A particle of charge q and mass m is projected with a velocity `v_0` toward a circular region having uniform magnetic field B perpendicular and into the plane of paper from point P as shown in Fig. 1.136. R is the radius and O is the center of the circular region. If the line OP makes an angle `theta` with the direction of `v_0` then the value of `v_0` so that particle passes through O is

Options

A. `(qBR)/(msin theta)`
B. `(qBR)/(2msin theta)`
C. `(2qBR)/(msin theta)`
D. `(3qBR)/(2msin theta)`

Answer

b

Explanation

If the particle passes through O, the situation can be shown in the figure below. Let r the radius of circular path then from the given figure
`sin theta=(R//2)/r=R/(2r), r=(mv)/(qB)`
`sin theta =(RqB)/(2mv), v_0=(qBR)/(2msin theta)`
.