Electric - Magnetic Eddy Currents

In electromagnetics it is so important to understand the Maxwell-Ampere equation and the Maxwell-Faraday equation. What better way to understand these equations then an example. The magnetic brake that generates electric eddy currents is a fun example.

A conducting copper disc is spun with the North pole of a magnet above and the South pole of a magnet beneath. The disc is hard to turn due to the magnets and it generates heat. The question is, of course, why?

The disc in the figure above spins counter clockwise when viewed from above. Eddy currents develop near the magnets. The diagram above shows the direction of electron travel rather than the direction of current travel. The magnets are releasing spinning electrons that are spinning quite tightly in the counter-clockwise direction. This generates a tight spinning set of electrons around the copper nuclei on the left side of the diagram. Angular momentum must be preserved so larger curls of current develop in the copper disk.

The eddy current flows within the conductor and outside the conductor. Even though these electron flows are shown in the diagram to be in a few radial positions with one radius, they occur at all radial positions and with a statistically varying radius. The eddy currents circulate end to end throughout the conductor to some extent. The eddy currents circulate outside the conductor most vigorously near to the conductor and less so as one extends away from the conductor. As in the conductor these eddy currents occur at all radial positions and they circulate throughout the dielectric surrounding the conductor until they are too small to be measured.

Under the magnets the electrons in the copper disc spin with the spin induced by the magnets' ejected electrons. As an area of the disc spins away from the magnets the angular momentum continues thought the tight spins get wider as the spinning electrons dissipate and the spin becomes random again.

The disc warms up due to the excess change in angular momentum first to match the magnets and then to preserve angular momentum. All of these non-random re-arrangements of electrons cause interactions with the copper lattice. This causes heat.

Another way to see the eddy brake is to consider the Maxwell Faraday equation with respect to the change in magnetic field and the effect that will have on the electric field in the disc. The Maxwell Ampere equation applies to the circulating current due to the magnetic field.