A charged particle +q in an electric field E experiences a force in the direction of the electric field. As a result, its kinetic energy changes.…

A charged particle +q in an electric field $\displaystyle \overrightarrow{\mathrm{E}}$ experiences a force in the direction of the electric field. As a result, its kinetic energy changes. Similarly, the charged particle also experiences a force when it moves in a magnetic field $\displaystyle \overrightarrow{\mathrm{B}}$. But this magnetic force is perpendicular to both velocity $\displaystyle \overrightarrow{\mathrm{v}}$ of the charged particle and the magnetic field $\displaystyle \overrightarrow{\mathrm{B}}$, so it cannot change the kinetic energy of the charged particle. Consider two charged particles $\displaystyle 1$ and $\displaystyle 2$ of masses m and $\displaystyle \frac{\mathrm{m}}{2}$ having charges -q and +$\displaystyle 2$ q respectively. They are accelerated from rest through the same potential difference V and acquire kinetic energy $\displaystyle \mathrm{K}_{1}$ and $\displaystyle \mathrm{K}_{2}$. Then they enter in a region of uniform magnetic field $\displaystyle \overrightarrow{\mathrm{B}}$ perpendicular to their velocities.

The ratio of their kinetic energies $\displaystyle \left(\frac{\mathrm{K}_{1}}{\mathrm{~K}_{2}}\right)$ is :

$\displaystyle \frac{1}{2}$

$\displaystyle \frac{1}{4}$

$\displaystyle 4$ (D) $\displaystyle 1$ (ii) The ratio of the radii of the circular paths described by them $\displaystyle \left(\frac{\mathrm{r}_{1}}{\mathrm{r}_{2}}\right)$ is :

$\displaystyle \frac{1}{\sqrt{2}}$

$\displaystyle \sqrt{2}$

$\displaystyle \frac{1}{2}$

$\displaystyle 2$ (iii) Suppose particles $\displaystyle 1$ and $\displaystyle 2$ enter the magnetic field $\displaystyle \overrightarrow{\mathrm{B}}=\mathrm{B}_{0} \widehat{\mathrm{k}}$ with velocities $\displaystyle \vec{\mathrm{v}}_{1}=\mathrm{v}_{1} \hat{i}$ and $\displaystyle \vec{\mathrm{v}}_{2}=\mathrm{v}_{2} \hat{i}$. Then :

both particles revolve clockwise

both particles revolve anticlockwise

particle $\displaystyle 1$ revolves clockwise while particle $\displaystyle 2$ revolves anticlockwise

particle $\displaystyle 1$ revolves anticlockwise while particle $\displaystyle 2$ revolves clockwise