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.

Answer 1

Answer: (C)

When a particle moves in a magnetic field of intensity $B$ pointing downwards into the page and particle is moving with a speed of $v$ on the plane of paper:

$F=qvB$ (Force of charged particle in a magnetic field)

And we know that

$F=\frac{m{v}^2}{r}$ ($r$ is the radius of motion and $m$ is mass of particle)

$\Rightarrow qvB=\frac{m{v}^2}{r}$

$\Rightarrow r=\frac{mv}{Bq}$

Now as we know that

$\omega =\frac{v}{r}$

$\Rightarrow \omega =\frac{Bq}{m}$

Time period, $T=\frac{2\pi }{\omega }$

$\Rightarrow T=\frac{2\pi m}{Bq}$

And this shows that it is independent of both radius and velocity.