Question

A proton and an electron travelling along parallel paths enter a region of uniform magnetic field, perpendicular to their paths. Which of them will move in a circular path with higher frequency?

Answer 1

When a charge particle enters a region of uniform magnetic field, perpendicular to their paths, they move in a circular path.

And the time period of their motion is given by

$T=\frac{2\pi m}{qB}$

But, $f=\frac{1}{T}$

$f=\frac{qB}{2\pi m}$

Since B and q is same for electron and proton,

so $f\propto \frac{1}{m}$

Since mass of electron is smaller than that of proton, hence it will have higher frequency.