091 - 02-04-02 - The Energy of a Point Charge Distribution: d

Work to arrange 1st charge , then the work needed to place a distance away from , then the work needed to place distances away from charges ,

(finally) the work needed to place distances away from charges ,

The total work done to assemble the four charges is gotten by summing and ,

This formula is readily generalized to point charges,

A Mathematica script can easily be written to calculate the energy of any finite number of point-charges,

Alternate ways to write the sum: We can write the sum as follows,

We can also write the work in terms of the potential,