The electric field in a region is given by $\vec{E}=(2 \hat{i}+4 \hat{j}+6 \hat{k}) \times 10^3 \ N/C$. The flux of the field through a rectangular surface parallel to the $x-z$ plane is $6.0 \ N m^2 C^{-1}$. The area of the surface is . . . . . . $cm^2$.

Flux coming out from a positive charge of $8 \ C$,placed in a medium of dielectric constant $4$ is

It is not convenient to use a spherical Gaussian surface to find the electric field due to an electric dipole using Gauss's theorem because

The net electric flux due to a uniform electric field of $3 \times 10^3 \hat{i} \text{ NC}^{-1}$ through a cube of side $20 \text{ cm}$ oriented such that its faces are parallel to the coordinate planes is

The figure shows the electric field lines around three point charges $A, B$,and $C$.
$(a)$ Which charges are positive?
$(b)$ Which charge has the largest magnitude? Why?
$(c)$ In which region or regions of the picture could the electric field be zero? Justify your answer.
$(i)$ Near $A$ $(ii)$ Near $B$ $(iii)$ Near $C$ $(iv)$ Nowhere

In a certain region of space,there exists a uniform electric field of value $2 \times 10^2 \hat{k} \ Vm^{-1}$. $A$ rectangular coil of dimension $10 \ cm \times 20 \ cm$ is placed in the $xy$-plane. The electric flux through the coil is......$Vm$.