A charge particle q of mass m is placed at a distance d from another charge particle -2q of mass 2m in a uniform magnetic field B as shown. If particle are projected towards each other with equal speed $V_{0}$ , the maximum value of projection speed $V_{0}$ , so that the two particles do not collide is (Assume only magnetic interaction).

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$\frac{q B d}{m}$

$\frac{q B d}{2 m}$

$\frac{2 q B d}{m}$

$\frac{3 q B d}{2 m}$

answer is B.

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Detailed Solution

Particles will move in circular path, as velocity vector is perpendicular to field. For collision not to take place perpendicular to field.

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

$o r \frac{m v}{q B} + \frac{2 m v}{2 q B} < d o r \frac{2 m v}{q B} < d o r v < \frac{q B d}{2 m}$

Therefore, maximum speed should be $\frac{q B d}{2 m}$ .
Hence, choice (b) is correct.

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