Electrostatics Questions

An electric charge $10^{-3}\mu \text{C}$ is placed at the origin $(0,0)$ of $X-Y$ co-ordinate system. Two points $A$ and $B$ are situated at $(\sqrt{2},\sqrt{2})$ and $(2,0)$ respectively. The potential difference between the points $A$ and $B$ will be:

A battery is used to charge a parallel plate capacitor till the potential difference between the plates becomes equal to the electromotive force of the battery. The ratio of the energy stored in the capacitor and the work done by the battery will be:

Charges $+q,+q,-q,-q$ are placed at the vertices $A,B,C,D$ of a square respectively. Let $\vec{E}$ be the electric field and $V$ the potential at the centre. If the charges on $A$ and $B$ are interchanged with those on $D$ and $C$ respectively, then:

The potential at a point $x$ (measured in $\mu \text{m}$) due to some charges situated on the $x$ -axis is given by $V(x)=20/(x^2-4)$ Volts. The electric field $E$ at $x=4\mu \text{m}$ is given by:

A parallel plate condenser with a dielectric of dielectric constant $K$ between the plates has a capacity $C$ and is charged to a potential $V$ volts. The dielectric slab is slowly removed from between the plates and then reinserted. The net work done by the system in this process is:

If $g_E$ and $g_m$ are the accelerations due to gravity on the surfaces of the earth and the moon respectively and if Millikan's oil drop experiment could be performed on the two surfaces, one will find the ratio of electronic charge on the moon to electronic charge on the earth to be: