Where does the electric field come from in a closed circuit?

Question

What I understand thus far:

• Electric potential (voltage) is the potential energy a charge possesses due to its location in the electrical field
• An electric and magnetic field is created when a current runs through a wire.
• Electrons are not what carries the energy in a circuit, it is the photons in the electromagnetic field that carry the energy.

My question is where the electric field comes from and why it behaves the way it does. From my understanding, the electric field is formed due to a difference in electric potential between two points. But, however this can't hold true because otherwise there would be an electric field between the positive and negative terminals of a battery that would short it. What do that actual electrons have to do with how the field behaves and the direction it points. As known, the electrons simply have a drift velocity due to the field pointing away from the negative terminal. So they can't be the ones carrying the energy.

Answer 1

But, however this can't hold true because otherwise there would be an electric field between the positive and negative terminals of a battery that would short it.

No, there is an electric field that points from the positive terminal of the battery to the negative terminal inside the body of the battery. The chemical makeup of the battery is such that this field is not enough to make (net) charge move from positive to negative inside the battery (a battery is not an ideal conductor!). The charge instead has to seek a path through the load. Conversely, a "freshly-mixed" battery with no charge separation and no macroscopic electric field will spontaneously develop one as the chemical reaction separates charges and deposits them on the terminals. As the electric field across the battery grows, the chemical reaction moves less net charge (the backwards reaction becomes more preferred), and the battery voltage is the voltage at which the reaction is at equilibrium.

The chemistry of the battery moves electrons from one terminal to the other. The charges on the terminals (excess protons on one side, excess electrons on the other) generate electric fields. The movement of that charge creates magnetic fields. Both contribute to an energy density in the electromagnetic field. Power moves in the electromagnetic field whenever the electric and magnetic fields are not parallel.

Answer 2

When the circuit is open, the electrons in the wire occupy the lowest energy available states in the band structure. Each state also corresponds to a momentum, and there is a random distribution of them. There is no net momentum.

When the circuit is closed, the electrochemical reaction inside the battery requires a flow of electrons from the negative to the positive pole to continue. The reaction is the source of the electric field. Due to this E-field, some electrons in the wire jump to higher energy states, and there is now a net momentum.

The net flow of electrons result in a magnetic field around the wire.

Electrons are not what carries the energy in a circuit, it is the photons in the electromagnetic field that carry the energy.

The electric field from the battery results in some electrons jumping to higher energy states. The scattering of them with the nuclei and lattice defects change their momentum and energy back to lower energy states, releasing photons (Joule effect). The emission of photons are thermal energy associated with a electrical resistance, but the energy is not transfered from a point to another of the circuit by photons.