Tesla Pratt, 6/19/24 — Professor Littman
An eddy current is a loop of current created within a conductive body by a changing magnetic field – relative motion between the conductor and magnet. Eddy currents follow Faraday’s Law of Induction, 
and are created in planes perpendicular to the direction of the magnetic field. The strength of an eddy current is directly proportional to the strength of the magnetic field, the area of the conductive surface, and the rate of change of flux.
Objective: Study the shape and formation of eddy currents within different conducting bodies and relative motion.
Senario 1 – Spinning Disc:
In the case of a rotating disc, the speed at which the disc rotates determines the rate of change in flux, so angular velocity is directly proportional to the strength of the eddy current. This statement is confirmed by my comsol simulation of different disc speeds – in the images below, as we decrease speed by factors of ten, the current density (visible in a scale on the right) decreases by the same factor.
Angular Velocity of Disc – Effect on Current
100RPM, Scale(A/m^2): x10^6 10RPM, Scale(A/m^2): x10^5 1RPM, Scale(A/m^2): x10^4
Disc Velocity Increasing from Zero
When the disc is at rest, there is no relative movement between the conductive body, and magnetic field so no eddy currents are present. Right as the disc starts to move eddy currents begin to form in the plate, and continue to increase in strength as the disc picks up speed. This is consistent with our data above.
[Animation of how eddy currents form within the disc when it starts from 0 and speeds up to 0.1m/s, Disc rotates ~5.7° in this time frame]
Why the loops?
In this clearer image with current density streamlines, we can see that the eddy currents form large symmetrical loops on either side of the magnet.
As one part of the disc passes through the magnetic field lines, the induced electric currents look to escape from the high concentration of changing flux, seeking the path of least resistance. The current spreads throughout the disc, forming circular loops that allow them to effectively oppose the changing magnetic field – Lenz’s law states that induced electromotive force always gives rise to a current whose magnetic field opposes the original change in magnetic flux – by forming closed loops of current, the eddy currents produce magnetic fields of their own, counteracting that of the original magnet. The strongest current occurs on either side of the magnet – greatest change in magnetic flux.
Direction of Current
We can theoretically establish the direction of current, based on the principles of Lenz’s law. By Lenz’s law, the induced eddy currents will want to counteract the changing flux:
As the top part of the disc exits the field, the eddy current would want to create a magnetic field that attracts the disc back towards the magnet (opposing the motion that created it). While the bottom part of the disc (entering the field) would want to repel the magnet.
Now that we know the theoretical polarity of magnetic fields in the induced currents, we can find the direction of current using Maxwell’s right-hand grip rule. Looking from a top view tells us that the currents on the right side of the magnet will move in the counterclockwise direction, while the currents on the right will move clockwise:
This hypothesis is confirmed by my current flow model in comsol:
Scenario 2: Metal Block Moving Under Magnet
For this next exploration I modeled a large copper block with a velocity of 1m/s in the positive x-direction, and a small magnet hovering above the block. Eddy currents again form on either side of the magnet, strongest where the greatest changes in flux occur.
In determining the direction of current, we can again employ Lenz’s law:
Left side of the magnet: the block is entering the magnetic field, so the induced eddy current should create a field that points away from the magnet. For this to be the case, the induced current must flow in the counterclockwise direction.
Right side of the magnet: the block is exiting the magnetic field, so the induced eddy current should create a field that points towards the magnet. For this to be the case, the induced current must flow in the clockwise direction.
Again, my comsol model illustrates that our hypothesis was right – arrows circulate counterclockwise on the left and clockwise on the right.
Surface Area Effect
Parametrically moving the magnet across the surface of the metal (bottom block still moving forward with constant velocity) the eddy currents in the block adapt to fill the open space, again seeking the path of least resistivity. As one side of the magnet approaches the end of the block, the eddy currents on that side shrink to conform to the tighter space – there is more surface area for the electrons to fill on the other side of the magnet, so the loops are larger and more concentrated.
Conclusion:
Eddy currents are a product of induced the EMFs within a conductive surface and produce magnetic fields that act in opposition to the field that created them. In all cases, whether in a disc or a block, eddy currents look for the path of least resistivity, and form closed loops of current that allow them to effectively create their own magnetic fields. We can use Lenz’s law and Maxwell’s right hand grip rule to determine the direction of eddy currents, while speed, strength of field, and the area of the conductive surface will tell us how strong the current is.
Compressed COMSOL 6.2 file – moving block
Compressed COMSOL 6.2 file – rotating disc