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A uniform magnetic field B and electric ...

A uniform magnetic field B and electric field E exist along y and negative z axis respectively. Under the influence of these field a charge particle moves along OA undeflected. If electric field is switched off, find the pitch of helical trajectory in which the particle will move.

A

`(2 pi mE)/(qB^(2)cot theta)`

B

`(4 pi mE)/(qB^(2)tan theta)`

C

`(4 pi mE)/(qB^(2)cot theta)`

D

`(2 pi mE)/(qB^(2)tan theta)`

Text Solution

Verified by Experts

The correct Answer is:
D
Since the particle is moving undeflected, so magnetic force =electric force
`implies qvB sin theta=qE implies (E )/(B sin theta)`
Pitch, `d=v` cos theta `T= v cos thata (2 pi m)/(qB)`
`(E)/(B sin theta) cos theta (2 pi m)/(qB)=(2 pi mE)/(qB^(2)tan theta)`.
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