Question

Why volume integral of electrostatic energy density not goes to zero?

Answer 1

Consider a collection of $N$ static point charges $q_i$ located at position vectors ${\bf r}_i$ (where $i$ runs from 1 to $N$). What is the electrostatic energy stored in such a collection? Another way of asking this is, how much work would we have to do in order to assemble the charges, starting from an initial state in which they are all at rest and very widely separated?

We know that a static electric field is conservative, and can consequently be written in terms of a scalar potential.