Question

A particle of charge $=1$ $\mu C$ and mass m = $1$ $gm$ starts moving from origin at $t=0$ under the electric field of ${10}^{3}N/C$ along x-axis and magnetic field of $10$ $tesla$ along the same axis with the velocity of $v=20\hat{j}$ $m/s$ as shown, the speed of the particle at the time of $20\sqrt{3}$ $sec$ is $n$ $m/s$. The value of $n$ is $m/s$

Answer 1

Let the velocity along x-axis and y-axis be $v_x$ and $v_y$ respectively.
Force along x-direction = $qE$
So, the velocity along x-direction can be given by $v_x=\frac{qE}{m}t$
As $v^2=v_x^2+v_y^2$
$=(\frac{qE}{m}t{)}^2+(20{)}^2=(\frac{{10}^{-6}{10}^3}{{10}^{-3}}20\sqrt{3}{)}^2+(20{)}^2=1600m^2/s^2$
$v=40$ $m/s$