September 16 2026

Oops, I forgot to mention in my summary about energy.

To find potential energy, we can consider putting particles that are infinitely away together one by one, and calculating the negative of the total work done by the electric force on the particles.

This ends up, in general, creating a pretty nice expression:

::: note Potential Energy The total potential energy in an arrangement of charges is:

$$\frac{1}{2}\frac{1}{4 \pi \epsilon_0} \sum^N_{j=1} \sum_{k \neq j} \frac{q_jq_k}{r_jk}$$

Where we have the factor of one half to stop overcounting. :::