Question

A charged particle +q of mass m is placed at a distanced from another charged particle -2q of mass 2m in a uniform magnetic field B as shown
in fig. If the particles are projected towards each other with same speed v,
find the time after which collision occurs between the particles if projection speed equal $2v_m$

Answer 1

From symmetry, it can be concluded that collision occurs at $d/2$ at
$v=2v_m=\frac{qBd}{m}$
$r=\frac{mv}{qB}=dsin\theta =\frac{d/2}{d}=\frac{1}{2};\theta =\frac{\pi }{6}$
$t=T\left(\frac{\theta }{2\pi }\right)=\frac{2\pi m}{qB}\left(\frac{\pi /6}{2\pi }\right)=\frac{\pi m}{6qB}$