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

To move on circular path in magnetgic field, a centripetal force is provided by the magnetic force.
When magneitc field is perpendicular to motion of charged particle, then
Centipetal force = magnetic force
That is `(mv^(2))/(R) = Bqv` or `R = (mv)/(Bq)`
Further, timn period of the motion
`T = (2pi R)/(v) = (2pi ((mv)/(Bq)))/(v)` or `T = (2pi m)/(Bq)`