Magnetoconda

Magnetoconda, a magnet-serpent of the Paradox Parlour, coils through a ring of copper wire and asks the question Einstein opened his 1905 relativity paper with: is it the magnet that moves, or the wire?

The Physics

Move a magnet past a loop of wire and a current flows. Hold the magnet still and move the wire instead, at the same relative speed, and exactly the same current flows. Yet the textbook stories differ. If the magnet moves, a changing magnetic field makes an electric field that drives the charges. If the wire moves, there is no electric field in the magnet's frame, and the magnetic force on the moving charges does the job. A rod of length L moving at speed v across a field B gets the same emf either way.

ε = vBL

• ε: induced emf (volt, V)
• v: relative speed of rod and magnet, perpendicular to the field (m/s)
• B: magnetic flux density (tesla, T)
• L: length of the rod across the field (m)

Einstein began “Zur Elektrodynamik bewegter Körper” (Annalen der Physik 17, 891, 1905) with this asymmetry: the observed effect depends only on the relative motion, but the theory of the day explained the two cases in different ways. Special relativity removes the asymmetry: electric and magnetic fields are two views of one electromagnetic field, and how they split depends on the observer's frame.

Honest caveat: ε = vBL is the simple case of a straight rod moving perpendicular to a uniform field at speeds much less than light. It is not two different effects: only the description changes from frame to frame, not the current you measure.

On the sticker

Magnetoconda twists through a copper ring as a cyan-white loop of current glows in his hand. Printed text: MAGNETOCONDA with the line ε = vBL. Pixel-art kiss-cut vinyl sticker, white, in 2″, 3″, 4″ and 6″ sizes.