Magnetic Effects Of Current Question 415
Question: A particle of mass m and charge q enters a region of magnetic field (as shown) with speed v. There is a region in which the magnetic field is absent, as shown. The particle after entering the region collides elastically with a rigid wall. Time after which the velocity of particle becomes antiparallel to its initial velocity is
Options:
A) $ \frac{m}{2qB}(\pi +4) $
B) $ \frac{m}{qB}(\pi +2) $
C) $ \frac{m}{4qB}(\pi +2) $
D) $ \frac{m}{4qB}(2\pi +3) $
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Answer:
Correct Answer: A
Solution:
[a] $ r=\frac{mv}{qB} $ $ \sin ,\theta =\frac{x}{r}=\frac{\frac{mv}{\sqrt{2}qB}}{\frac{mv}{qB}}=\frac{1}{\sqrt{2}} $ or $ \theta =\frac{\pi }{4} $ Time to complete the circle $ (2\pi ) $ , $ T=\frac{2\pi m}{qB} $
$ \therefore $ time taken to traverses $ \frac{\pi }{4} $ , $ t=\frac{\pi m}{4qB} $ Time taken to travel horizontal distance $ t_{1}=\frac{\frac{mv}{\sqrt{2}qB}}{\frac{v}{\sqrt{2}}}=\frac{m}{qB} $ Total time taken $ =2t+2t_{1}=\frac{m}{2qB}(\pi +4) $
BETA
