What causes the potential energy in non-submerged electrons?

[jaydnul]

How about this. A battery has a net positive end and a net negative end. When you connect a wire in between them, The electrons in the wire are attracted to the positive end and repelled from the negative end. But as they leave the wire and onto the positive battery terminal, they leave behind the positive protons in the copper. This attracts more electrons from the negative battery terminal. This continues until the battery runs out of energy, which comes from the chemical reaction that does work to separate the charge.

Is that a correct explanation?

 

[Dale]

Now I'm asking what causes the electrons who aren't submerged in the magnetic field to have a higher potential energy. We've already established that electron on electron interactions don't, as well as excess charge on the surface. So what causes this higher potential in the non-submerged electrons? You said it here:

OK, since you are interested in fields and charges (outside of the context of a circuits class) and since you emphasized the word "causes", my answer would be Jefimenko's equations:

https://en.wikipedia.org/wiki/Jefimenko's_equations

Pay particular attention to the section about the retarded potentials.

The reason that I would go to Jefimenko's equations is that for A to cause B then A must happen before B. So a causal relationship is expressed by something of the form $B(t) = f(A(t'))$ where $t'<t$. Maxwell's equations are not of this form, so they cannot express a causal relationship. Jefimenko's equations are.