First slide

Magnetic force

Question

An electron is accelerated from rest through a potential difference V. This electron experiences a force F in a uniform magnetic field. On increasing the potential difference to $V^{1}$ , the force experienced by the electron in the same magnetic field becomes $2 F$ . Then, the ratio $(\frac{V^{1}}{V})$ is equal to

Moderate

A

$1 / 4$
B

$2 / 1$
C

$1 / 2$
D

$4 / 1$

Solution

$K = \frac{1}{2} m v^{2} = e V$ or $v = \sqrt{\frac{2 e V}{m}}$
Also, $F = e v B = e [\sqrt{\frac{2 e V}{m}}] \times B$
Therefore, $\frac{F}{2 F} = \sqrt{\frac{V_{1}}{V_{2}}} = \sqrt{\frac{V}{V^{1}}}$
$∴ \frac{V_{1}}{V} = \frac{4}{1}$ .

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