Force That ClicksEpisode 2 / Peeling back the true nature of force, one layer at a time

Episode 1: force was the name of a relationship → Episode 2: peel back the everyday "push" and electromagnetism comes out

The True Nature of "Pushing"
Is All Electromagnetism Push a desk, and there's resistance. Something is pushing back. But ── your hand isn't even touching the desk.
"Contact," the most familiar sensation of all, is the first thing to be peeled away.

Tools you'll need: Episode 1, a picture of the atom, reading graphs Contact force = electromagnetism between electron clouds

In Episode 1 we said, "force is not a thing a body holds, but the name of a relationship between two parties." From here on, we'll peel back the true nature of that "relationship" one layer at a time. The first quarry is the most familiar one: "pushing." Push a desk with your hand, and you're certainly pushed back. What actually produces that resistance? The answer is surprising, and it also marks the first appearance of this series' cast member ── the electromagnetic force: your palm has never once touched the surface of the desk.

01Atoms are mostly empty ── yet they can't overlap

Both your hand and the desk are made of atoms. An atom is a tiny nucleus at the center, with a cloud of electrons spread around it. Most of an atom's size is taken up by this "empty space" of the electron cloud. So the reason things are hard is not "because they're packed full inside."

As you bring your hand toward the desk, the electron clouds of the atoms on your hand's surface and those on the desk's surface gradually try to overlap. Here, the electrons repel each other fiercely. Negatively charged electron clouds are approaching, so they repel electromagnetically ── and on top of that, the rules of quantum mechanics (no two electrons can occupy the same state) strongly refuse the overlap too. This repulsion is the true nature of the "resistance" you feel.

The core this time ── nobody is touching anything

The atoms of your hand and the desk stop a nanometer short, held apart by electron-cloud repulsion. The nuclei, of course, don't "touch," and neither do the electron clouds.
The reality behind the sensation of "I touched it" is the electromagnetic repulsion between electron clouds. Contact is an illusion; you are always, ever so slightly, floating.

02The closer you get, the more suddenly it pushes back

This repulsion has a distinct feature. From far away it barely does anything, yet once you get within a certain distance it grows abruptly strong. Plot the "potential energy" between two atoms as a function of distance, and there's a valley (a stable spacing); get closer than that, and it rises like a wall. Force is the steepness of the slope (the gradient) of this potential energy ── \(F=-\dfrac{dV}{dr}\).

Figure: The potential energy V(r) between two atoms. Get closer than the valley and it rises like a wall, producing strong repulsion (= the resistance that pushes back). Force is the slope of the incline

The closer you push, the steeper the slope, and the more the pushing-back force surges ── this is the sensation of "hardness." Conversely, pull it a little past the valley, and now they weakly attract (this attraction is the seed of next episode's "sticking force" ── tension and adhesion). A single valley in the potential energy generates both the pushing force and the pulling force.

Of the four forces, why only electromagnetism? Of the four forces listed in Episode 1, the only one that matters for the everyday "push" is electromagnetism. Gravity is weaker by orders of magnitude (you don't feel the gravity between your hand and the desk), and the strong and weak forces act only over ranges smaller than an atomic nucleus. So the one force that handles all of "touching, pushing, supporting" at the human scale is the single electromagnetic force. The reason you don't fall through your chair, too, is that the floor's electron clouds push your electron clouds back electromagnetically.
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03What the peeling revealed ── "contact" is a paraphrase of a relationship

The backbone of Episode 1 kicks in right away. The force of "pushing" is not a thing your hand possesses on its own toward the desk, but a electromagnetic relationship between two electron clouds. The word "touch" is merely an everyday-language paraphrase of that relationship. Peel it back, and the naive picture of contact vanishes, leaving only interaction mediated by the electromagnetic field.

The first step of the replacement

"The hand pushes the desk" → the reality is "the electron cloud on the hand's surface and the electron cloud on the desk's surface repel each other electromagnetically."
From force = a thing, to force = a relationship mediated by a field. In Episode 6 we'll dig into this "mediation by a field" more deeply (force = an exchange of particles).

An honest line ── it isn't just "same charge, so they repel"

"Electrons are both negative, so they repel" is an entry-level explanation, and strictly speaking it falls a little short. An atom is electrically neutral overall, so simple electrostatic repulsion alone doesn't easily produce a strong repulsive force. The lead role in the strong repulsion at close range is quantum mechanics' Pauli exclusion principle (electrons can't pile into the same state, and forcing them closer makes the energy shoot up), and that operates within the framework of electromagnetism. So more precisely, "electromagnetism + quantum rules." That said, this episode's conclusion ── that among the four forces this is electromagnetism's domain ── does not change.

The potential-energy curve in the figure (valley + repulsive wall) is a schematic tracing the typical shape of an intermolecular potential; it is not measured data for any specific substance.

Practice problems
  1. A "hard object" is hard, but not because it's packed full inside. So why?
    See the answer
    Atoms are mostly empty, but the electron clouds on their surfaces repel each other strongly and electromagnetically (+ the Pauli exclusion principle), so they can't overlap any further. Hardness = the strength of the repulsion, not being packed full.
  2. Write the relationship between force and potential energy V(r) as an equation. What happens to the force at the bottom of the valley in the figure?
    See the answer
    \(F=-dV/dr\) (force is the negative of the slope of the potential energy). The bottom of the valley has zero slope, so the force is also zero = the stable spacing. Closer than that gives repulsion, further away gives attraction.
  3. In one line, why do only electromagnetism, of the four forces, matter for the everyday "push and support"?
    See the answer
    Gravity is too weak, and the strong and weak forces reach only over the ultra-short range of an atomic nucleus. The only force that can handle touch at the human scale is electromagnetism.

SummaryPushed back, even though nothing touches

Both hand and desk are made of atoms, and an atom is empty space with an electron cloud spread through it. Bring them close and the electron clouds repel strongly and electromagnetically (+ the Pauli exclusion principle), stopping a nanometer short. The true nature of the "resistance" you feel is this repulsion ── nobody is touching anything. Force is the slope of the potential energy, \(F=-dV/dr\), and closer than the valley it repels like a wall.

Just as Episode 1's backbone predicted, "pushing" was not a thing the hand holds on its own, but a electromagnetic relationship between two electron clouds. Of the four forces, the one that handles all everyday contact and support is the single electromagnetic force. Next time we'll see that friction, tension, and normal force too ── the differently named everyday forces ── are in fact all this same electromagnetism in different makeup.

This document is Episode 2 of the "Force That Clicks" series, a reading for physics-loving high-schoolers and undergraduates. That the impenetrability of solids, contact forces, and the normal force derive from the electromagnetic interaction, and that the Pauli exclusion principle (electron degeneracy) is essential to the strong repulsion at close range, is established physics. An atom is mostly space occupied by the electron cloud, and macroscopic "contact" refers to a state in which electron clouds repel and cannot approach closer than a few nanometers. The relationship between force and potential is \(F=-dV/dr\). The intermolecular potential in the figure (attractive valley + short-range repulsive wall) is a conceptual diagram modeled on the Lennard-Jones form, not a measurement of any specific substance. Of the four fundamental interactions, everyday-scale contact, friction, and support all reduce to the electromagnetic force. ── To print, use your browser's "Print" and "Save as PDF" (in the print version the slider and answers are static and hidden).

Print / PDF: ⌘+P (Ctrl+P on Windows). On screen, the slider lets you see the repulsion rise abruptly as you bring the atoms close. Click "See the answer" to open a solution.