Is there a reason that a proton has a positive charge while an electron has a negative charge? Are these just names that were given to the charges or was there a reason for making a proton have a positive charge?
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Positive and negative are just conventions. What is not a convention however is that electrons and protons have charges of opposite sign so that $q_{\text{electron}} q_{\text{proton}}<0$. – Omar Nagib Oct 06 '15 at 13:25
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As a word of warning: while everybody agrees that the charge of the electron is negative, there is no agreement over whether the electron has charge $e$ (with $e<0$) or charge $-e$ with $e>0$. – Jonas Greitemann Oct 06 '15 at 13:28
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4Possible duplicate of Who (and Why) started the "electrons are negative, protons are positive" convention? – John Rennie Oct 06 '15 at 13:55
2 Answers
There is no particular reason why one should be of such a sign and the other of the other. The choice is mostly historical and the opposite choice (positive charge for the electron and negative for the proton) would work as well with just some slight sign changes in the equations. The only important part is that their charge be opposites.

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Protons are not an elementary particle, whilst electrons are. Protons are made up of Quarks, electrons aren't made up of difference constituent parts; they're just electrons. I'll leave it to you to look up the constituent parts of protons; they have individual charges within themselves.
The actual reason that one is positive and one is negative is slightly more tricky. If that's the answer that you're looking for you need to perhaps ask a more specific question.

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News to me. What would those reasons be? It's just a matter of convention, elementary or otherwise. (See what I did there) – Jonas Greitemann Oct 06 '15 at 13:25
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Electrons are also made of multiples of quarks of magnitude $\frac{2}{3}$e and $\frac{1}{3}$e . But these quarks do not exist in nature. The electron does as a whole. Re-consider your point. – SchrodingersCat Oct 06 '15 at 14:01
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1@Aniket I'm tempted to swear and blind and tell you to reconsider your own point, but I'll just politely ask you to point me to any reasonable source that says an electron (a lepton) is made up of quarks. Or alternatively, politely ask you to google what a lepton is. – Matt Oct 06 '15 at 14:36
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@Jonas I meant it in a purely historical sense. If one is asking about the history of terminology, one should be specific, in my book. – Matt Oct 06 '15 at 14:38
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2@Aniket - electrons are elementary particles - no quarks were harmed in their construction... – Jon Custer Oct 06 '15 at 14:53
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You've linked a book about electromagnetic theory. I don't understand how that's relevant. You've also created your link such that your original search is left in the search bar when one opens your link. Just a heads up. – Matt Oct 06 '15 at 15:04
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Page 29 bottom paragraph of https://books.google.co.in/books?id=1EDK4wv9KxYC&pg=PA29&lpg=PA29&dq=&hl=en#v=onepage&q&f=false..to be precise – SchrodingersCat Oct 06 '15 at 15:44