Chapter 19 - Magnetism - Learning Path Questions and Exercises - Exercises - Page 688: 11

(b) $q_{A}=2q_{B}$

Since magnetic force = centripetal force, For both particles A and B, $q_{A}Bsin\theta=\frac{m_{A}v_{A}}{r_{A}}$ $q_{B}Bsin\theta=\frac{m_{B}v_{B}}{r_{B}}$ Taking ratio of above two equations, $\frac{q_{A}}{q_{B}}=\frac{m_{A}v_{A}r_{B}}{m_{B}v_{B}r_{A}}$ Since, for A and B, masses are same , also velocities are same, so, $\frac{q_{A}}{q_{B}}=\frac{r_{B}}{r_{A}}=\frac{50}{25}=2$ Hence, (b) is the answer.