Subtleties on energy calculations in the image method

Physics – Classical Physics

Scientific paper

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9 pages, 2 figures; Major change in this version: subsection added to Sect.4 (theorem generalization). Minor changes: title re

Scientific paper

In this pedagogical work we point out a subtle mistake that can be done by undergraduate or graduate students in the computation of the electrostatic energy of a system containing charges and perfect conductors if they naively use the image method. Specifically, we show that the naive expressions for the electrostatic energy for these systems obtained directly from the image method are wrong by a factor 1/2. We start our discussion with well known examples, namely, point charge-perfectly conducting wall and point charge-perfectly conducting sphere and then proceed to the demonstration of general results, valid for conductors of arbitrary shapes.

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