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Q.

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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a

qb+aB2m

b

qaBm 

c

qb-aBm

d

qbBm 

answer is B.

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Detailed Solution

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(ba)
 

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 Now, r=mvqB(ba) or vq(ba)Bmνmin=q(ba)Bm

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