /( v ) = ( 2pi (( mv ) /( Bq))) /( v ) or T = ( 2pi m ) /( B q ) `
It is independent of both R and v.