Question

A beam of electrons is moving with constant velocity in a region having electric and magnetic fields of strength $20{\text{Vm}}^{-1}$ and $0.5\text{T}$ at right angles to the direction of motion of the electrons. What is the velocity of the electrons ?

Answer 1

Lorentz's force is given by

$\overrightarrow{F}=q[\overrightarrow{E}+(\overrightarrow{v}\times \overrightarrow{B}\left)\right]$

$\because$ velocity $\overrightarrow{v}$ is constant.

$\therefore \overrightarrow{F}=0$

$\Rightarrow q\overrightarrow{E}=-q(\overrightarrow{v}\times \overrightarrow{B})$

$\Rightarrow |\overrightarrow{E}|=|\overrightarrow{v}\times \overrightarrow{B}|$

Given that $\overrightarrow{B}\perp \overrightarrow{v}$

$E=vB\sin {90}^{\circ }=vB$

$\therefore v=\frac{E}{B}=\frac{20}{0.5}=40\text{m/s}$

Therefore, option $\left(d\right)$ is the right choice.

Why this question ? Tip: It is an example of velocity selector.