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Question
A particle of mass m and charge q moves with a constant velocity v along the positive x direction. It enters a region containing a uniform magnetic field B directed along the negative z direction, extending from x = a to x = b. The minimum value of v required so that the particle can just enter the region x > b is
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Solution
The correct option is B q(b−a)B/m
In the figure, the z-axis points out of the paper, and the magnetic field is directed into the paper, existing in the region between PQ and RS. The particle moves in a circular path of radius r in the magnetic field. It can just enter the region x > b for r≥(b−a)
Now, r=mvqB≥(b−a)
or v≥q(b−a)Bm⇒ vmin=q(b−a)Bm
In the figure, the z-axis points out of the paper, and the magnetic field is directed into the paper, existing in the region between PQ and RS. The particle moves in a circular path of radius r in the magnetic field. It can just enter the region x > b for r≥(b−a)
Now, r=mvqB≥(b−a)
or v≥q(b−a)Bm⇒ vmin=q(b−a)Bm
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