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
Answer & explanation
Correct answer: option 1
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