The convention of which sign of charge is positive
and which is negative is purely arbitrary. In fact,
it was Benjamin Franklin who proposed in the mid 1700's
that charge is conserved -- that total charge remains the
same even though positive charges can be separated from
negative ones. He proposed that electric charge was
some kind of fluid, and that objects that gained fluid
have positive charge and object that lost it gained a
negative charge. He based his convention on which
signs of charges were deposited by either glass or amber
on an object that was rubbed on them. We've lived with
his convention ever since.
Other kinds of charge exist! The electromagnetic force is just one
of several that particles interact with in nature. The weak nuclear
force introduces other kinds of charge (often called "hypercharge" or
just weak charge) which are actually related in a very wonderful way to
the electrical charges; the weak nuclear force and the electromagnetic
force are described together in a beautiful model which describes how
at very high energies they are one and the same kind of interaction.
The strong nuclear force (for which the 2004 Physics Nobel Prize
was awarded to Gross, Politzer and Wilczek just a couple of days before
I am writing this), involves additional kinds of charge, which interact
with the carriers of the strong nuclear force, called gluons. These are
a lot like photons (which interact with anything with electrical
charge), except that the gluons themselves carry strong-force charge
and therefore interact with each other, making a gluey, sticky mess.
We do not know why charge should exist. (I guess if it didn't,
there wouldn't be interactions, and we wouldn't exist if the elementary
building blocks of matter didn't interact with each other).
Tom
p.s. Some of those other kinds of charge cannot be expressed as
simple positive or negative numbers at all, but require more
complicated mathematical representation. I think we have an old answer
on that topic. / Mike W
(published on 10/22/2007)