Abstract
The mathematical steps that generalize the expression for the electrostatic energy of a set of point charges to the corresponding expression for a continuous charge distribution involve a few subtleties that are not usually discussed in standard introductory or advanced electromagnetic textbooks. In this paper, we point out such subtleties and discuss how to deal with them in cases of volume and surface charge distributions. We also show explicitly that it is not possible to define electrostatic energy for a linear charge distribution, since this energy would be divergent. Finally, we use dimensional analysis to recover our results in a simpler and more elegant form.
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