How many electrons should be removed from a coin of mass $1.6 \,g$,so that it may float in an electric field of intensity $10^9 \,N/C$ directed upward?

$A$ proton and an $\alpha$-particle having equal kinetic energy are projected into a uniform transverse electric field as shown in the figure.

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

An electron of mass $m$ and charge $q$ is accelerated from rest in a uniform electric field of strength $E$. The velocity acquired by the electron when it travels a distance $L$ is

Acceleration of a charged particle of charge $q$ and mass $m$ moving in a uniform electric field of strength $E$ is

Two charges $-q$ each are fixed and separated by a distance $2d$. $A$ third charge $q$ of mass $m$ placed at the midpoint is displaced slightly by $x$ $(x \ll d)$ perpendicular to the line joining the two fixed charges as shown in the figure. Show that the charge $q$ will perform simple harmonic motion with a time period $T = \left[\frac{8 \pi^{3} \epsilon_{0} m d^{3}}{q^{2}}\right]^{1 / 2}$.