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The proton is composed of three elementary particles called quarks.

These quarks are influenced by the electromagnetic force and therefore have a charge.

The quark makeup of one proton is 'uud', or 2 up quarks and one down quark.

The charge of a proton is +1 e (as opposed to that of an electron; -1 e)

The charge of an up quark is +2⁄3 e and that of a down quark is -1/3 e.

Therefore you get +2⁄3 e + +2⁄3 e + -1/3 e which amounts to +1 e.

The reason a neutron is neutral is for the same reason.

It's composition is 'udd', or one up quark and two down.

I won't actually write it out again, but when the charge of one up quark and two down is added the charge is 0 e

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