Eddy Currents

Eddy currents occur whenever there is a change in magnetic flux in bulk pieces of metal. They are sometimes beneficial and sometimes not. They can be beneficial in electromagnetic breaking, metal detectors, induction furnaces etc. The change in flux in any metal plate causes the eddy currents in the metal plate which is undesirable in some situations such as in the transformer core.

Let's first understand what these eddy currents are and how they are formed with examples. In Figure 1 you can see a metal wheel rotating in anticlockwise direction where it's small portion experiences a magnetic field $\vec B$.

Figure 1 A metal wheel is rotating in anticlockwise direction.

The portion where the wheel experiences magnetic field, undergoes a change in magnetic flux as the wheel rotates and hence induction of current takes place on the metal wheel. The induced currents are called eddy currents. The direction and the idea of how these eddy currents are formed is given by Lenz's law.

Figure 2 Eddy currents are formed as the wheel rotates.

As you can see in Figure 2, that the wheel is rotating in anticlockwise direction. The cause of flux change is the rotation of the wheel. Now according to Lenz's law, the eddy currents are induced on the wheel in such a way that the rotation of the wheel is opposed. In other words, the eddy currents are formed to apply a breaking effect on the wheel. This kind of breaking is called electromagnetic breaking and it is widely used in electromagnetic breaking systems.

So to make the Lenz's law valid, the magnetic force on the currents induced must be towards the left. We know, the magnetic force on a current as $\vec F_B = I \vec L \times \vec B$. Accroding to right hand rule the currents formed within the portion of magnetic field in the wheel are all upwards so that the force can be applied by the magnetic field to the left (to oppose motion of the wheel to the right). Note that $\vec L$ has the same direction as that of the current. The return currents outside the magnetic field portion do not experience the magnetic force. The result is the circular currents similar to that shown in Figure 2.

Other explanations of the same Lenz's law can be valid. In the region $a$, the magnetic flux is increasing (if the area vector has the same direction of magnetic field). In this region, accroding to Lenz's law, the increase in flux is opposed by the opposing magnetic field out of the wheel (you can check by right hand rule to check the direction of magnetic field). Similarly, in region $b$, the magnetic flux is decreasing (with the same direction of area vector as before), and according to Lenz's law, the decreasing magnetic flux is opposed by the opposing magnetic field into the wheel.

Similarly another explanation can be made in terms of Lenz's law that, in region $a$, the eddy currents are produced in such as way that the magnetic field has outward direction (out of the wheel) and this field is similar to that of a bar magnet and has attractive effect to the magnetic field into the wheel which was already there. In other words this induced magnet pulls the magnet at the center. Similarly, the magnetic field formed into the reason $b$ due the the change in flux has the same polarity as the magnet at the center (original field which was already there) and repels or in other words it pushes the magnet at the center. The net effect is to oppose the rotation of the wheel.

Electromagnetism
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