Question

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

• A. depends on $R$ and not on $v$.
• B. is independent of both $v$ and $R$.
• C. depends on both $v$ and $R$.
• D. depends on $v$ and not on $R$.

Answer 1

The correct option is B is independent of both $v$ and $R$.

For the circular motion in a cyclotron,
$qvB=\frac{m{v}^2}{R}\Rightarrow qB=\frac{mv}{R}=m\times \omega =m\times \frac{2\pi }{T}$
$\therefore T=\frac{2\pi m}{qB}$ is independent of $v$ and $R$.