A charged particle is fired at an angle `theta` to a uniform magnetic field directed along the `x-`axis. During its motion along a helical path, if the pitch of the helical path is equal to the maximum distance of the particle from the `x-` axis

Options

A. `cos theta=(1)/(pi)`
B. `sin theta=(1)/(pi)`
C. `tan theta=(1)/(pi)`
D. `tan theta=pi`

Answer

D

Explanation

Pitch `=(2pi(m)/(QB))v cos theta`
Also , `mv sin theta=QBr` for motion perpendicular to the magnetic field or `r=(mv)/(QB) sin theta`
Maximum distance of the particle fom the `x-` axis `=2r`
`:. (2pi (m)/(QB)) v cos theta =2.(mv)/(QB) sin theta ` or `tan theta =pi`