In the figure shown a charge `q` moving with a velocity v along the x-axis enter into a region of uniform magnetic field. The minimum value `v` so that the charge `q` is able to enter the region `xgtb`

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 `x gt b" for "r ge (b-a`

Now, `r=(mv)/(qB) ge (b-a) Or, v ge (q(b-a)B)/(m)`
`rArr v_(min)=(q(b-a)B)/(m)`