$A$ sphere '$1$' with radius $R$ has charge $q$. Sphere '$2$' with radius $3R$ is far from sphere '$1$' and is initially uncharged. If the two spheres are now connected with a thin conducting wire,then the ratio $\frac{\sigma_1}{\sigma_2}$ of the surface charge densities is

$A$ and $B$ are two concentric conducting spherical shells. $A$ is given a positive charge $+Q$ while $B$ is earthed. Then:

Show that electrostatic potential is constant throughout the volume of the conductor and has the same value (as inside) on its surface.

Two isolated metallic spheres of radii $R$ and $2R$ are charged such that both have the same charge density $\sigma$. The spheres are then connected by a thin conducting wire. If the new charge density of the larger sphere is $\sigma_1$. The ratio $\sigma_1$ to $\sigma$ is

$A$ point charge $q$ is placed in a cavity in a metal block. If a charge $Q$ is brought outside the metal,then the electric force experienced by $q$ is

Two charged conducting spheres of radii $a$ and $b$ are connected to each other by a wire. What is the ratio of electric fields at the surfaces of the two spheres? Use the result obtained to explain why charge density on the sharp and pointed ends of a conductor is higher than on its flatter portions.