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I learned to keep track of the conversion from SI to Gaussian units for electromagnetism as \begin{align} \frac{e^2}{[4\pi\epsilon_0]} &= \alpha \hbar c \end{align} where the factor in [brackets] is unity in CGS units and isn't in SI. This is a nice way to remember things because it makes clear that Coulomb's law for two fundamental charges, $$ \vec F = ...


You've been done a disservice if your earlier teachers didn't even mention the existence of Gaussian units (a cm-gram-sec system with "unrationalized" E&M). Not that I like them, but simply because they were very common in the mid twentieth century and they still have their adherents (some even on Physics SE). The unit of charge goes by several names ...

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