Simple Is as Simple Does

The Electricity of Imagination

A formal education doesn’t teach a level of imagination that is often needed for solutions. Trivial insights could be surprisingly rare.

Faraday delivering a Lecture at the Royal Institution in 1856.

Michael Faraday, one of the most influential scientists in history, had little formal education. His research on magnetic fields established the basic law of electromagnetism, known as Faraday’s law. He discovered that the variable magnetic flux from a magnet moving through a loop of conducting wire, induces an electric current in the wire.

Last month I gave a physics colloquium about The Galileo Project at the University of Connecticut. After my lecture, a retired MIT Professor, Walter Lewin, asked me a question about whether Faraday’s Law holds in a perfectly superconducting circuit with zero resistivity. He was bothered by this problem for several years and asked distinguished physicists at Princeton and MIT for the answer without a resolution. To me the solution appeared trivial, so shortly after reading his email I sent him the answer.

Photo by andreas s on Unsplash

Walter’s question was formulated as follows: “I have a coil exclusively made of a perfectly superconducting wire. The ends of the coil are connected also with a superconducting wire. Thus, the circuit is a superconducting closed loop. I move a magnet in and out of the coil. There is a magnetic flux which changes in time (Faraday’s Law does hold). Will there flow an electric current in the closed loop and if so, how does it change in time? There cannot be an electric field in superconducting wires, so how can there be a current?”

My answer was simple: “No current inside the superconductor, where the electric and magnetic fields vanish. Only surface currents. At any time, the surface currents are such that they produce an opposite magnetic field internally and cancel the external field inside the wire. Given that the external magnetic field varies in time, these currents vary in time so as to cancel the external field at any time. Therefore, you end up with a surface current that satisfies Faraday’s Law outside the wire, by generating an electric field that satisfies Maxwell’s equations. But there is no current in the interior of the wire.”

Electric currents flow through the bulk of ordinary metal wires which possess resistivity. The currents are driven by voltage differences, induced by a battery for example. But an ideal superconductor has no resistivity, so any voltage difference across the wire will create an infinite current that will cancel out the voltage difference instantly. Hence the puzzle.

The insight of the solution is that a superconductor can have surface currents on its skin, where the superconducting properties do not hold since that surface represents the interface of the wire with the outside world.

These surface currents are familiar from the Meissner Effect, which implies that magnetic fields are repelled from the interior of a superconductor. The surface currents are key to explaining how Faraday’s Law is preserved in a superconducting circuit, despite the fact that the interior of the superconducting wire cannot carry them.

I convinced myself that this must be the solution from the analogy with the case of a current that alternates very rapidly inside a normal wire. In the limit of infinite rapidity for the alternations, collisions of the electrons that conduct the alternating current are unimportant because the chance for a collision is negligible during the period of time between alternations. Therefore, in this regime resistivity is negligible within the bulk of the wire — which resembles a superconductor with no collisions at all. Indeed, it is well known that the current under these circumstances flows on the surface of the wire, leading to the well-known “skin effect” in conductors.

The answer required this trivial bit of imagination. Walter produced a video summarizing my answer, which received 30,000 views within a few days. The fact that others found the answer non-trivial was a surprise to me.

This experience, which is in line with Faraday’s legacy of imagination on the backdrop of being self-educated, carries an important lesson. Imagination is a quality that cannot be taught. Yet, its benefits could be considerable. It enables scientists like myself to get paid for an activity that is rather effortless at their end.

But more importantly, imagination allows all of us to open new realms — like Faraday’s discoveries of electromagnetism — which promote a more prosperous future for humanity.

Here’s hoping that one of these frontiers is the search for interstellar equipment from more advanced extraterrestrial civilizations, to be pursued by the newly announced Galileo Project. If Michael Faraday was alive today, I would have invited him to serve on the project’s research team.

About the Author— Avi Loeb is the founding director of Harvard University’s Black Hole Initiative, director of the Institute for Theory and Computation at the Harvard-Smithsonian Center for Astrophysics, and the former chair of the astronomy department at Harvard University (2011–2020). He is the bestselling author of “Extraterrestrial: The First Sign of Intelligent Life Beyond Earth” and a co-author of the textbook “Life in the Cosmos.”

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Avi Loeb

Avi Loeb is the Frank B. Baird Jr Professor of Science and Institute director at Harvard University and is the bestselling author of “Extraterrestrial”.