The electric field in a region is given by $\vec E = a\hat i + b\hat j$. Here $a$ and $b$ are constants. Find the net flux passing through a square area of side $l$ parallel to the $y-z$ plane.

$A$ 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:

Units of electric flux are

The linear charge density of a wire is $8.85 \ \mu C/m$. The radius and height of the cylinder are $3 \ m$ and $4 \ m$ respectively. Find the electric flux passing through the cylinder.

$A$ point charge of $2.0 \; \mu C$ is at the centre of a cubic Gaussian surface $9.0 \; cm$ on edge. What is the net electric flux through the surface?

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 $\frac{\lambda L }{ n \varepsilon_0}$ (where $\varepsilon_0$ is the permittivity of free space),then the value of $n$ is