For a uniformly charged plane sheet, the variation of electric field $(E)$ with distance $(d)$ is correctly shown graphically in graph:

$A$ charge $q$ is placed at one corner of a cube. The electric flux through any of the three faces adjacent to the charge is zero. The flux through any one of the other three faces is

$A$ long, hollow conducting cylinder is kept coaxially inside another long, hollow conducting cylinder of larger radius. Both the cylinders are initially electrically neutral. Then

An infinite line charge produces a field of $7.182 \times 10^8 \, N/C$ at a distance of $2 \, cm$. The linear charge density is

This question has Statement-$1$ and Statement-$2$. Of the four choices given after the statements,choose the one that best describes the two statements.
An insulating solid sphere of radius $R$ has a uniformly positive charge density $\rho$. As a result of this uniform charge distribution,there is a finite value of electric potential at the centre of the sphere,at the surface of the sphere,and also at a point outside the sphere. The electric potential at infinity is zero.
Statement-$1$: When a charge $q$ is taken from the centre to the surface of the sphere,its potential energy changes by $\frac{q \rho R^2}{6 \epsilon_0}$.
Statement-$2$: The electric field at a distance $r (r < R)$ from the centre of the sphere is $\frac{\rho r}{3 \epsilon_0}$.

The total charge enclosed in an incremental volume of $2 \times 10^{-9} \, m^{3}$ located at the origin is ...... $nC$,if the electric flux density of its field is given by $\vec{D} = e^{-x} \sin y \hat{i} - e^{-x} \cos y \hat{j} + 2z \hat{k} \, C/m^{2}$.