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. qbB/m
• B. q(b – a)B/m
• C. qaB/m
• D. q(b+a)B/2m

Answer 1

Answer: (B)

q(b – a)B/m

Answer 2

As shown in the following figure, the $z -$ axis points out of the paper and the magnetic fields 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 $r \geq ( b - q )$

Now

$\Rightarrow$ $v \geq \frac { q ( b - a ) B } { m }$ $\Rightarrow v _ { \min } = \frac { q ( b - a ) B } { m }$.