Curious if there is any relationship between size of particles and charge. If the proton was the same size as an electron, would their charges no longer cancel eachother out?
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This is a bit hard to explain on an eli5 level, but basically, charge has nothing to do with size really. Charge comes from the even smaller particles in protons and other Hadrons called quarks, which carry a fraction of an electric charge of an electron. As for shrinking down a proton’s size so that it is the size of an electron, this is kind of nonsensical and so a bit of a non starter. You cannot really squeeze down a proton to a smaller size.
Why does a proton have the same magnitude but opposite charge as an electron? A proton is made up of (at least) 3 quarks. There are always (at least) 2 up quarks and 1 down quark. The exact.same can be said of a neutron but with 2 down and 1 up.
An up quark has +2/3 q(e) (where q(e) is called the fundamental charge. An electron has exactly -1q(e)). And a down quark has -1/3q(e). So 2↑+1↓ = (2/3)+(2/3)-(1/3) = (2+2-1)/3 = +1q(e). Meanwhile for the neutron, 1↑+2↓ = (2/3)-(1/3)-(1/3) = (2-1-1)/3 = 0 charge.
Obviously, none of this answers your question. The problem is, every fact about physics is either explainable or fundamental. If something seems fundamental now, but is explained later, then whatever piece of knowledge we gained to explain it is also either fundamental or explainable. So no matter how many “why?” questions we answer in physics, we can never answer all of them. Right now, the fact that the electron has exactly 1.60217663*10^(-19) coulombs seems to be a fundamental fact of our universe. It is not explainable because we have no idea whether something out there causes it, or because it just is and that’s the way it is. For all we know, either could be true. The same can be said of the charge on quarks. For all we know, it just is.
Perhaps a 5-dimensional race of beings that can hop at will throughout the multiverse could probe their creation to understand exactly what caused these facts to be the way they are, but humans never will. Or perhaps no matter how advanced the race is, it is fundamentally unknowable. Or perhaps a new breakthrough in physics will explain it next year. Nobody knows.
We do not know about the size of an electron. We only know it is not larger than 10^−18 m The model we have is that it is a point particle so it has no size.
A proton on the other hand has a size, but it is not a fundamental particle it is made up of quarks. A proton contains 2 up quarks and 1 down quark.
A quark is a fundamental particle like the electrons with no known size and might be a point particle. An up quark has a charge of +2/3 and a down square of -1/3 and the result is a net charge of 0
They have fractional change because we defined a change as what an electron has. We could replace it and now an electron is at -3, an up quark at 2, and a down quark at -3. So do not let the fraction bother you.
That protons have a size even if the quarks have no size is not any different from how the atoms have a size that is determined by how electrons move around the core. The size is the volume where the point particles move around, for both protons and atoms.
I have to say I do not know enough about the https://en.wikipedia.org/wiki/Standard_Model to know if there is an explanation for why elections and quakes have a different amount of change but know all of them could have zero sizes.
There is the concept of conservation of charge as well as a few others. If we imagine beta decay where a neutron “turns into” a proton the charge is reduced by 1. Conveniently an electron has this exact same charge to allow the charge part of the accounting to add up. I guess any number of electrons with partial charge could do the job.
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