Discuss some points about Gauss’s law.
$(i)$ The total charge contained in the closed surface is zero, then the net electric flux through a closed surface is zero.
$(ii)$ Gauss's law is true for any closed surface, no matter what its shape or size.
$(iii)$ The charges may be located anywhere inside the surface.
$(iv)$ In the situation when the surface is so chosen that there are some charges inside and some outside the electric field, whose flux appears on the left side of Equ : $\phi=\frac{\Sigma q}{\epsilon_{0}}$ is due to all the charges both inside and outside S. The term $q$ on the right side of Gauss's law, however, represents only the total charge inside S.
$(v)$ The surface that we choose for the application of Gauss's law is called the Gaussian surface.
$(vi)$ Gauss's law is often useful towards a much easier calculation of the electrostatic field when the system has some symmetry.
$(vii)$ Gauss's law is based on the inverse square dependence on distance.
Is electric flux scalar or vector ?
What is the flux through a cube of side $a$ if a point charge of $q$ is at one of its comer?
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 $\frac{\lambda L }{ n \varepsilon_0}\left(\varepsilon_0=\right.$ permittivity of free space $)$, then the value of $n$ is
Gauss’s law should be invalid if
Draw electric field by positive charge.