Question

An electron is accelerated from rest through a potential difference $V$. This electron experiences of force $F$ in a uniform magnetic field. On increasing the potential difference to $V^{{}^{\prime }}$, the force experienced by the electron in the same magnetic field becomes $2F$. Then, the ratio $\frac{V^{{}^{\prime }}}{V}$ is equal to

• A. $\frac{4}{1}$
• B. $\frac{2}{1}$
• C. $\frac{1}{2}$
• D. $\frac{1}{4}$

Answer 1

The correct option is A $\frac{4}{1}$

$K.E.=\frac{1}{2}m{v}^2=eV$

$\therefore v=\sqrt{\frac{2eV}{m}}$
$F=eVB=e\sqrt{\frac{2eV}{m}}B$
Given $F^{\prime }=2F=e\sqrt{\frac{2e{V}^{{}^{\prime }}}{m}}B$
$\Rightarrow 2e\sqrt{\frac{2eV}{m}}B=e\sqrt{\frac{2e{V}^{\prime }}{m}}B$
$\Rightarrow V^{{}^{\prime }}=4V$