For students, as for all of us, the first step into physics is via classical mechanics. Motion and force, as observed in familiar phenomena and everyday examples. A ball in play, a waka pulled through the water by its paddlers, the construction of Stonehenge: to a physics teacher, these are all classical mechanics problems.
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Conversely, electricity and magnetism first needed to be discovered before they could be explored in the classroom. Lightning, static electricity, and lodestones (naturally magnetic rocks) were all known to the ancients. But it took us centuries to realise that these individually intriguing phenomena are islands connected by the submarine geography of electromagnetism.
It’s a story that takes us through Ben Franklin’s kite, twitching frogs’ legs (a real-life mad-scientist movie), and the breakthrough achievements of of Michael Faraday (1791-1867).
Apprenticed as a bookbinder from the age of 14, Faraday followed his nose towards science, securing a job as a lab technician with chemist Humphry Davy in 1813 and eventually becoming a renowned scientist in his own right.
In the 1820s and 30s, Faraday explored induction. He showed how loops of wire moving near magnets generate electrical currents, and how electrical currents can run motors to do mechanical work. These twin discoveries make possible a great deal of what powers our modern world.1
It was also Faraday who described electricity and magnetism as fields that exist independently of magnets, currents and specific charges. This concept was fleshed out mathematically by James Clerk Maxwell in the 1860s. The results, known as Maxwell’s equations, constituted a sharp jump in mathematical sophistication for physics as a whole. The same big step is faced today by students as they come to grips with the subject of vector calculus.
One irony here is that Faraday was the last of the great pure experimentalists. He was a genius in the lab, but his own mathematics would not get him through a modern high school, much less university. Maxwell’s equations would have been far beyond Faraday’s ken, even though he’d laid the foundations for them.
For physics students, electromagnetism can be seen as a Hero’s Journey. We begin with a few simple facts about electricity and magnets and, after six weeks or so, we reach Maxwell’s eponymous equations and the complex mathematical language needed to write them.
The Hero[ine]’s Journey is as old as humanity; a young person sets out on an adventure, steadily masters their own talent and crucial new skills, encountering mentors and confronting adversity and adversaries along the way, to eventually emerge triumphant. Whether it is Star Wars, Moana, Frozen, The Hobbit, or the School of Rock, the template fits the tale.
The version that strikes a chord for me is The Karate Kid, in which young Daniel DeRusso, beleaguered by bullies, is taken under the wing of Mr Miyagi. Daniel’s lessons begin with cleaning a car: wax on, wax off. It is only when he is on the point of quitting this tedious drill that the story pivots, and his sensei reveals that Daniel has in fact been mastering the basic movements of a karate-ka as these same motions are key to parrying an opponent’s blows.
A novice martial artist focuses on pacing out each step in a kata, without being immediately able to summon the fluidity needed for its full performance. Likewise, a physics student getting to grips with a classic equation may follow each line of algebra without necessarily seeing the full story they tell.
That comprehension comes with practice, and when it does, it’s a beautiful thing. Right now, I am walking this path with a fresh cohort of young people. Unlike Mr Miyagi, though, I make clear to them from the outset the road we will follow.
There is a twist at the end of the Hero’s Journey of electromagnetism. If you add one last pinch of maths to Maxwell’s equations, you learn that the electric field and the magnetic field work in unison to move light throughout the universe.
With just a few strokes of chalk, we see that lightning and rainbows are drawn from the same well of knowledge. What’s delightful, from the teacher's perspective, is that this last step is much simpler than the arduous journey it takes to get there, so the proverbial pot of gold turns out to be guarded by a surprisingly amiable dragon.
It is the deepest magic. And it is quite something to be there each time it is written afresh by a new class of apprentices.
- The insight known as induction is at the heart of any electrical generator, whether it is spun by water falling over a dam, a windmill, or steam generated by burning coal or nuclear reactions, and it produces almost all of the world’s electricity. The one exception is photovoltaic power, aka solar panels. ↩︎
CODA: Attentive readers will note that this is my second post in a row on this semester’s teaching, and that the previous post related to a whole other course. It’s a busy old half-semester in the physics mines.
Excellent work – your students are extremely fortunate having somebody to present this material in a context-rich and enjoyable way. They will recall the wider context long after (some of them at least) have forgotten the details of Maxwell’s eqs and in many ways the “how science works” lesson is the most important to impart.