Electromagnetic Forces Everywhere

When your hand presses a wall, no atom of your hand ever touches an atom of the wall. Electric forces between their charges push back first. Almost every force you feel is electromagnetism in disguise.

Coulomb’s law#

On top of gravity, particles that carry electric charge exert electromagnetic forces on one another. For two charges $q_1$ and $q_2$ at rest relative to the observer, a distance $r$ apart:

Charges of the same sign repel; opposite signs attract. This is the force a rubbed plastic ruler uses to lift paper. Moving charges also feel magnetic forces, which makes the full electromagnetic force richer than Coulomb’s law; we meet that in electromagnetism.

Ordinary matter is built from electrons (charge −1.6 × 10⁻¹⁹ C each), protons (+1.6 × 10⁻¹⁹ C) and uncharged neutrons. Electromagnetic forces bind electrons to nuclei in atoms, bind atoms into molecules, and lie behind almost all of chemistry. Compared with gravity they are unimaginably strong:

Electromagnetism in everyday forces#

(a) Contact forces between surfaces

Put a book on a table. The atoms at the bottom of the book come very close to those at the top of the table, and their charged constituents push on each other strongly. The net result is a measurable force: the table pushes the book up, and (third law) the book pushes the table down.

Contact forces usually act along the common normal (perpendicular) to the touching surfaces, as a push. But they can also have a component along the surfaces. That component is friction, the subject of a later chapter. An idealised surface that can only push perpendicular to itself is called smooth or frictionless.

(b) Tension in a string or rope

In a tug-of-war the rope is pulled from both ends. It stretches a tiny, usually invisible amount and is said to be under tension. A rope holding a hanging bucket is in tension too: the atoms at its lower end pull on the atoms of the bucket’s handle, and the resultant of all those electromagnetic forces holds the bucket up. A taut string always pulls on whatever is tied to its ends.

(c) The spring force

Coil a metal wire and you have a spring. The straight-line distance between its ends is its length; with no forces on it, that length is its natural length $x_0$. Stretch it and it pulls on whatever is attached; compress it and it pushes. As long as the change in length is not too large, the size of the force is proportional to that change:

Why gravity wins at large distances#

If electric forces are so much stronger, why does gravity rule the motion of planets and falling apples? Because large objects are almost perfectly neutral. The attractions and repulsions between the charges of one body and those of another very nearly cancel. Gravitational forces never cancel: every particle attracts every other, so they all add up. A 1 kg block 100 m above the ground feels about 9.8 N of gravity from the Earth and essentially zero electric force, even though both are packed with charged particles.