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 gt b` is

Options

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

Answer

b

Explanation

When a charged particle enters in a region of the magnetic field, it tends to move in a circular path having radius r.
The radius of the circular path must be greater than (b-a) to cross the magnetic field region.
`r = (mv)/(qB) rArr (mv)/(qB) gt (b - a)`
`rArr " " v gt (qB (b - a))/m`
Hence, option (b) is correct.