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

Answer

B

Explanation

In a uniform magnetic field, a charged particle is moving in a circle of radius R with constant speed v. Then the required centripetal force is provided by the magnetic force.
`:. (mv^(2))/(R )= Bqv or, R= (mv)/(Bq)`…(i)
`:.` Time period, `T= (2pi R)/(v ) = (2pi mv)/(Bqv) = (2pi m)/(Bq)`...(ii)
Time period T does not depend on both R and v because when v is changed, R is also changed proportionately and for period, it is R/v that is considered.