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
qbBm
q(b−a)Bm
qaBm
q(b+a)B2m
A
qbBm
B
q(b−a)Bm
C
qaBm
D
q(b+a)B2m
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Solution
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Radius of curvature has to be greater than the width of magnetic field for the particle to enter the region x>B.
∴mvqB>(b−a)
⇒v>qB(b−a)m
∴vmin=qB(b−a)m
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