Question

A non-relativistic charge q of mass m originates at a point A lying on x-axis and moves with velocity v at an angle to the x-axis. A screen is located at a distance l from A. If the distance r from the x-axis to the point on the screen into which the charge strikes is $r=\frac{a\ast mvsin\alpha }{qB}sin\left(\frac{qB}{2m}\frac{1}{vcos\alpha }\right)$. Find a.

Answer 1

Time taken by particle to reach the screen: $t=\frac{l}{vcos\alpha }$
Radius of helical path: $R=\frac{mvsin\alpha }{qB}$
Angle rotated in time: $\theta =\omega t=\frac{qB}{m}t$
Required distance:
$r=2Rsin\left(\frac{\theta }{2}\right)=\frac{2mvsin\alpha }{qB}sin\left(\frac{qB}{2m}\frac{1}{vcos\alpha }\right)$