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

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 (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

Tardigrade Admin · Accepted Answer

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
ie,

\frac{m v ^{2}}{R} = Bq v

or

R = \frac{m v}{Bq}

Further, time period of the motion

T = \frac{2 π R}{v} = \frac{2 π ( \frac{m v}{Bq} )}{v}

or

T = \frac{2 πm}{Bq}

It is independent of both

R

and

v

.

Q. 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

depends on $v$ and not on $R$

depends on both $R$ and $v$

is independent of both $R$ and $v$

depends on $R$ and not on $v$

Q. 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

depends on v and not on R

depends on both R and v

is independent of both R and v

depends on R and not on v

Q. 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

depends on $v$ and not on $R$

depends on both $R$ and $v$

is independent of both $R$ and $v$

depends on $R$ and not on $v$