$A$ 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

Given below are two statements.
Statement $I$ : Electric potential is constant within and at the surface of each conductor.
Statement $II$ : Electric field just outside a charged conductor is perpendicular to the surface of the conductor at every point.
In the light of the above statements,choose the most appropriate answer from the options given below.

Two spheres of radius $a$ and $b$ respectively are charged and joined by a wire. The ratio of the electric field at the surfaces of the spheres is

Can there be a potential difference between two adjacent conductors carrying the same charge?

Two thin conducting concentric shells of radii $R$ and $2R$ are shown in the figure. The outer shell carries a charge $+Q$ and the inner shell is neutral. When the switch $K$ is closed,which of the following statement$(s)$ is/are correct?
$(a)$ The potential on the inner shell becomes zero.
$(b)$ The charge on the inner shell is $\frac{Q}{2}$.

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