A thin square plate is placed in $x-y$ plane as shown in fig. such that is centre coinsides with origine it's charge density at point $(x, y)$ is $\sigma  = \sigma _0xy$ (where $\sigma _0$ is constant). Find total charge on the plate.

If potential at centre of uniformaly charged ring is $V_0$ then electric field at its centre will be (assume radius $=R$)

Two identical charged spherical drops each of capacitance $C$ merge to form a single drop. The resultant capacitance

As shown in the fig. charges $+\,q$ and $-\,q$ are placed at the vertices $B$ and $C$ of an isosceles triangle. The potential at the vertex $A$ is

Consider a solid insulating sphere of radius $R$ with charge density varying as $\rho = \rho _0r^2$ ($\rho _0$ is a constant and $r$ is measure from centre). Consider two points $A$ and $B$ at distance $x$ and $y$ respectively $(x < R, y > R)$ from the centre. If magnitudes of electric fields at points $A$ and $B$ are equal, then 

What is the equivalent capacitance of the system of capacitors between $A$ and $B$ :-