A solid spherical conducting shell has inner radius a and outer radius $2a$. At the center of the shell a point charge $+Q$ is located . What must the charge of the shell be in order for the charge density on the inner and outer surfaces of the shell to be exactly equal?

Two parallel metal plates having charges $+ Q$ and $-Q$ face each other at a certain distance between them. If the plates are now dipped in kerosene oil tank, the electric field between the plates will

Four point $+ve$ charges of same magnitude $(Q)$ are placed at four corners of a rigid square frame in $xy$ plane as shown in figure. The plane of the frame is perpendicular to $z-$ axis. If a $-ve$ point charges is placed at a distance $z$ away from the above frame $(z << L)$ then

Three equal charges are placed at the corners of an equilateral triangle. Which of the graphs below correctly depicts the equally-spaced equipotential surfaces in the plane of the triangle? (All graphs have the same scale.)

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

Figures below show regular hexagons, with charges at the vertices, In which of the following cases the electric field at the centre is not zero.