Using the Electric Potential to Find the Vector Electric Field

Here is the normal routine in introductory physics class.

Start off with the electric field due to point charges. You can find the total electric field at some location by first determining the vector value of the electric field due to individual charges. Then, using the superposition principle, the total electric field is just the vector sum of these fields. It’s not always trivial since the electric field is a vector.

After that, you introduce the idea of the electric potential (with respect to…

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