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A particle of charge q and mass m is pro...

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

A

`(qBR)/(m sin theta)`

B

`(qBR)/(2m sin theta)`

C

`(2qBR)/(m sin theta)`

D

`(3qBR)/(2m sin theta)`

Text Solution

Verified by Experts

The correct Answer is:
B
Let r be the radius of circular path. If the particle passes through O, then from the given figure.
`sin theta =(R//2)/r = R/(2r)`………..(i)
As `r=(mv_(0))/(qB)`
`therefore v_(0) = (qBr)/(m) =(qBR)/(2m sin theta)` (Using (i))
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