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(B) When a charged particle of mass $m$ and charge $q$ moves in a uniform magnetic field $B$ with speed $v$ perpendicular to the field,it experiences

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is independent of both $R$ and $v$

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(B) When a charged particle of mass $m$ and charge $q$ moves in a uniform magnetic field $B$ with speed $v$ perpendicular to the field,it experiences a magnetic Lorentz force that acts as a centripetal force.The magnetic force is given by $F = qvB$.The centripetal force required for circular motion is $F = \frac{mv^2}{R}$.Equating the two forces: $qvB = \frac{mv^2}{R}$.Solving for the radius $R$: $R = \frac{mv}{qB}$.The angular velocity $\omega$ is given by $\omega = \frac{v}{R}$.Substituting $R$: $\omega = \frac{v}{(mv/qB)} = \frac{qB}{m}$.The time period $T$ is given by $T = \frac{2\pi}{\omega}$.Substituting $\omega$: $T = \frac{2\pi m}{qB}$.Since $T$ depends only on the mass $m$,charge $q$,and magnetic field $B$,it is independent of both the radius $R$ and the speed $v$.

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

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