Three concentric metallic spherical shells of radii $R, 2R, 3R$, are given charges $Q_1, Q_2, Q_3$, respectively. It is found that the surface charge densities on the outer surfaces of the shells are equal. Then, the ratio of the charges given to the shells, $Q_1 : Q_2 : Q_3$ is

A hollow closed conductor of irregular shape is given some charge. Which of the following statements are correct ?

Two isolated metallic solid spheres of radii $R$ and $2 R$ are charged such that both have same charge density $\sigma$. The spheres are then connected by a thin conducting wire. If the new charge density of the bigger sphere is $\sigma^{\prime}$. The ratio $\frac{\sigma^{\prime}}{\sigma}$ is

 Aspherical shell with an inner radius $'a'$ and an outer radius $'b' $ is made of conducting material. A point charge $+Q$ is placed at the centre of the spherical shell and a total charge $- q $ is placed on the shell.

Charge $- q $ is distributed on the surfaces as

$64$ 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

An empty thick conducting shell of inner radius $a$ and outer radius $b$ is shown in figure.If it is observed that the inner face of the shell carries a uniform charge density $-\sigma$ and the surface carries a uniform charge density $ '\sigma '$

If a point charge $q_A$ is placed at the center of the shell, then choose the correct statement $(s)$