The volume charge density of a sphere of radius $6 \,m$ is $2 \,\mu cm ^{-3}$. The number of lines of force per unit surface area coming out from the surface of the sphere is $....\times 10^{10}\, NC ^{-1}$.  [Given : Permittivity of vacuum  $\left.\epsilon_{0}=8.85 \times 10^{-12} C ^{2} N ^{-1}- m ^{-2}\right]$

Consider an atom with atomic number $Z$ as consisting of a positive point charge at the centre and surrounded by a distribution of negative electricity uniformly distributed within a sphere of radius $R$. The electric field at a point inside the atom at a distance $r$ from the centre is

A solid ball of radius $R$ has a charge density $\rho $ given by $\rho  = {\rho _0}\left( {1 - \frac{r}{R}} \right)$ for $0 \leq r \leq R$. The electric field outside the ball is

Two parallel infinite line charges with linear charge densities $+\lambda\; \mathrm{C} / \mathrm{m}$ and $-\lambda\; \mathrm{C} / \mathrm{m}$ are placed at a distance of $2 \mathrm{R}$ in free space. What is the electric field mid-way between the two line charges?

Consider a uniform spherical volume charge distribution of radius $R$. Which of the following graphs correctly represents the magnitude of the electric field $E$ at a distance $r$ from the centre of the sphere?

Obtain Coulomb’s law from Gauss’s law.