A particle of the 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 minimum value of `v` required so that the particle can just enter the region ` xgtb` is

Options

A. `qb B//m`
B. `q(b-a) B//m`
C. `qa B//m`
D. `q(b+a) B//2m`

Answer

B

Explanation

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 `xgtb` for `rge(b-a)`

Now, `r=(mv)/(qB)ge(b-a)`
or `vge(q(b-a)B)/(m)impliesv_(min)=(q(b-a)B)/(m)`