# Lorentz forces on loop cancel each other out so how do eddy current brakes work?

Let's take the pendulum example. When it passes through the magnetic field, eddy currents are induced. Those currents flow in circles and now with the presence of current and magnetic field lorentz forces are created against the pendulum.

However, if the current is flowing through a loop the forces cancel each other out because of the symmetry of the circle. I understand that the same doesn't apply for torque and I think that's the key to the explanation. And even if I'm right and that really is the case, a detailed answer would help others studying about eddy currents understand how the forces actually stop the pendulum.

Also, what would happen if the pendulum was superconducting? • I'd also be interested in what would happen if the pendulum were superconducting. – Simon Richter Jan 28 '17 at 11:11
• I'm in for that, let's add it. – John Katsantas Jan 28 '17 at 11:12

Imagine your metal plate to be much smaller - so small that it is in an uniform magnetic field when it moves between the poles. Then a constant voltage is generated between the upper and lower edges of the plate - just like in a generator. No current as soon as the electrons in the metal have piled to up or down. The eddy current is the result from the non-uniformity of the magnetic field - different induced voltages generate balancing current which is horizontal and make room for new electrons to pile vertically - that's the eddy.

But your picture is wrong. The balancing current is not a single circle, but two and their centers reside at the edges of the magnet. See the following Wikipedia image from "Eddy Current Brake" There's a continuous current in the metal that causes dissipation, but seemingly there still should not be any reason for braking because the two eddies work as electric magnets that push the plate towards the poles and that motion is prevented mechanically.

The exisistence of your question hints that you want to hear nothing about the energy - you want to see the forces that you see as the basic primary reasons for the braking and also for that so called energy which you see only as an artificial (= calculated only) result.

This is your major error. The force is caused by the change of the field energy, the energy is not caused by the force. If somewhere a motion causes the dissipation of the energy, then that motion needs energy and it must be produced by work. The force appears in such direction that the work will be done. In this case we see the braking.

Addendum for the superconductive plate: See the image. Let the plate just have arrived from the left. I've rotated the following image to horizontal to keep the directions same as the Wikipedia image had: The eddy current ie has generated. The curret is at the right side of our plate the same as ie in the picture . The backward current fills the left side. So - what is caused to the magnetic field? It has cancelled inside the plate. The non-lossy curret has grown just into the measures that cancels the magnetic field. No more effect is available. Because the total volume of the magnetic field has diminished, its total energy has got lower. This kind of total field energy change is attractive, so the plate is sucked into the space between the magnetic poles. That of course increases the speed of our pendulum and that speed boost helps the pendulum out of the hole, when the magnet tries to suck it back.

Conclusion: A superconductive pendulum will get a speed boost when it enters to the slot between the poles. That speed boost is lost when the pendulum gets over the middle position. No permanent acceleration or braking happens. Think about a ball that rolls over a gentle dimple.

• You couldn't explain it better . Thank you . And it's not that I don't wanna hear about energy , I just understood that part from the start. I wanted to see the actual force and not only imagine one stoping the pendulum because the conservation of energy says so . – John Katsantas Jan 28 '17 at 12:18
• @John Katsantas The superconduction is added. To be sure, see some text about "Magnetic levitation; a superconductor over a magnet". That couldn't be stable if my text is bullshit – user287001 Jan 28 '17 at 20:31
• "But your picture is wrong." In the OP's diagram the plate is entering a region of stronger magnetic field on one side and entering a region of weaker field on the other side. Your (Wikipedia) diagram has the two current loops because both effects are occurring simultaneously. – Farcher Aug 1 '17 at 7:50
• @Farcher : The questioner has 2 positions with the same current loop. The rightmost is wrong, it should be as in Wikipedia. – user287001 Aug 1 '17 at 8:26
• Sorry to have been a pain. I missed the fact that you were referring to the current direction. – Farcher Aug 1 '17 at 10:18

"the forces cancel each other out because of the symmetry of the circle" and I think this is where your understanding is off. It's only true if the full circle is in the same magnetic field.

Instead, remember that the current is induced where the magnetic field is changing.

So, (referring to your diagram) where the conductor is entering the field, a downward flowing current is induced. And the force exerted is backwards, i.e. retarding the pendulum. (As it must be from conservation of energy).

And where the conductor is leaving the field, the induced current is upward - because the direction of the change in flux has reversed. So the force exerted is still backwards, i.e. again retarding the pendulum. (conservation of energy again).

So the forces do add, but because of the reversal (leaving the field instead of entering it) they don't sum to 0, they sum to twice the individual force.

• I understand your point but that's not exactly what I meant by the cancelling . I agree that the force would have the same direction because the current flows the opposite way when the pendulum is leaving . The problem is that whatever area undergoing a ΔΦ will cause eddy currents that flow in circles . Those circles can't be half-circles. They are always whole and in each circle created by the eddy currents (no matter how many circles or how big - that depends on the area of ΔΦ change ) the forces cancel each other . – John Katsantas Jan 28 '17 at 11:59
• And how big do you think those circles are, and why? – Brian Drummond Jan 28 '17 at 12:05
• Turns out eddy currents don't work as I'd imagined. And since they don't, things will work out the way you said. Thank you for your help. – John Katsantas Jan 28 '17 at 12:27

The eddy current meets a resistance and heats up the pendulum, this energy needs to come from somewhere.

The current induced by the magnetic field itself creates a magnetic field, which does not match the field from the permanent magnet (it is weaker, because of resistive losses, and also has a different shape because the current cannot cross the edge of the pendulum), which is where the braking action comes from.

• Well, that sure makes sense but I'm trying to get my head around the forces working and not the energy. – John Katsantas Jan 28 '17 at 11:15