According to Gauss’ Theorem, electric field of an infinitely long straight wire is proportional to

Two large, thin metal plates are parallel and close to each other. On their inner faces, the plates have surface charge densities of opposite signs and of magnitude $17.0\times 10^{-22}\; C/m^2$. What is $E$:

$(a)$ in the outer region of the first plate,

$(b)$ in the outer region of the second plate, and

$(c)$ between the plates?

The region between two concentric spheres ofradii '$a$' and '$b$', respectively (see figure), have volume charge density $\rho = \frac{A}{r}$ where $A$ is a constant and $r$ is the distance from the centre. At the centre of the spheres is a point charge $Q$. The value of $A$ such that the electric field in the region between the spheres will be constant, is :

Obtain the formula for the electric field due to a long thin wire of uniform linear charge density $E$ without using Gauss’s law.

Obtain the expression of electric field by ......

$(i)$ infinite size and with uniform charge distribution.

$(ii)$ thin spherical shell with uniform charge distribution at a point outside it.

$(iii)$ thin spherical shell with uniform charge distribution at a point inside it.

Electric field intensity at a point in between two parallel sheets with like charges of same surface charge densities $(\sigma )$ is