Under the influence of a uniform magnetic field, a charged particle moves with constant speed $\mathrm{V}$…
Under the influence of a uniform magnetic field, a charged particle moves with constant speed $\mathrm{V}$ in a circle of radius $R$. The time period of rotation of the particle :
Depends on both $v$ and $R$
Depends on $v$ and not on $R$
Depends on R and not on $v$
Is independent of 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 \(R\).