[Coda]

Hmm... I can see where you're coming from. At first I was going to say that an electric current isn't a field at all, but then I realized that from the perspective of the circuit itself it IS sort of like the anode and cathode are generating a uniform field between them.

I couldn't find a simple answer so I manipulated it for a while to see if I could come up with something myself, and it turns out that the answer to your question is "yes."

E = ΔV/d

Electric field strength is force divided by charge:

F/q = ΔV/d
Fd/q = ΔV
Fd = ΔVq

Force times distance is energy:

E = ΔVq

This is a well-known formula for finding the energy required to move a charge against a uniform field without acceleration, or the kinetic energy of a charge after being accelerated by such a field.

Divide both sides by time:

E/t = Vq/t

Energy per unit time is power (P), measured in watts. Charge per time is current (I), measured in amperes.

P = I * V

So it turns out that uniform electrical fields are equivalent to one of the most fundamental equations in electrical engineering. This is basically the F=ma of electricity, and it gets used ALL THE TIME. Need to know how big of a fuse your circuit needs? P=IV. Need to know what kind of power adapter will charge your device? P=IV. And so on.

I worked on this for a LONG time. I did a TON of research to see if there was some exciting correlation to see if E = ΔV/d might be a meaningful description of the behavior of a length of superconducting wire connected across a battery. Unfortunately, things just weren't making any sense at all. The units weren't working at all and I was coming up with contradictions and absurdities.

Then I realized my mistake... I was treating E in that formula as energy, but it's electric field strength. That was a HUGE WASTE OF TIME. ^^() Once I fixed that, coming up with the rest of the derivation was easy.