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

Width of the magnetic field region (b-a)`leR`, where 'R' is
its radius of curvature inside magnetic field.
`:. R=(mv)/(qB) =(b-a) implies v_(min)=((b-a)qB)/m`
(b ) is the correct option.