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

For a spherical shell

A non uniformly shaped conductor is charged then at it's sharpest point

A hollow metal sphere of radius $5\,\, cm$ is charged so that the potential on its surface is $10\,\, V$. The potential at the centre of the sphere is.....$V$

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 another point charge $q_B$ is also placed at a distance $c ( > b) $ the center of shell, then choose the correct statements 

Can a metal be used as a medium for dielectric