A spherical conducting shell of inner radius $r_1$ and outer radius $r_2$ has a charge $Q$. A charge $q$ is placed at the centre of the shell. Find the surface charge densities on the inner and outer surface of the shell.

A soap bubble of radius $3 \mathrm{cm}$ is charged with $9\mathrm{nC}$. Find the excess pressure inside the bubble. Surface tension of the soap solution$=30\times {10}^{-3}{\mathrm{Nm}}^{-1}.$ 

Two square metallic plates having length of each edge $10 \mathrm{cm}$ are kept parallel to each other and a potential difference of $100 \mathrm{V}$ is established between them. What is the force of attraction between them ?

Two long straight parallel wires carry charges ${\lambda }_1$ and ${\lambda }_2$ per unit length. The separation between their axes is R. Find the magnitude of the force exerted on unit length of one due to the charge on the other.

Three concentric spherical metallic shells $A,B$ and $C$ of radii $a,b$ and $c(a<b<c)$ have surface charge densities $\sigma ,-\sigma$ and $\sigma$ respectively.

Find the potential of the three shells $A,B$ and $C$.

Three concentric spherical metallic shells $A,B$ and $C$ of radii $a,b$ and $c(a<b<c)$ have surface charge densities $\sigma ,-\sigma$ and $\sigma$ respectively. If the shells $A$ and $C$ are at the same potential, obtain the relation between the radii $a,b$ and $c.$