$64$ 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

Two conducting spheres of radii $5\, cm$ and $10\, cm$ are given a charge of $15\,\mu C$ each. After the two spheres are joined by a conducting wire, the charge on the smaller sphere is.......$\mu C$

A positive charge $q$ is placed at the centre of a neutral hollow cylindrical conducting shell with its cross-section as shown in the figure below. Which one of the following figures correctly indicates the induced charge distribution on the conductor? (Ignore edge effects)

Figure shows three concentric metallic spherical shells. The outermost shell has charge $q_2$, the inner most shell has charge $q_1$, and the middle shell is uncharged. The charge appearing on the inner surface of outermost shell is

If $q$ is the charge per unit area on the surface of a conductor, then the electric field intensity at a point on the surface 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 the outer surface of the shell is earthed, then identify the correct statement(s)