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Discuss some points about Gauss’s law.
Solution
$(i)$ 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.
