$A$ negatively charged plate has a surface charge density of $2 \times 10^{-6} \, C/m^2$. Find the minimum initial distance of an electron moving toward the plate such that it does not strike the plate,given that its initial kinetic energy is $200 \, eV$.

$A$ clock dial has point charges $-q, -2q, -3q, \ldots, -12q$ at the positions of the corresponding numbers on the dial respectively. The time at which the hour hand points in the direction of the net electric field at the centre of the dial is (Assume clock hands do not influence the net electric field). (in $:30$)

Six point charges are placed at the vertices of a regular hexagon of side $a$ as shown. If $E$ represents the electric field and $V$ represents the electric potential at the center $O$,then:

Which of the following patterns of electric field lines is $NOT$ possible for an electrostatic field due to static charges?

Two positively charged particles $X$ and $Y$ are initially far away from each other and at rest. $X$ begins to move towards $Y$ with some initial velocity. The total momentum and energy of the system are $p$ and $E$.

Two identical charged spheres are suspended by strings of equal lengths. The strings make an angle of $30^{\circ}$ with each other. When suspended in a liquid of density $0.8 \; g \, cm^{-3}$,the angle remains the same. If the density of the material of the sphere is $1.6 \; g \, cm^{-3}$,the dielectric constant of the liquid is: