Question

Two charged particles $A$ and $B$ having the same charge, mass and speed enter into a magnetic field in such a way that the initial path of $A$ makes an angle of $30^{\circ}$ and that of $B$ makes an angle of $90^{\circ}$ with the field. Then the trajectory of

• A. $B$ will have smaller radius of curvature than that of $A$
• B. both will have the same curvature
• C. $A$ will have smaller radius of curvature than that of $B$
• D. both will move along the direction of their original velocities.

Answer 1

Answer: (A)

use $qvB \sin \theta=\frac{m v^{2}}{r}$
$r \propto \frac{1}{\sin \theta}$ for the same values of $m, v, q$ and $B$
$\therefore \frac{r_{A}}{r_{B}}=\frac{\sin 90^{\circ}}{\sin 30^{\circ}}=2$
or $r_{A}=2 r_{B}$ or $r_{B}<\,r_{A}$