As I understand it, the concept of potential energy arises from analytical mechanics. Yet I often see the concept of electric potential $\phi$ introduced without mention of analytical mechanics. For example, Electricity and Magnetism by Purcell doesn't discuss analytical mechanics. I have always found this confusing because I don't get why it's not called electric potential energy.
Why is this? Am I just reading the wrong books? Am I mistaken that electric potential is a form of potential energy and therefore related to analytical mechanics? What's going on here?
Note: I understand electric potential is the analog of gravitational potential. That fact however hasn't helped me answer the above.