Question

A charged particle of charge $+q$, mass $m$ is moving with initial velocity '$v$' as shown in figure in a uniform magnetic field $B(-k)$. Select the correct alternative / alternatives :

Answer 1

Refer to the figure.
angle between the initial velocity and the boundary of the field $={30}^0$
$\angle AOC={60}^0$
Thus, the particle trajectory subtends an angle of ${60}^0$ at the center of the circle.
$\therefore$ time spent by the particle inside the magnetic field is $\frac{1}{6}$th the time period T.
Since $T=\frac{2\pi m}{qB}$, time spent inside the magnetic field is $\frac{1}{6}\times \frac{2\pi m}{qB}=\frac{\pi m}{3qB}$