The tiny ball at the end of the thread shown in the figure has a mass of $0.5 \, g$ and is placed in a horizontal electric field of intensity $500 \, N/C$. It is in equilibrium in the position shown. The magnitude and sign of the charge on the ball is .....$\mu C$.

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

The bob of a simple pendulum has mass $2\,g$ and a charge of $5.0\,\mu C$. It is at rest in a uniform horizontal electric field of intensity $2000\,V/m$. At equilibrium,the angle that the pendulum makes with the vertical is (take $g = 10\,m/s^2$)

The electric potential varies in space according to the relation $V = 3x + 4y$. $A$ particle of mass $0.1 \, kg$ starts from rest from point $(2, 3.2)$ under the influence of this field. The charge on the particle is $+1 \, \mu C$. Assume $V$ and $(x, y)$ are in $S.I.$ units. The time taken to cross the $x$-axis is.....$s$

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

An electron with kinetic energy $K_{1}$ enters between parallel plates of a capacitor at an angle $\alpha$ with the plates. It leaves the plates at an angle $\beta$ with the plates. If the kinetic energy of the electron when leaving is $K_{2}$,then the ratio of kinetic energies $K_{1}:K_{2}$ is ....... .