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It sounds like what you're asking for is a Feynman diagram to represent electromagnetic interactions. You can get that with a discussion on Wikipedia: https://en.wikipedia.org/wiki/Quantum_electrodynamics.
Meanwhile, I'll take the opportunity to somewhat modify Tom's presentation. We routinely say things like 'virtual photons .. are constantly being emitted and re-absorbed by the electron' but that isn't really what we mean. Two particles that are interacting electromagnetically are indeed surrounded by a virtual photon cloud. However, in familiar cases (e.g. a hydrogen atom) that cloud is completely unchanging in time. Nothing at all is going on. The words about things fluctuating around are a rough way to convey one of the peculiar properties of quantum fields. The electric and magnetic fields have not only average values but also ranges of possible values around the average. That's what's so different from classical fields. (It's just like the positions of quantum particles, which have ranges around the average position, unlike classical particles.) You can convey an image of that range by pretending that the fields are jumping around between the different possible values, just like you can pretend that a particle is jumping around among the different positions in its cloud. However, the fields (including their spread of values) no more need to be jumping around than do the particles in space. In a nice stable atomic state, for example, nothing changes in time. The static range of possibilities turns into an actual range of outcomes only when the system interacts in particular ways with the bigger world outside.
Mike W.
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