We have obtained the expression for the potential of the field of a point charge using numerical methods. When you have learned to difierentiate, prove that formula (18.25) leads to the expression for the field intensity of a point charge known from the Coulomb law.

Explanation

In this case equipotential surfaces are spheres with a common centre at the source, and radii normal to the surfaces. If the potential is `varphi=q..4pi epsi_(0)r,` the field strength is
`E=(dvarphi)/(dr)=-(d)/(dr)((q)/(4pi epsi_(0)r))=(q)/(4pi epsi_(0)r^(2))` and just this was to be proved.