Question

Protons move rectilinearly in the region of space where there are uniform mutually perpendicular electric and magnetic fields E and B.The trajectory of protons lies in the plane xz as shown in the figure and forms an angle $\theta$ with x-axis.Find the pitch of the helical trajectory along which the protons will move after the electric field is switched off.

Answer 1

When they are moving rectilinearly,net force is zero.
$\therefore qE=Bqvsin({90}^o-\theta )$
$\therefore v=\frac{E}{Bcos\theta }$

When electric field is switched off:
$p=(\frac{2\pi m}{Bq}\left)vcos\right({90}^o-\theta )$

$=\frac{2\pi mEtan\theta }{q{B}^2}$