Question

An electron is projected at an angle $\theta$ with a uniform magnetic field. If the pitch of the helical path is equal to its radius, then the angle of projection is

• A. $ta{n}^{-1}\pi$
• B. $ta{n}^{-1}2\pi$
• C. $co{t}^{-1}\pi$
• D. $co{t}^{-1}2\pi$

Answer 1

The correct option is B $ta{n}^{-1}2\pi$

$r=\frac{mv\sin \theta }{qB}$

Pitch: $p=v\cos \theta T=v\cos \theta \frac{2\pi m}{qB}$

Given $r=p$

$\therefore \frac{mv\sin \theta }{qB}=v\cos \theta \frac{2\pi m}{qB}$

$\Rightarrow \tan \theta =2\pi$

$\Rightarrow \theta ={\tan }^{-1}\left(2\pi \right)$