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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 the figure. The particle will not collide if,

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$v_{1} = v_{2}$

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

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

$d < \frac{m}{Bq} (v_{1} + v_{2})$

answer is C.

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Detailed Solution

for particle to not collide

$(2 r_{1} + 2 r_{2}) < d$

$2 (\frac{{mv}_{1}}{qB} + \frac{{mv}_{2}}{qB}) < d$

$d = \frac{2 m}{qB} (v_{1} + v_{2})$

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