Question

A charge particle having charge q is accelerated through a potential difference V and then it enters a perpendicular magnetic field in which it experiences a force F. If V is increased to 5V, the particle will experience a force

• A. $F$
• B. $5F$
• C. $\frac{F}{5}$
• D. $\sqrt{5}F$

Answer 1

The correct option is D $\sqrt{5}F$

$\frac{1}{2}m{v}^2=qV\Rightarrow v=\sqrt{\frac{2qV}{m}}$. Also $F=qvB$
$\Rightarrow F=qB\sqrt{\frac{2qV}{m}}$ hence $F\propto \sqrt{V}$ which gives $F^{\prime }=\sqrt{5}F$.