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Circular Kinematics

Two identical...

Question

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

A

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

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B

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

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C

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

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D

v_{1} = v_{2}

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Solution

The correct option is C $d > \frac{2 m}{B q} (v_{1} + v_{2})$
The particles will not collide if $d > 2 (r_{1} + r_{2})$

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

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