A particle of mass $m$ and charge $q$ travelling with a velocity $v$ along the $X$-axis enters a uniform electric field $\mathbf{E}$ directed along the $Y$-axis. What will be the trajectory of the particle?

A large metal plate has a surface charge density of $8.85 \times 10^{-6} \mathrm{C} / \mathrm{m}^2$. An electron having initial kinetic energy of $8 \times 10^{-17} \mathrm{~J}$ is moving towards the centre of the plate. If the electron stops just before reaching the plate, then the initial distance between the electron and the plate is

[take $\varepsilon_0=8.85 \times 10^{-12} \mathrm{C}^2 / \mathrm{N}-\mathrm{m}^2$ ]

An electron is released from a distance of 4 m from a stationary point charge 20 nC . What will be the speed of the electron, when it is

2 m away from the point charge?

(Charge of electron $=1.6 \times 10^{-19} \mathrm{C}$, mass of electron

$$ =9 \times 10^{-31} \mathrm{~kg}, \frac{1}{4 \pi \varepsilon_0}=9 \times 10^9 \text { SI unit) } $$

In a uniformly charged sphere of total charge $Q$ and radius $R$, the electric field $E$ is plotted as function of distance from the centre of the sphere. The graph which would correspond to the above description will be