Two infinitely long parallel wires having linear charge densities $\lambda_1$ and $\lambda_2$ respectively are placed at a distance of $R$ meters. The force per unit length on either wire will be $(K = \frac{1}{4\pi\varepsilon_0})$.

Obtain Coulomb's law from Gauss's law.

An early model for an atom considered it to have a positively charged point nucleus of charge $Ze$,surrounded by a uniform density of negative charge up to a radius $R$. The atom as a whole is neutral. For this model,what is the electric field at a distance $r$ from the nucleus?

$A$ spherically symmetric charge distribution is characterised by a charge density having the following variations:
$\rho (r) = \rho_0 \left( 1 - \frac{r}{R} \right)$ for $r < R$
$\rho (r) = 0$ for $r \ge R$
Where $r$ is the distance from the centre of the charge distribution and $\rho_0$ is a constant. The electric field at an internal point $(r < R)$ is:

$A$ very long charged solid cylinder of radius 'a' contains a uniform charge density $\rho$. The dielectric constant of the material of the cylinder is $k$. What will be the magnitude of the electric field at a radial distance '$x$' $(x < a)$ from the axis of the cylinder?

Within a spherical charge distribution of charge density $\rho(r)$,$N$ equipotential surfaces of potential $V_0, V_0 + \Delta V, V_0 + 2\Delta V, \dots, V_0 + N\Delta V$ (where $\Delta V > 0$) are drawn and have increasing radii $r_0, r_1, r_2, \dots, r_N$,respectively. If the difference in the radii of the surfaces is constant for all values of $V_0$ and $\Delta V$,then: