This derivation sheet explores the interaction of static electric and magnetic forces within a defined volume, focusing on the unique properties of boundaries known as equipotential surfaces. By utilizing the Divergence Theorem, the study shifts the analytical focus from the complex interior of a volume to its surface, simplifying the calculation of field interactions. It demonstrates a "vanishing act" where, due to the uniform potential of the surface and the fact that magnetic field lines always form closed loops, the net magnetic flow through the boundary— and thus the internal interaction—becomes zero.
Furthermore, the research examines the spatial distribution of field energy, contrasting the rapid decay of energy from electric point charges with the contained, uniform energy found within magnetic solenoids. Finally, this sheet addresses the calculation of total energy in the universe. It concludes that despite an expanding boundary, total energy remains finite because the strength of electromagnetic fields decays at a faster rate than the surface area of the volume grows, ensuring zero energy leakage at the infinite edge of space.
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