A charge $Q$ is distributed over two concentric hollow spheres of radii $r$ and $R(r<R)$, such that the surface densities are equal. Find the potential at the common centre.

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 $c.$

A non-conducting disc of radius a and uniform positive surface charge density $\sigma$ is placed on the ground, with its axis vertical. A particle of mass $m$ and positive charge $q$ is dropped, along the axis of the disc, from a height $H$ with zero initial velocity. The particle has$\frac{q}{m}=4{\epsilon }_{0 }g/\sigma$. Find the value of $H$ if the particle just reaches the disc.

Sketch the potential energy of the particle as a function of its height and find its equilibrium position. A non-conducting disc of radius a and uniform positive surface charge density $\sigma$ is placed on the ground, with its axis vertical. A particle of mass $m$ and positive charge $q$ is dropped, along the axis of the disc, from a height $H$ with zero initial velocity. The particle has$\frac{q}{m}=4{\epsilon }_0 g/\sigma$.

An infinite wire having line charge density $\lambda$ passes through one edge of cube having edges of length $a.$ Find the flux passing through the cube.

An infinite wire having line charge density $\lambda$ passes through one edge of cube having edges of length $a.$ Find the flux passing through the surface which are is constant with the wire,