First slide

Force on a charged particle moving in a magnetic field

Question

Two identical particles having the same mass m and charges +q and -q separated by a distance d enter in a uniform magnetic field B directed perpendicular to paper inwards with speeds $v_{1}$ and $v_{2}$ as shown in figure. The particles will not collide if

Moderate

A

$d > \frac{m}{q B} (v_{1} + v_{2})$
B

$d < \frac{m}{q B} (v_{1} + v_{2})$
C

$d > \frac{2 m}{q B} (v_{1} + v_{2})$
D

$v_{1} = v_{2}$

Solution

The particles do not collide, if they do not touch each other when they complete their circles
$\begin{array}{l} d > 2 r_{1} + 2 r_{2} \\ d > 2 (\frac{m v_{1}}{q B} + \frac{m v_{2}}{q B}) \\ d > \frac{2 m}{q B} (v_{1} + v_{2}) \end{array}$

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