Q 12-04-188JEE MainJEE Main 2020 (7 Jan, Shift 2)Medium
A particle of mass $m$ and charge $q$ has an initial velocity $\vec v = v_0\hat j$. If an electric field $\vec E = E_0\hat i$ and magnetic field $\vec B = B_0\hat i$ act on the particle, its speed will double after a time:
Answer: (C) $\dfrac{\sqrt3mv_0}{qE_0}$
The magnetic field is along $x$, so it only rotates the velocity component in the $y$-$z$ plane, keeping its magnitude $v_0$.
The electric field accelerates the particle along $x$: $v_x = \dfrac{qE_0}{m}t$.
Speed doubles when $v_0^2 + v_x^2 = 4v_0^2$, i.e. $v_x = \sqrt3v_0$:
$$t = \frac{\sqrt3mv_0}{qE_0}$$
Solution by Sreeraj P, M.Sc Physics