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

Four metal conductors having different shapes

$1.$  A sphere     $2.$  Cylindrical

$3.$  Pear            $4.$  Lightning conductor

are mounted on insulating stands and charged. The one which is best suited to retain the charges for a longer time is

If electric potential of the inner sphere is $10\, volt$ and that of the outer shell is $50\, volt$ then potential at common centre is :-......$V$

Consider the shown system of two concentric thin metal shells. The inner hell has charge $Q$, while the outer shell is neutral. Potential difference between the shells is $V$. If the shell are joined by metal wire, then potential of the inner shell is

Write important results regarding electrostatic of conductors.

$64$ small drops of mercury, each of radius $ r$ and charge $q$ coalesce to form a big drop. The ratio of the surface density of charge of each small drop with that of the big drop is