An infinitely long positively charged straight thread has a linear charge density $\lambda \mathrm{Cm}^{-1}$. An electron revolves along a circular path having axis along the length of the wire. The graph that correctly represents the variation of the kinetic energy of electron as a function of radius of circular path from the wire is :

Two concentric conducting thin spherical shells of radii $a$ and $b\  (b > a)$ are given charges $Q$ and $ -2Q$ respectively. The electric field along a line passing through centre as a function of distance $(r)$ from centre is given by

Let a total charge $2Q$ be distributed in a sphere of radius $R$, with the charge density given by $\rho(r) = kr$, where $r$ is the distance from the centre. Two charges $A$ and $B$, of $-Q$ each, are placed on diametrically opposite points, at equal distance, $a$, from the centre. If $A$ and $B$ do not experience any force, then

In the figure, a very large plane sheet of positive charge is shown. $P _{1}$ and $P _{2}$ are two points at distance $l$ and $2 \,l$ from the charge distribution. If $\sigma$ is the surface charge density, then the magnitude of electric fields $E_{1}$ and $E_{2}$ at $P _{1}$ and $P _{2}$ respectively are

Obtain Gauss’s law from Coulomb’s law.

Consider a sphere of radius $\mathrm{R}$ which carries a uniform charge density $\rho .$ If a sphere of radius $\frac{\mathrm{R}}{2}$ is carved out of it, as shown, the ratio $\frac{\left|\overrightarrow{\mathrm{E}}_{\mathrm{A}}\right|}{\left|\overrightarrow{\mathrm{E}}_{\mathrm{B}}\right|}$ of magnitude of electric field $\overrightarrow{\mathrm{E}}_{\mathrm{A}}$ and $\overrightarrow{\mathrm{E}}_{\mathrm{B}}$ respectively, at points $\mathrm{A}$ and $\mathrm{B}$ due to the remaining portion is