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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)` towards circular region having uniform magnetic field B perpendicular and into the plane of paper, from point Pas shown in figure. R is the radius and O is the centre 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)/(msin theta)`

B

`(qBR)/(2msin theta)`

C

`(2qBR)/(msin theta)`

D

`(3qBR)/(2msin theta)`

Text Solution

Verified by Experts

The correct Answer is:
b
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)`
.
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