Problem 8.1 - Charge and Energy, Poynting’s Theorem: Introduction to Electrodynamics

The entire chapter has to deal with how charges and currents are conserved and thus energy, momentum, etc. is conserved. This is different than what we may have seen before, since this is thought of in densities, since the fields can occupy different spaces, etc. So, densities allow us freedoms to talk in general and we can integrate to find the local values, a more powerful statement.

"Poynting’s theorem says, then, that the work done on the charges by the electromagnetic force is equal to the decrease in energy remaining in the fields, less the energy that flowed out through the surface."

So, then Poynting’s Vector is the energy per unit time, per unit area, transported by the fields. Also known as the energy flux density.

☞ 📚📖📓= Griffiths, David J. “Chapter 8 Conservation Laws.” 𝘐𝘯𝘵𝘳𝘰𝘥𝘶𝘤𝘵𝘪𝘰𝘯 𝘵𝘰 𝘌𝘭𝘦𝘤𝘵𝘳𝘰𝘥𝘺𝘯𝘢𝘮𝘪𝘤𝘴, Pearson, Boston, MA, 2014, pp. 356–381.
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