What is the flux through a cube of side $a$ if a point charge of $q$ is at one of its corners?

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 $\vec{D} = e^{-x} \sin y \hat{i} - e^{-x} \cos y \hat{j} + 2z \hat{k} \, C/m^{2}$.

An infinite sheet carrying a uniform surface charge density $\sigma$ lies on the $xy$-plane. The work done to carry a charge $q$ from the point $A = a(\hat{i} + 2\hat{j} + 3\hat{k})$ to the point $B = a(\hat{i} - 2\hat{j} + 6\hat{k})$ (where $a$ is a constant with the dimension of length and $\varepsilon_{0}$ is the permittivity of free space) is

Charges are uniformly spread on the surface of a conducting sphere. The electric field from the centre of the sphere to a point outside the sphere varies with distance $r$ from the centre as:

$A$ spherical portion has been removed from a solid sphere having a charge distributed uniformly in its volume as shown in the figure. The electric field inside the emptied space is

What is the electric field intensity at a point at a distance $r$ $(r < R)$ from the center of a charged spherical conductor of radius $R$ carrying a charge $Q$?