An infinitely long uniform line charge distribution of charge per unit length $\lambda$ lies parallel to the $y$-axis in the $y-z$ plane at $z=\frac{\sqrt{3}}{2} a$ (see figure). If the magnitude of the flux of the electric field through the rectangular surface $A B C D$ lying in the $x-y$ plane with its center at the origin is $\frac{\lambda L }{ n \varepsilon_0}\left(\varepsilon_0=\right.$ permittivity of free space $)$, then the value of $n$ is

An electron revolves around an infinite cylindrical wire having uniform linear change density $2 \times 10^{-8}\,Cm ^{-1}$ in circular path under the influence of attractive electrostatic field as shown in the figure. The velocity of electron with which it is revolving is $.........\times 10^6\,ms ^{-1}$. Given mass of electron $=9 \times 10^{-31}\,kg$

An electric field converges at the origin whose magnitude is given by the expression $E = 100\,r\,Nt/Coul$, where $r$ is the distance measured from the origin.

A metallic shell has a point charge ‘$q$’ kept inside its cavity. Which one of the following diagrams correctly represents the electric lines of forces

Using thomson's model of the atom, consider an atom consisting of two electrons, each of charge $-e$, embeded in a sphere of charge $+2e$ and radius $R$. In equilibrium each electron is at a distance $d$ from the centre of the atom. What is the equilibrium separation between electrons

For a closed surface $\oint {\overrightarrow {E \cdot } } \,\overrightarrow {ds} \,\, = \,\,0$, then