Let $P(r) = \frac{Q}{\pi R^4} r$ be the charge density distribution for a solid sphere of radius $R$ and total charge $Q$. For a point $P$ inside the sphere at distance $r_1$ from the centre of the sphere,the magnitude of the electric field is

Two spherical,nonconducting,and very thin shells of uniformly distributed positive charge $Q$ and radius $d$ are located a distance $10d$ from each other. $A$ positive point charge $q$ is placed inside one of the shells at a distance $d/2$ from the center,on the line connecting the centers of the two shells,as shown in the figure. What is the net force on the charge $q$?

Obtain an expression for the electric field at the surface of a charged conductor.

The electric field at a distance $R$ from the surface of a uniformly charged nonconducting sphere of radius $R$ is $20 \,V/m$. The electric field at a distance $\frac{R}{2}$ from the centre of the sphere is $.... \,V/m$.

Two infinite parallel metal planes contain electric charges with charge densities $+\sigma$ and $-\sigma$ respectively,and they are separated by a small distance in air. If the permittivity of air is $\varepsilon_{0}$,then the magnitude of the field between the two planes with its direction will be:

Obtain the expression for the electric field due to:
$(i)$ An infinite plane sheet with uniform charge distribution.
$(ii)$ $A$ thin spherical shell with uniform charge distribution at a point outside it.
$(iii)$ $A$ thin spherical shell with uniform charge distribution at a point inside it.