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The most important thing before answering your question is to understand what is electricity and how do we generate it.
The flow of charged particles due to a potential difference is electricity. The work done by these charged particles during their flow from high potential to low potential is what we get in the form of heat, light etc. The reason behind this flow of charged particles is the potential difference and that’s how we generate electricity. We develop potential difference using electromagnetic circuits that obey Newton’s third law of conservation of energy (to know more, study Lenz’s law and electromagnetic circuits).
Now, the charged particle that I mentioned could be a positively charged particle or a negatively charged particle as well.
Let’s answer your question now. I hope you know the structure of atom - nucleus (containing neutrons and positively charged protons) and orbiting electrons. The electrons (especially the one in the outermost orbit) can be knocked out of their orbit by fulfilling their energy requirement called as energy band gap. Materials which are good conductors of electricity have sufficiently low band gap and are easily fulfilled. These electrons then become free electrons that can flow due to the potential difference.
In case of proton, it is tightly bound in the nucleus. The reason behind this is mesons (a sub-atomic particle). Thus protons can’t come out of nucleus and become the free charged particle.
Besides, imagine if it could come out of nucleus. Electricity conduction would have been so much slower than it is now. That’s because protons are very heavy as compared to electrons.
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