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 :
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