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Question

Uniform electric and magnetic fields with strength E and induction B, respectively, are along y -axis as shown in the figure. A particle with specific charge q/m leaves the origin 0 in the direction of x -axis with an initial non relativistic velocity v0. The coordinate yn of the particle when it crosses the y -axis for the nth time is


A
2π2mn2EqB2
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B
π2mn2EqB2
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C
π2mn2E3qB2
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D
3pi2mn2EqB2
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Solution

The correct option is A 2π2mn2EqB2
We know, from given

Fy=qE

ay=qEm

Time period T=2πmqB

given t=nT=2πnmqB

Now,
y=y0+uyt+12at2

y=y0+uyt0+12at2

y=12×qEm(2πnmqB)2

=2π2mn2EqB2

Watch the next video for detailed solution.

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