978 - 1 - 107 - 07820 - 8 - Electricity and Magnetism for Mathematicians : A Guided Path from Maxwell ’ s Equations

Who knows when our ancestors first became aware of electricity and magnetism? I imagine a primitive cave person, wrapped up in mastodon fur, desperately trying to stay warm in the dead of winter, suddenly seeing a spark of static electricity. Maybe at the same time in our prehistory someone felt a small piece of iron jump out of their hand toward a lodestone. Certainly lightning must have been inspiring and frightening, as it still is. But only recently (meaning in the last four hundred years) have these phenomena been at all understood. Around 1600, William Gilbert wrote his infuential De Magnete, in which he argued that the earth was just one big magnet. In the mid-1700s, Benjamin Franklin showed that lightning was indeed electricity. Also in the 1700s Coulomb’s law was discovered, which states that the force F between two stationary charges is F = q1q2 r2 ,