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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
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
As shown in the following figure, the 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 provided,
r=mvqB≥(b−a)
⇒ v≥q(b−a)Bm⇒vmin=q(b−a)Bm .
As shown in the following figure, the 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 provided,
r=mvqB≥(b−a)
⇒ v≥q(b−a)Bm⇒vmin=q(b−a)Bm .
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