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Question

A charged particle of charge +q, mass m is moving with initial velocity 'v' as shown in figure in a uniform magnetic field B(k). Select the correct alternative / alternatives :
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A
Time for which the particle was in magnetic field is πm6qB
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B
Time for which the particle was in magnetic field is πm3qB
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C
Distance travelled in magnetic field is πmv6qB
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D
The particle will never come out of magnetic field
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Solution

The correct option is C Time for which the particle was in magnetic field is πm3qB
Refer to the figure.
angle between the initial velocity and the boundary of the field =300
AOC=600
Thus, the particle trajectory subtends an angle of 600 at the center of the circle.
time spent by the particle inside the magnetic field is 16th the time period T.
Since T=2πmqB, time spent inside the magnetic field is 16×2πmqB=πm3qB
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