How energy is transferred between charges?

Question

When we move an electron(e1) towards another electron(e2, not fixed), the work we do is stored as potential energy in e1 but from where does e2 get energy to be repelled?  What is source of potential energy in e2?

anna v · Accepted Answer

Let us clear up that there exist two theoretical models that fit the data and observations we have and are also predictive of new data. The classical electrodynamics, represented by Maxwell's equations and is used for dimensions larger that the microscopic ones , and quantum electrodynamics, which is the quantum theory for elementary particles and atoms and molecules, and electrons are elementary particles.
At present physics theories assume that the underlying level of nature has to be described by quantum mechanical equations, from which level classical theories emerge.  The classical  models are mathematically consistent with the quantum mechanical models in the overlap region of variables.
So if you are really asking about electrons and not point charges of the classical physics, the electrons interact and are modeled with QED , a perturbative expansion of the crossection of electron electron scattering /interaction, it is modeled with Feynman diagrams. The first order ones are

So an electron interacts with an electron with an exchange of a virtual photon, and that is what generates the repulsion , not action at a distance. Important to note that all quantum calculation predictions for interactions are probabilistic, the probability of the interaction happening is determined by the calculations, and the calculations fit the data very well.
For everyday macroscopic usage classical electrodynamics is adequate to describe the behavior of charges as described in the other answer.

jonas · Answer

Since e1 and e2 are continously interacting with each other through the electrostatic force, there is no sense in speaking about the potential energy of only e1 or only e2. One can only speak about the potential energy of the system of e1 and e2. You can think about this by looking at the equation for the electrostatic potential $$E_text{pot} = -frac{1}{4piepsilon_0}frac{e_1 e_2}{|vec{r}_1-vec{r}_2|}$$ and you see that it depends on quantities of both particles that interact with each other.
Therefore, the work that we do by moving e1 is stored in the system of e1 and e2 as a mixture of potential energy between the charges and kinetic energy of e2(the kinetic energy of e1 is fixed since we move it). Usually, one talks about the easy case when e2 is fixed and only potential energy plays a role. However, the calculation in our case is still possible, but may need another approach than just energy conservation. It turns out that this is just another form of the Kepler problem that we know from astronomy.

How energy is transferred between charges?

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