Show that Poisson’s equation follows from Gauss’s law for electrostatics. Write the general form of Poisson’s equation and its solution and apply it for electrostatic potential due to a charge distribution.

Gauss’s law for electrostatics states that the total electric flux through a closed surface is proportional to the total charge enclosed within the surface. Mathematically,  

\[
\oint_{\text{S}} \mathbf{E} \cdot d\mathbf{S} = \frac{Q_{\text{enc}}}{\varepsilon_0}
\]

where \( \mathbf{E} \) is the electric field, \( d\mathbf{S} \) is an infinitesimal surface element, \( Q_{\text{enc}} \) is the enclosed charge, and \( \varepsilon_0 \) is the permittivity of free space.  

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