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Charge is the fundamental property of forms of matter that exhibit electrostatic attraction or repulsion in the presence of other matter. Electric charge is a characteristic property of many subatomic particles.

Nitpicking again - the fields are a working mathematical description but, as far as I know, we don't know if or in what sense they are real things, whatever real thing even means. The electrical and magnetic fields change when you switch reference frames, so that does not sound like something that really exists independent of an observer. The vector potential on the other hand does not change but it does not seem real either because it has gauge symmetry.

We know that the A field is more fundamental (at least Feynman thought so):

http://en.wikipedia.org/wiki/Aharonov%E2%80%93Bohm_effect

Interesting. Does it explain permanent magnets too?

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