# Why does the Electric Field of a charge apply force to positive and negative charges in opposite directions?

I understand 'why' questions are often sometimes hard to answer in science. I am just curious if there has been any discovery or explanation (maybe in quantum mechanics?) as to why say the electric field of a positive charge applies a force to another positive charge "x" distance away outwards (repulsion), but if a negative charge was the same "x" distance away the force applied to it would be equal in magnitude, but opposite in direction (i.e. pull, attraction). I understand how we model this with electric field lines directions being relative to positive test charge in all that...just wondering if there is any explanation into 'like charges repelling and opposites attracting". Cheers!

• @HolgerFiedler Thanks fpr sharing that link to that post! Would you be able to clarify more so how “virtual photons” work and how they are the “repulsive & attractive” forces of the electric field??
– Jake
Oct 19, 2022 at 17:05

The most fundamental explanation I know has to be derived directly from the standard model, where you can look for the non-relativistic (small velocities/energy) limit of the process where an electron and a proton interact through the exchange of a photon. We can picture this with a feynman diagram :

In the non-relativistic limit, we can compute scattering amplitudes (probabilities of the interaction happening for given values of the final momentum) and there is a quantum theory called scattering theory, which deduces a relation (called the Born rule) between the scattering amplitude and the potential energy which would lead to such a scattering amplitude.

Doing the calculations, we find that the potential related to this process in the non-relativistic limit is precisely the Coulomb potential, which is attractive when charges are opposite and repulsive when charges are of the same sign.

Note that this computation can be done with any charged particle, I just chose the proton for concreteness, but if you took two electrons we would also get the corresponding Coulomb potential.

If you want to see more details you can look in the Peskin&Schroeder QFT book, Chapter 4.8

Virtual photons are not the best model to explain in detail why like charges repel and unlike charges attract, emitting energy in the process.

To obtain a model of these forces, the electric field requires more detailed modelling. This could look like this, for example:

• The field is quantised and the quanta are dipoles.
• The orientation of the quanta is along field lines and decreases cluster-like from the source to the individual quantum dipole.
• The ends of quantum dipoles with the same name are inherent. Where the field lines of one charge are located, there cannot be any quantum dipoles of a second charge with the same name. The field lines are elastic and give way to each other when the charges are forced to approach each other. They are resilient and restore the distance when the external force is removed.
• The ends of unlike charges react with each other, their quantum dipoles or clusters unite along the field lines and are emitted as real photons.
• Because of the different structure of the electrons and protons, this process of approach and photon emission stops at the known orbital distances in the atom.

This is, very briefly, a possible concept for the quantisation of electric fields that does without virtual photons and describes the real observed photon emission when the electron approaches the atomic nucleus.

Physics is an experimental science. Experiments and observations are fundamental. Experimentally, opposite charges attract, same charges repel. Any theory of electromagnetic interaction must respect this, or we will reject it. But what this means is that appealing to theory for an explanation demands circular reasoning.

You may reasonably ask "How is the theory constructed to capture the attractive/repulsive nature of the interaction seen in experiments?"