But good sir, what is electricity?
A quick look at the physics of conductors, insulators, and electric charges.
A recurring theme of this Substack are my attempts to build out an accessible curriculum for hobby electronics. The target audience are folks who want real answers, but who aren’t keen on academic textbooks brimming with obtuse jargon and advanced calculus. I’m particularly fond of the following foundational articles:
Today, I’d like to take a step back and tackle a more basic question that isn’t always satisfactorily answered in high school: what is electricity and what makes certain materials “conduct” it in the first place?
The structure of the atom
Most readers should be familiar with the basic structure of the atom: a nucleus consisting of neutrons and protons, surrounded by a swarm of electrons that are stratified into a number of “shells”. In pop-science articles and videos, the concept is usually illustrated using the dated but intuitive model developed by Niels Bohr around 1918. The model envisions electrons that travel around the nucleus in circular orbits:
Today, it’s no longer believed that these electrons zoom around in circles; instead, they appear to settle into oddly-shaped orbitals that represent solutions to an underlying wave function — but don’t map to a trajectory of a discrete particle in classical mechanics.
If this sounds cryptic, it’s important to note that things only get worse. We don’t have philosophically satisfying insights into the universe at subatomic scales. We have quantum mechanics: a set of equations that are good at predicting the behavior of elementary particles, but that don’t line up with our intuition about the macroscopic world. We don’t know if the equations are a crude approximation of some deeper, yet-unseen reality; or if the fabric of the universe is just weird math. In fact, the harder we try to come up with intuitive analogies, the more off-base we get. For example, despite what most YouTube educators claim, there’s no straightforward explanation of what the captive electron actually does: it’s not orbiting the nucleus or spinning around its own axis in any conventional sense. Most simply, it just exists as a particular distribution of an electrostatic field in space.
In any case, the shape of orbitals is of relatively little significance to electronics; it matters in chemistry because it helps model chemical reactions and predict the properties of materials. For our purposes, it suffices to say that each atom or molecule has a certain number of electrons and that they are organized into a certain number of shells.
In the same vein, we don’t need to dwell on the structure of the nucleus. In brief, the nucleus is held together by a powerful but extremely short-range field known as the residual strong force. This force is thought to be a consequence of the make-up of protons and neutrons, each of which appears to be made out of three more exotic elementary particles known as quarks. Pay no mind: it’s enough to say that most nuclei on Earth were formed through nuclear fusion in stars and won’t undergo any change on the timescales of interest to electronics — or to terrestrial life.
A more pertinent observation is that the structure of the atom is also shaped by a weaker but far-reaching electrostatic force. The force acts only on certain subatomic particles; these particles are said to be charged. In this specific context, the “charge” is an intrinsic property of a given type of particles and not something they can gain or lose: a proton is always positive, an electron is always negative, and a neutron just doesn’t play along. Similar charges repel and dissimilar charges attract, so protons in the nucleus can pull in an equal number of electrons. The electrons are then captured — bound — by the electrostatic field extending from the nucleus. The result is a stable atom with no net charge.
Another important insight from quantum mechanics is that the parameters that describe the state of a bound electron appear to be quantized — that is to say, they only take specific values or change in discrete increments. Once again, we don’t have a satisfying explanation why. We know that these quantum numbers correspond to standing-wave solutions of a three-dimensional wave function that we pulled out of thin air. We also know that the model works better than any alternatives. But we don’t know what any of it really means — or if it means anything. Either way, the bottom line is that there are specific energy levels that an electron in an atom can hop across, with no option to dwell halfway between. This is why we see a progression distinct electron shells, from lowest to highest energies.
The remaining conundrum is why don’t all the electrons settle in the most energetically-favorable, innermost shell. The relevant constraint is known as the Pauli exclusion principle. The state of a bound electron is seemingly fully described by a handful of parameters, and the electrons must remain distinct — i.e., their quantum parameters can’t be all the same. This means that each shell has a limited seating capacity: once all the combinations of “lesser” quantum numbers are exhausted, the next electron needs to bump up the remaining variable: the principal quantum number that corresponds to the shell it occupies.
Insulators and static charges
In most cases, the electrons that populate innermost shells do relatively little: they have low energy, are bound tightly to the nucleus, and tend to be shielded from outside influence. The story is different for higher-energy valence electrons; for example, chemistry as we know it arises from atoms exchanging or sharing these weakly-attached particles. In a covalent bond, some electrons from both participating atoms shift to a newly-formed, energetically-favorable multi-atom orbital. In ionic bonding, one or more electrons migrate from one atom to another. In the latter case, the new molecule is held together by the resulting electrostatic field.
Even without chemical bonding, it’s not difficult to temporarily dislodge some valence electrons. The most familiar example is the triboelectric effect that’s responsible for the harmless zaps of static electricity we sometimes feel around the home. The effect isn’t fully understood, but we know that depending on the shape and orientation of molecules, different surfaces exhibit variable affinity to electrons. In part because of this, when two dissimilar materials are brought together, there can be a slight imbalance in the number of electrons that randomly migrate across the boundary. If the pieces are then pulled apart, some charge carriers end up getting stuck where they don’t belong.
It should be noted that the scale of this imbalance is minuscule: the displacement of about 1011 electrons is enough to give you a good zap. This might seem like a big number, but consider that there are roughly 81,000,000,000,000 times as many electrons in a single ounce of table salt. In other words, the magnitude of the phenomenon is comparable to taking a bucket of water out of Lake Erie.
This brings us to solid-state insulators: in such materials, valence electrons can still be pulled off or deposited onto the surface with relative ease, but the resulting charges stay in place and can’t propagate through the bulk of the substrate. This is often because there are no suitable vacancies in the shells of nearby molecules. To move around, the electrons would need to be knocked into a higher-energy state.
Conduction in metals
This situation is different in metals. The atoms form a dense, homogeneous lattice with sparsely-populated orbitals that essentially merge together, extending throughout the material and no longer exhibiting clearly-quantized energy levels that are characteristic of electrons bound to a single nucleus. In this environment, valence electrons are free to skate around the lattice at will. The electrostatic interaction with protons still confines the bulk of the mobile charge carriers to the conductor, but in most other respects, the behavior of a metallic conductor can be modeled as that of a free-flowing electron gas.
The key property of conductors is that in contrast to insulators, any static charges can quickly equalize. Consider the scenario shown below, where a single electron is plucked off by an external actor and then injected back on the other side of the wire:
The remaining electrons promptly scamper away due to electrostatic repulsion; if the process continues, we can observe a steady drift of electrons along the length of the wire. This motion of charges is the flow of electricity. The movement of electrons in a conductor, mediated through electrostatic fields that extend into the surrounding space, can be harnessed to operate electronic components and perform other useful work.
It’s important to note that while the charge equalization process is fast, the drift of individual electrons is not. The field propagates close to the speed of light in vacuum (circa 300,000 km/s); individual electrons in a copper wire typically slither at average speeds measured in centimeters per hour or less. A crude analogy is the travel of sound waves in air: if you yell at someone, they will hear you long before any single air molecule makes it from here to there.
There are other modes of conduction. In vacuum, thermionic emission can cause thermally-excited electrons to travel significant distances; in plasma and in highly polar solvents, mobile ions can move around too. None of this is particularly common in modern electronic circuits, but it’s a good topic for another article down the line.
👉 For an explanation of current, voltage, and impedance, click here. For the behavior of semiconductors, see this followup article. Finally, for a basic treatment of magnetic fields, see here.
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> This situation is different in metals. The atoms form a dense, homogeneous lattice with sparsely-populated orbitals that essentially merge together, extending throughout the material and no longer exhibiting clearly-quantized energy levels that are characteristic of electrons bound to a single nucleus.
With quantum mechanics, we can sort of solve three-body problem of the H_2^+ molecule, that is two protons and an electron. With larger amount of atoms one has to make use of approximation methods, like the perturbation theory.
For two atoms, quantum physics predicts that the valence electrons which had the same energy when atoms were separated, split into two different but close energy states when atoms are close together. One can think of those states as the state where electrons "orbits" in such way that it is present between atoms, one one state where electrons "orbits" around two atoms at once.
With the very large amount of atoms in a macroscopic solid, this results in the number of energy levels that is proportional to the number of atoms, but where gaps between those quantized levels are very small. This means that it is easier to treat this dense set of very close energy levels not as quantized energy levels, but as an energy band (hence: electronic band structure).
I'd add "conduction in everything else." In the natural world, metals are scarce, and conductivity involves salt water, also acids and alkali solutions ...which also applies to biology. There are no flowing electrons there. Electron-flows are a metals-only phenomenon (metals, also plasmas.)
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The basic list...
- Protons flow in acids
- Na+ and Cl- flow in salt water, wet dirt, etc.
- OH- ions flow in alkaline solutions
- Current in cells, bio tissues (incl nerves/brains) is flowing Na,+ Cl-, K+, Mg+, OH- protons and various large molecules.
Too complicated! That's why physics uses CC "Conventional Current," where we add all these various charge-flows together, forming just a single number. Amperes in a conductor, that's a measure of CC. Ammeters measure CC. If you want to unpack it into "charge flows," then even in metal wires, we must include proton-motions arising whenever the wire is moved. Moving metals cause electrons to move. But they produce zero current, because a moving metal includes exactly equal currents of net proton-flow and electron-flow, summing to zero. Which leads to a simple concept...
- typical electric current is a differential flow, not a simple "charge flow."
In metal wires, the protons remain still, while the mobile electrons migrate past them. With a simple circuit we can reverse this, by slowly rotating the entire circuit backwards. Move it just fast enough that the flowing electrons stop, and now the entire amperes is caused by moving copper nuclei (flowing protons.) A Hall-effect experiment will then show that the charge-carriers in the rotating copper loop are the positive ones! (Physics teachers get to do all the fun stuff. Also look up the Tolman experiment, wherein we destructively stick a plank into a whirling bicycle wheel, where an unpowered coil was wrapped around that wheel. The coil halts, but the electrons keep going!)
Try to avoid the common misconception "electrons flow through salt water," or "electrons flow through human bodies during shocks." Completely wrong. In salt water, the conductor is full of positive and negative charge, the dissolved Na+ and Cl-, and during electric current, these populations flow past each other in the same spot. (What then is the "one true direction" of the amperes? There isn't one. That's why we use Conventional Current, since it applies to salt water, ground-dirt, and human bodies. And also of course, acid-conductivity is based on proton-flows, not electron-flows.)
Joke: Ben Franklin chose right! But his choice only applies to kite-twine. In electrolytic conductors such as twine (in humid conditions,) the conductivity would normally be Na+ and Cl- flows ...but twine, like newsprint, is typically acidic. So, the currents in kite-twine are mostly flows of H+ ions, i.e. mobile protons. (It's modern science which messed it all up. Too-expensive metals once were confined to coatings on Leyden-jars, and sharp-edged foil strips would mess up your electrostatic experiments ...so conductive hookups were made with damp paper strips or string (or wealthy French experimenters used street urchins, suspended by silk ropes.)