Question

A charged particle is shot at an angle $\theta$ to a uniform magnetic field along directed X-axis. Duration its motion along a helical path, whose pitch is equal to the maximum distance from X-axis, the particle will :

• A. Never move parallel to x-axis
• B. $tan\theta =2/pi$
• C. $sin\theta =1/pi$
• D. $tan\theta =\pi$

Answer 1

Answer: (A), (D)

The correct options are
A Never move parallel to x-axis
D $tan\theta =\pi$

Pitch =$\left(2\pi \frac{m}{\varphi B}\right)vcos\theta$

Also $mvsin\theta =QBR$

For motion perpendicular to the magnetic field

Or,$r=\frac{mv}{QB}sin\theta$

Maximum distance of the particle from the x-axis = 2r

$\therefore \left[2\pi \frac{m}{QB}\right]vcos\theta =2\frac{mv}{QB}sin\theta$

or, $tan\theta =\pi$

Hence (A) & (D) are correct.