First slide

Magnetic force

Question

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 2V, the electron in the same magnetic field will experience a force.

Moderate

A

$F$
B

$F / 2$
C

$\sqrt{2} F$
D

$2 F$

Solution

$F = B q v$
But $\frac{1}{2} m v^{2} = e V$ or $v = \sqrt{\frac{2 e V}{m}}$
$∴ F = B q \sqrt{\frac{2 e V}{m}}$
$\Rightarrow F \propto \sqrt{V} a n d$
$F^{1} \propto \sqrt{2 V}$
$∴ \frac{F^{1}}{F} = \sqrt{2} o r F^{1} = \sqrt{2} F$ .

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