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.

Options

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)`

Answer

D

Explanation

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)`.