Charge at the Microscopic Level

We have been talking about positive and negative charges moving around without actually saying what they are. This was intentional, because for the purposes of this book the identity of these charges is, for the most part, irrelevant. However, we can't get away without saying something about it.

Everyday objects are made up of atoms, and atoms are made up of three types of particles: positive protons, neutral neutrons, and negative electrons. The protons and neutrons reside in the atomic nucleus at the center of the atom, while electrons exist in a "cloud" around the nucleus. A common picture of the atom has electrons spinning around the nucleus like planets around a sun, and while quantum mechanics says that this is nonsense, it's a convenient picture for our purposes. It is relatively easy to add or remove electrons to an atom, causing it to become a negative or positive ion. Adding or removing a proton, on the other hand, is much more dramatic: for example, adding a proton to the nucleus of hydrogen actually turns it into helium, in a process called nuclear fusion. If you figure out how to do that easily, you will discover a great source of energy and probably receive a Nobel Prize. (Good luck!)

While protons and electrons are by far the most important charged particles, they aren't the only ones. In the past century physicists have discovered dozens of subatomic particles, many of which have electric charge: muons, pions, kaons, positrons and antiprotons, and so forth. Electric charge, like mass, seems to be an inherent property of particles: all electrons have the same charge regardless of how they were made.

In the SI system of units, charge is measured in coulombs, but in the subatomic realm charge is usually measured in units of the proton charge, which is called e (where e = 1.6 x 10-19 C). The electron has charge –e, equal in magnitude but opposite in sign to the proton, which is why an atom with equal numbers of protons and electrons is neutral. The fact that the two particles cancel one another so completely is rather a surprise, because otherwise they have very little in common. The proton is almost 2000 times more massive than the electron, for one thing. Also, the electron is so small that we are unable to measure its radius (if it even has one, and isn't a point particle), while a proton not only has a size but an internal structure, being made up of three component pieces called quarks. It is fortunate that they have exactly opposite charges, however: if the electron had a charge of -1.01e instead, then most atoms would not be neutral, and chemistry would be a lot different.

A stranger coincidence emerges when we look at all subatomic particles, and discover that every particle has a charge which is an integer multiple of e. You can find particles with charge e, –e, 2e, 5e, –3e, but never with charge e/2 or 0.2e or 1.01e. This property is called charge quantization, and while there are theories which might explain it, it isn't really understood.

Quark composition of a proton, a neutron, and a positive pion

The one known exception to this rule are the quarks mentioned above. Quarks have charges which are one-third or two-thirds that of the proton. However, no one has ever seen a free quark: quarks are always found bound together in combinations which have a net charge which is an integer multiple of e. For example, a proton is made up of two up quarks (+⅔ e each) and one down quark (–⅓ e) for a total charge of e. Quarks are held together by gluons which pull harder the more you stretch them, as if they really don't want to violate charge quantization.


Like several other properties in physics, electric charge is conserved. This means that the total charge of a system cannot change without adding charge to it or taking charge away: charge does not spontaneously appear or disappear. This is rather trivial in macroscopic systems, where the total charge of a system depends on the number of protons and electrons: the only way you can change its charge is to add or remove electrons or protons. But charge conservation holds true even in cases where particles themselves can be spontaneously created or destroyed. For example, a neutron (with no charge) cannot spontaneously turn into a proton (q=+e), because some positive charge would come out of nowhere. However, a neutron can suddenly decay into a proton (q = +e), an electron (q = -e), and an antineutrino (q = 0), because the total charge of that combination is the same as the total charge of the neutron.