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Question

A particle of mass M and positive charge Q, moving with a constant velocity u1=4^ims1, enters a region of uniform static magnetic field normal to the x-y plane. The region of the magnetic field extends from x=0 to x=L for all values of y. After passing through this region, the particle emerges on the other side after 10 milliseconds with a velocity u2=2(3^i+^j)ms1. The correct statement(s) is (are)

A
the direction of the magnetic field is -z direction
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B
the direction of the magnetic field is +z direction
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C
the magnitude of the magnetic field 50πM3Q units
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D
the magnitude of the magnetic field 100πM3Q units
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Solution

The correct options are
A the direction of the magnetic field is -z direction
C the magnitude of the magnetic field 50πM3Q units
Time period of circular motion T=2πMQB
Time spent inside the magnetic field is t=π6×T=π62π×2πMQB=πM6QB
Give, t=10ms=10×103s
πM6QB=10×103
B=50πMQB
As seen from the figure, u=4^i
Since the partcile bends upward, B has to be in ^k direction since v×B is in ^j direction.

219690_168215_ans_7f692ba1269e419594ee1b9f7637c493.png

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