Theme
Fields, not forces
Replacing action at a distance with something that fills space, and what that buys.
Electromagnetism
Field lines are a choice, not a discovery
Nothing in space is arranged in lines. The lines are a drawing convention — and an unusually good one, because three separate facts about the field survive the translation.
ElectromagnetismThe field before the lines were drawn on it
A field is a vector attached to every point of space. Drawing it as arrows on a grid is honest and ugly; drawing it as lines is beautiful and throws information away.
ElectromagnetismCounting what comes out, and never looking inside
Draw any closed surface. The field crossing it depends only on the charge enclosed — not on where that charge sits, not on its shape, not on anything outside.