Does electric force follow distance the way gravity does?

That time, that place

In the late eighteenth century electricity was a spectacle — rub glass, draw sparks, jolt a row of volunteers.

But nobody could say in numbers how strong the force was. It was too weak to weigh.

Why this question

Coulomb was a military engineer who built bridges. His method was to twist a thread.

Hang a rod from a fine fibre and, as it turns, the fibre resists with a force you can read off the angle. The force is tiny and precisely measurable. He turned a thread into a balance.

It is the same principle Cavendish used to weigh the Earth.

What was found

The result: double the distance and the force between two charges drops to a quarter; triple it and it drops to a ninth. Inverse square.

Exactly the form of Newton's gravitation. Two entirely different phenomena obeying the same shape of law.

From here electricity stopped being a spectacle and became something you could compute. The moment you can measure a thing, it becomes a subject.