We can derive Coulomb's law from Gauss's law, by assuming that the charge is stationary.
Consider a spherical Gaussian surface of radius r around the charge. The electric field intensity is uniform at all points of the sphere. The electric field intensity will be along the outward drawn normal at every point of the sphere.
We also take area as a vector, whose direction is along normal to the plane of area.
According to Gauss’s law,
Now, suppose a charge q0 is placed at a point where the electric field due to the charge q is present, then the force exerted by q on q0 is given by,