Two large parallel plates have uniform surface charge densities $+\sigma$ and $-\sigma$. The electric field between the plates is:

Consider a sphere of radius $R$ with charge density distributed as:
$\rho(r) = kr$ for $r \leq R$
$\rho(r) = 0$ for $r > R$
$(a)$ Find the electric field at all points $r$.
$(b)$ Suppose the total charge on the sphere is $2e$ where $e$ is the elementary charge. Where can two protons be embedded such that the force on each of them is zero? Assume that the introduction of the protons does not alter the charge distribution.

Electric field inside a uniformly charged sphere of radius $R$ is (where $r$ is the distance from the centre,$r < R$):

What is the electric field intensity at a point at a distance $r$ $(r < R)$ from the center of a charged spherical conductor of radius $R$ carrying a charge $Q$?

$A$ long, hollow conducting cylinder is kept coaxially inside another long, hollow conducting cylinder of larger radius. Both the cylinders are initially electrically neutral. Then

Three infinite sheets are placed as shown in the figure. Find the electric field at point $P$.