Two uniformly charged spherical conductors $A$ and $B$ of radii $5 mm$ and $10 mm$ are separated by a distance of $2 cm$. If the spheres are connected by a conducting wire, then in equilibrium condition, the ratio of the magnitudes of the electric fields at the surface of the sphere $A$ and $B$ will be .

Three concentric conducting spherical shells have radius $ r, 2r$ and $3r$ and $Q_1, Q_2$ and $Q_3$ are final charges respectively. Innermost and outermost shells are already earthed as shown in figure. Choose the wrong statement.

 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 inner surface of the shell is earthed, then identify the correct statement(s)

Figure shows a charged conductor resting on an insulating stand. If at the point $P$ the charge density is $\sigma $, the potential is $V$ and the electric field strength is $E$, what are the values of these quantities at point $Q$

Charge density        potential        Electric intensity

$64$ 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