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  4. Two particles A and B of masses m and 2m have charges q and 2q respectively. Both particles moving with velocities upsilon 1 and upsilon 2 respectively in the same direction and enter the same magnetic field B acting normally to their direction of motion. If the two forces FA and FB acting on them are in the ratio of 1:2, the ratio of their velocities is

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Q. Two particles A and B of masses m and 2m have charges $ q $ and $ 2q $ respectively. Both particles moving with velocities $ {{\upsilon }_{1}} $ and $ {{\upsilon }_{2}} $ respectively in the same direction and enter the same magnetic field B acting normally to their direction of motion. If the two forces $ {{F}_{A}} $ and $ {{F}_{B}} $ acting on them are in the ratio of $ 1:2, $ the ratio of their velocities is

MGIMS WardhaMGIMS Wardha 2014

Solution:

The magnetic Lorentz force acts on charge particle given by $ F=qvB\text{ }sin\theta $ $ \frac{{{F}_{A}}}{{{F}_{B}}}=\frac{{{q}_{1}}{{v}_{1}}B\sin 90{}^\circ }{{{q}_{2}}{{v}_{2}}B\sin 90{}^\circ } $ Or $ 1/2=(q/2q)({{v}_{1}}/{{v}_{2}}) $ $ \therefore $ $ \frac{{{v}_{1}}}{{{v}_{2}}}=1/1 $