Re: Why/how is electric charge quantized?

Excellent question! Easy answer first: electrons are fermions, which means
that they always have spin of + or - 1/2. Nothing else, ever! This spin is
a physical property that isn't like a spinning top; it's more of a label.
But the spin does matter as it determines how many electrons can fit into a
given energy state. In the case of electrons, it is two: one spin up and
one spin down. If the electron had spin 0, or 1, or some other integer,
than it would be a boson and you could put as many as you'd like into the
same energy state. Look for information on the Pauli Exclusion Principle if
you want to learn more.

As for the quantization of charge, this was demonstrated beautifully in the
Millikan oil drop experiments. We certainly know for an experimental fact
that charge is quantized (and for quarks the quantization is 1/3 or 2/3 of
the electron charge, depending on what sort of quark one has). But why?
First, why not? We have smallest pieces of light, such as photons, and of
matter, such as electrons, quarks, neutrinos, etc (ignoring string theory).
So why shouldn't charge have a smallest amount, too? Imagine if different
electrons had different charges-- which would be the case if charge wasn't
quantized. Then not all electrons would be the same, in fact, all electrons
would be different. That would make the distinguishable particles, which
would give quantum mechanics fits! So there's one reason: to make quantum
mechanics work. Yes, that's a bit circular. So... The next argument
involves magnetic monopoles. If there was a particle with a north or south
magnetic charge (instead of both), then the math absolutely requires a
magnetic monopole. But we've never seen one, and not for lack of looking.
So... not the best argument. The best argument comes from the gauge
theories of how the forces interact, and they require quantized charge. But
that's a bit beyond this particular answer!

Hope this helps...