People already knew that a changing magnetic field makes the electric field curl around. But in 1861, Maxwell proposed that also a changing electric field makes the magnetic field curl around. This means that electric and magnetic fields can form waves, with each one changing the other. Maxwell computed the speed of these waves and got an answer close to the speed of light! The rest is history...
... in a way. Maxwell reached his conclusions using a strange mechanical model involving "molecular vortices". In this model magnetic fields are spinning vortices - the black hexagons here - while electric fields are the displacement of little particles between these vortices - the green circles.
It took him a few years to drop this model and simply write equations governing fields. And it took longer for Heaviside and others to take Maxwell's 20 equations, throw some out, and boil the rest down to 4 vector equations - the ones we now learn in school.
I want to understand Maxwell's molecular vortices because they're the key to how he guessed that a changing electric field makes the magnetic field curl. People already knew a lot about the electric and magnetic fields from experiments. But Maxwell's extra effect completed our theory of electromagnetism!
There are modern ways to see that this extra effect is necessary. Few people go back and try to understand Maxwell's original thinking. Here's one great exception:
