JEE Advanced 2018 — Paper 1 — Question 12

In the $x y$-plane, the region $y>0$ has a uniform magnetic field $B_{1} \hat{k}$ and the region $y<0$ has another uniform magnetic field $B_{2} \hat{k}$. A positively charged particle is projected from the origin along the positive $y$-axis with speed $v_{0}=\pi \mathrm{ms}^{-1}$ at $t=0$, as shown in the figure. Neglect gravity in this problem. Let $t=T$ be the time when the particle crosses the $x$-axis from below for the first time. If $\mathrm{B}_{2}=4 B_{1}$, the average speed of the particle, in $\mathrm{ms}^{-1}$, along the $x$-axis in the time interval $T$ is $\_\_\_\_\_$ .