An electron accelerated through a potential difference $V$, passes through a uniform transverse magnetic field and experiences a force $F$. If the accelerating potential is increased to $2 \mathrm{~V}$, the electron in the same magnetic field will experience a force.

• A

  $F$
• B

  $\frac{F}{2}$
• Correct answer
  C

  $\sqrt{2} F$
• D

  $2 F$

Solution

$\because$ Magnetic force, $$ \begin{aligned} F & =q(\mathbf{v} \times \mathbf{B}) \\ & =q v B \sin \theta \end{aligned} $$ For uniform transverse magnetic field, $\theta=90^{\circ}$ So, $$ F=q v B=q\left(\sqrt{\frac{2 q V}{m_e}}\right) B $$ when electron accelerated through a potential difference,
When electron accelerated through a potential difference $2 V$. $$ F^{\prime}=e\left(\sqrt{\frac{2 e(2 V)}{m_e}}\right) B $$ From Eqs. (i), we get $F^{\prime}=\sqrt{2} F$

Hence, the correct answer is option: 'C'.