Commons

z / Panel 1 shows the electromagneticspectrum. Panel2 shows how an electromagneticwave is put together. Imagine thatthis is a radio wave, with a wavelengthof a few meters. If youwere standing inside the waveas it passed through you, youcould theoretically hold a compassin your hand, and it wouldwiggle back and forth as the magneticfield pattern (white arrows)washed over you. (The vibrationwould actually be much torapid to detect this way.) Similarly,you’d experience an electricfield alternating between upand down. Panel 3 showshow this relates to the principle ofinduction. The changing electricfield (black arrows) should createa curly magnetic field (white). Is itreally curly? Yes, because if weinserted a paddlewheel that respondedto electric fields, the fieldwould make the paddlewheel spincounterclockwise as seen fromabove. Similarly, the changingmagnetic field (white) makes anelectric field (black) that curls inthe clockwise direction as seenfrom the front.ProblemsKey√∫⋆A computerized answer check is available online.A problem that requires calculus.A difficult problem.1 Albert Einstein wrote, “What really interests me is whetherGod had any choice in the creation of the world.” What he meant bythis is that if you randomly try to imagine a set of rules — the laws ofphysics — by which the universe works, you’ll almost certainly comeup with rules that don’t make sense. For instance, we’ve seen thatif you tried to omit magnetism from the laws of physics, electricalinteractions wouldn’t make sense as seen by observers in differentframes of reference; magnetism is required by relativity.The magnetic interaction rules in figure m are consistent with thetime-reversal symmetry of the laws of physics. In other words, therules still work correctly if you reverse the particles’ directions ofmotion. Now you get to play God (and fail). Suppose you’re goingto make an alternative version of the laws of physics by reversingProblems 129