Under the influence of a uniform magnetic field, a charged particle moves with constant speed $v$ in a…
Under the influence of a uniform magnetic field, a charged particle moves with constant speed $v$ in a circle of radius $R$. The time period of rotation of the particle
depends on $v$ and not on $R$
depends on $R$ and not on $v$
is independent of both $v$ and $R$
depends on both $v$ and $R$
Solution
The time period of circular motion of the charged particle is given by
$\begin{aligned}
& \mathrm{T}=\frac{2 \pi \mathrm{r}}{\mathrm{v}}=\frac{2 \pi}{\mathrm{v}} \times \frac{\mathrm{mv}}{\mathrm{Bq}} \\
& \mathrm{T}=\frac{2 \pi \mathrm{m}}{\mathrm{Bq}}
\end{aligned}$
Hence, time period of rotation of the charged particle in uniform magnetic field is independent of both $v$ and $R$.