Two particles A and B of masses $m$ and $2m$ have charges $q$ and $...

Question

Two particles A and B of masses $m$ and $2m$ have charges $q$ and $2q$ respectively. They move with velocities $v_1$ and $v_2$ in the same direction in the same magnetic field $B$ acting normally. If the forces $F_A$ and $F_B$ are in the ratio 1:2, find the ratio $v_1 : v_2$.

Accepted Answer

Magnetic force: $F = qvB$
$$F_A = qv_1B, \quad F_B = 2qv_2B$$
$$\frac{F_A}{F_B} = \frac{qv_1B}{2qv_2B} = \frac{v_1}{2v_2} = \frac{1}{2}$$
$$\frac{v_1}{2v_2} = \frac{1}{2} \Rightarrow v_1 = v_2$$
$$v_1 : v_2 = 1 : 1$$

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