15.3.3 Eddy Current (Magnetic Braking)

How does a car brake work? A traditional car brake basically clamps the wheel and uses friction to convert the KE of the car into heat energy. Over time, the brake pads and brake discs undergo wear and tear and must be replaced. Wouldn’t it be nice if the braking can be achieved without physical contact? Magnetic braking does just that.

Take for example an aluminium plate sliding under a stationary permanent magnet. Aluminium is conducting, but non-ferromagnetic. The magnet will not exert any magnetic force on the plate if it were stationary. It is a different story if the plate were moving.

As the plate slides along in the magnetic field, it “cuts” the magnetic flux, resulting in induced emf in the plate. Since aluminium is conducting, an induced current is produced in the plate. Since the cause of induction is the motion of the plate, Lenz’s Law dictates that the induced current will produce a retardation force to slow down the plate.

Now let’s look at the scenario in more detail. It is best to think of the plate as being made up of wires. Then as the plate slides along in the magnetic field, only the “wires” passing under the magnet will be “cutting” the magnetic flux. So emf is induced only across the “wires” passing right under the magnet and nowhere else. Those “wires” behave like batteries trying to push current upward (use FRHR).

However, the entire plate is conducting. This results in induced currents that flow in closed loops. We call this kind of current eddy current.

Next, we note that the “wires” under the magnet are now current-carrying conductors moving in a B-field. What does that give us? The $\displaystyle {{F}_{b}}=BIL$ magnetic force! Using the FLHR, it is clear that the plate will be experiencing a leftward braking force, an outcome easily predicted by Lenz’s Law.