Question

An electron is projected with Velocity $V_0$ in a uniform electric field $E$ perpendicular to the field. Again it is projected with velocity $V_0$ perpendicular to a uniform magnetic field $B$. If $r_1$ is initial radius of curvature jsut after entering in the electric feld and $r_2$ is initial radius of curvature jsut after entering in magnetic field then the ratio $\frac{r_1}{r_2}$ is equal to

• A. $\frac{B{V}_0^2}{E}$
• B. $\frac{B}{E}$
• C. $\frac{E{V}_0}{B}$
• D. $\frac{B{V}_0}{E}$

Answer 1

The correct option is D $\frac{B{V}_0}{E}$

Electron is projected with velocity $V_0$ perpendicular to uniform electric field $E$.
Force on the electron, $F=eE$

This force is responsible for initial radius of curvature $\left(r_1\right)$.
$\therefore eE=\frac{m{V}_0^2}{r_1}$
$r_1=\frac{m{V}_0^2}{eE}$ ....(1)

Again electron is projected with velocity $V_0$ perpendicular to uniform magnetic field $B$. Electron will describe a circular motion.
Its radius $r_2$ is given as, $r_2=\frac{m{V}_0}{eB}$ ...(2)

From equation (1) and (2):
$\frac{r_1}{r_2}=\frac{B{V}_0}{E}$