# What is doing work in eddy current braking?

Suppose we throw a metallic plate through the space between two poles of a horseshoe magnet. There is no gravity or air drag. Eddy currents will be generated in the metal, which will try to oppose change of magnetic flux through it, and the plate will slow down.

However, since the magnetic field can't do work, what is slowing the loop down? Here there is no battery or external agent which might do work.

I know that the kinetic energy of the metal will be converted to heat. But here I am asking about the force (it must be some electric force) which is doing negative work on the metal.

Something similar to this is done in Introduction to Electrodynamics by David J. Griffiths (in the chapter magnetostatics, where it turns out that the magnetic field it forcing the current source to do work), but there is no such current source.

when a piece of aluminum is moved in such a way as to cut through the field lines of a nearby magnet, a current loop is thereby induced within the aluminum. the direction of the induced current is such that the magnetic field it induces opposes the original field and thereby exerts a force on that magnet; the resulting reaction force opposes the movement of the aluminum piece. Meanwhile, the resistivity of the aluminum acts to dissipate the flow of current as ohmic heating. for the case in which the original magnet is locked in position and cannot be moved, all the kinetic energy of the moving piece of aluminum will be converted into heat in the aluminum.

However, since magnetic field cannot do any work, what is slowing the loop down

This is really is nothing more than a definitional confusion. We define the magnetic field as the tangential component of the real underlying physical force, which is EM. The EM field is certainly capable of doing work.

If you look at the system "more closely", there is a complex interaction between the fields and resulting currents. We don't see that work in the magnet because, generally, its mechanically strong. Instead, it comes out as heat.

• I am exactly asking about those interactions. – Archisman Panigrahi Apr 6 '18 at 17:57

When an eddy current forms inside the conducting plate, the current would then be converted into heat because of the resistance of the plate. The kinetic energy, after a series of energy conversion, is turned into heat. The disk loses it kinetic energy and stops.

• I am not asking where the energy is going. I am asking about which force is doing work to stop the metallic plate. – Archisman Panigrahi Apr 6 '18 at 17:55
• Obviously, it is the magnetic force. A current is formed in the plate due to Faraday's law. The magnetic force is applied to the conducting plate with current. Isn't it? – user115350 Apr 6 '18 at 18:05
• Magnetic force $q v$ x$B$ acts perpendicular to the velocity of charge. So, it can do no work. – Archisman Panigrahi Apr 6 '18 at 18:06
• Good point. I read the book again. My understanding is the induced current produces a magnetic field. The new magnetic and the existing magnetic has the same polar so they attract each other braking the movement. – user115350 Apr 6 '18 at 18:50
• For the same reason, magnetic force cannot do work when the two poles attract each other. Some kind of electric force is doing the work here. – Archisman Panigrahi Apr 7 '18 at 4:36

The dissipation to heat is not essential to your question, so let's make the metal plate a superconductor: no dissipation of energy.

As you state, the motion through the magnetic field induces eddy current, the eddy current gives rise to a magnetic field with opposite orientation. As you know, opposing magnetic fields exert a repulsive force on each other.

So yeah, the plate slowing down is a two-stage process; work is done inducing eddy current, the work of decelerating the plate is done by the resulting repulsive force.

Removing the dissipation to heat emphasizes the repulsive force between the inducing magnetic field and the induced magnetic field.

• If it is a super conductive metal, the current will never diminish. Then the repulsive force exerted on the metal will not disappear. In this case, can we say the kinetic energy is converted to electromagnetic energy i.e. both induced magnetic energy and induced electric energy. – user115350 Apr 7 '18 at 14:58
• @user115350 Yes, to make current flow requires an electromotive force. In fact, at one point an energy storage facility was proposed that would use precisely that property. A large conducting coil is cooled to superconduction temperature. Electric energy is stored by causing a current to flow. Such energy storage will not have any losses. Danger: if for any reason the cooling equipment fails then the energy must be transferred out of the facility before the loss of supercondution. If you can't off-load the stored energy then there will be a catastrofic meltdown. – Cleonis Apr 7 '18 at 15:38
• Continuing my comment about energy storage: I looked it up: it's called SMES; Superconducting Magnetic Energy Storage. Currently there are a couple of places in the world where SMES is used to help keep a power distribution grid stabilized. – Cleonis Apr 7 '18 at 15:58
• Thanks. If there is no emf as there is no magnetic flux change based on Faraday's law, can current keeps flowing? I believe it can...but how. I guess it is in superconducting physics field which I am not familiar with. – user115350 Apr 7 '18 at 16:38