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) → \( V/u \)
In the accelerating field the work done by the field becomes kinetic energy. In the magnetic field the magnetic force provides the centripetal force.
\( \displaystyle qV = \frac{1}{2}mu^{2} \;\Rightarrow\; m = \frac{2qV}{u^{2}} \)
\( \displaystyle quB = \frac{mu^{2}}{r} \;\Rightarrow\; r = \frac{mu}{qB} \)
Substituting \( m \) in \( r \):
\( \displaystyle r = \frac{2qV}{u^{2}} \times \frac{u}{qB} = \frac{2V}{uB} \)
For a given field \( B \), \( r \propto V/u \).