First slide

Force on a charged particle moving in a magnetic field

Question

A beam of electrons is accelerated though a potential difference V. It is then passed normally through a uniform magnetic field where it moves in a circle of radius r. It would have moved in a circle of radius 2r, if it were initially accelerated through a potential difference of

Moderate

A

$\sqrt{2} V$
B

2 V
C

$2 \sqrt{2} V$
D

4 V

Solution

$r = \frac{mv}{qB} \frac{P^{2}}{2 m} = qV p = \sqrt{2 mqV} r = \frac{\sqrt{2 mqV}}{qB} r \propto \sqrt{V}$
$∴ \frac{2 r}{r} = \frac{\sqrt{V'}}{\sqrt{V}} \Rightarrow V' = 4 V .$

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