I don’t actually know ❗
What a fantastic question!
Charged matter has an electric field because… it does!
Electric fields are fundamental properties of charged matter – but WHY THEY HAPPEN is a “spooky action-at-a-distance” phenomenon that I honestly don’t fully understand. This might be a great question to ask the Physicists in the Quantum Zone – I bet they could give you a better answer than I could!
This question is a great example of the fact that scientists tend to specialise on certain (often very small) areas, but this does not mean that they know everything about subjects outside their specialisation!
This is definitely physics beyond my understanding I’m afraid. Most of the articles I looked at explaining electric fields and charged particles made my brain hurt. Like David said, track down a physicist and make them sweat as much as you made us. You may even get an answer. Something to do with protons and electrons maybe?
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