First slide

Force on a charged particle moving in a magnetic field

Question

Under the influence of a uniform magnetic field a charged particle is moving in a circle of radius R with constant speed v. The time period of the motion

Easy

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

Solution

To move on circular path in a magnetic field, a centripetal force is provided by the magnetic force. When magnetic field is perpendicular to motion of charged particle, then
Centripetal force = magnetic force
That is $\frac{{mv}^{2}}{R} = Bqv or R = \frac{mv}{Bq}$
Further, time period of the motion
$T = \frac{2 πR}{v} = \frac{2 π (\frac{mv}{Bq})}{v} or T = \frac{2 πm}{Bq}$
It is independent of both R and v.

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