In a uniform electric field,if a charge is fired in a direction different from the line of the electric field,then the trajectory of the charge will be a

$A$ proton and an $\alpha$-particle are both accelerated from rest in a uniform electric field. The ratio of work done by the electric field on the proton and the $\alpha$-particle in a given time is

$A$ block of mass $m$ containing a net negative charge $-q$ is placed on a frictionless horizontal table and is connected to a wall through an unstretched spring of spring constant $k$ as shown. If a horizontal electric field $E$ parallel to the spring is switched on,then the maximum compression of the spring is:

An oil drop having charge $2e$ is kept stationary between two parallel horizontal plates $2.0 \, cm$ apart when a potential difference of $12000 \, V$ is applied between them. If the density of oil is $900 \, kg/m^3$,the radius of the drop will be

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 $T = \left[\frac{8 \pi^{3} \epsilon_{0} m d^{3}}{q^{2}}\right]^{1 / 2}$.

The kinetic energy of an electron which is accelerated through a potential of $100 \, V$ is: