Resolution of Conundrum: No Magnetic Field on the Axis of a Coil

Posted on 2006-08-18 as part of the Photonics Spotlight (available as e-mail newsletter!)

Permanent link: https://www.rp-photonics.com/spotlight_2006_08_18.html

Author: Dr. Rüdiger Paschotta, RP Photonics AG

Abstract: Here is the resolution of a tricky physics conundrum, as recently presented in the Photonics Spotlight: an apparent proof saying that a coil cannot generate a magnetic field on its symmetry axis.

Here is the resolution of a tricky physics conundrum, as recently presented in the Photonics Spotlight: an apparent proof saying that a coil cannot generate a magnetic field on its symmetry axis.

Some people suspected that this strange issue is related to some subtleties associated with the concept of infinity – field lines going to infinity might leave some room for surprises. However, the resolution is really not that subtle: it is the uncovering of a simple mathematical trick. It is true that the magnetic field strength has no x and y components on the symmetry axis, but from that we cannot conclude that <$\partial B_x / \partial x = \partial B_y / \partial y = 0$>. Therefore, <$\partial B_z \ / \partial z$> doesn't have to be zero, and the whole argument breaks down. At least in this case, we don't have to rewrite the textbooks!

It is surprising how easily one falls into this trap. It happened to professors (not stupid ones), so never mind if it happened to you!

This article is a posting of the Photonics Spotlight, authored by Dr. Rüdiger Paschotta. You may link to this page and cite it, because its location is permanent. See also the RP Photonics Encyclopedia.

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