In a region of space,the electric field is given by $\vec E = 8\hat i + 4\hat j + 3\hat k$. The electric flux through a surface of area $100 \text{ units}$ in the $x-y$ plane is...

$A$ square surface of side $L$ meters is in the plane of the paper. $A$ uniform electric field $\vec{E} \text{ (V/m)}$ is also in the plane of the paper,limited only to the lower half of the square surface. The electric flux associated with the surface in $SI$ units is:

$A$ square of side $20 \ cm$ is enclosed by a spherical surface of radius $80 \ cm$. The centers of the square and the sphere are the same. Four charges $2 \times 10^{-6} \ C, -5 \times 10^{-6} \ C, -3 \times 10^{-6} \ C$,and $6 \times 10^{-6} \ C$ are placed at the four corners of the square. The total flux coming out of the spherical surface in $N \cdot m^2/C$ is:

$A$ point charge causes an electric flux of $-2 \times 10^4 \ Nm^2 C^{-1}$ to pass through a spherical Gaussian surface of $8.0 \ cm$ radius,centred on the charge. The value of the point charge is: (Given $\epsilon_0 = 8.85 \times 10^{-12} \ C^2 N^{-1} m^{-2}$)

Consider the four surfaces $S_1, S_2, S_3,$ and $S_4$ enclosing the same charge $q_1$ as shown in the figure. Compare the electric flux through these surfaces.

$A$ linear charge having linear charge density $\lambda$ penetrates a cube diagonally and then it penetrates a sphere diametrically as shown. What will be the ratio of flux coming out of the cube and the sphere?