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
ie, `(mv^(2))/(R)=Bqv`
or `R=(mv)/(Bq)`
Further, time period of the motion
`T=(2piR)/(v)=(2pi((mv)/(Bq)))/(v)`
or `T=(2pim)/(Bq)`
It is independent of both R and v.