A charged particle accelerated through a potential difference of V volts acquires a speed u. The particle is then made to enter perpendicularly in a uniform magnetic field B. The radius of the circular path followed by the charged particle will be proportional to

$V/u$

The correct answer is Option (1) → $V/u$

The kinetic energy gained by a charged particle after being accelerated through a potential difference V is

$eV = \frac{1}{2}mu^2$

⟹ $u^2 = \frac{2eV}{m}$

⟹ $u = \sqrt{\frac{2eV}{m}}$

When it enters a magnetic field B perpendicularly, the magnetic force provides the centripetal force:

$\frac{mu^2}{r} = e u B$

⟹ $r = \frac{mu}{eB}$

Now from the energy relation, $u = \sqrt{\frac{2eV}{m}}$

⟹ $r = \frac{m}{eB} \sqrt{\frac{2eV}{m}} = \frac{\sqrt{2mV/e}}{B}$

Thus, $r \propto \frac{V}{u}$

Correct option: V/u