Faraday Law

Topics: Magnetic field, Electromagnetism, Maxwell's equations Pages: 82 (18543 words) Published: February 15, 2013

This is the Nearest One Head


Before this vending machine will deliver its product, it conducts several tests on the coins being inserted. How can it determine what material the coins are made of without damaging them and without making the customer wait a long time for the results? (George Semple)

c h a p t e r

Faraday’s Law

Chapter Outline
31.1 31.2 31.3 31.4
Faraday’s Law of Induction Motional emf Lenz’s Law Induced emf and Electric Fields

31.5 (Optional) Generators and

31.6 (Optional) Eddy Currents 31.7 Maxwell’s Wonderful Equations




Faraday’s Law


he focus of our studies in electricity and magnetism so far has been the electric fields produced by stationary charges and the magnetic fields produced by moving charges. This chapter deals with electric fields produced by changing magnetic fields. Experiments conducted by Michael Faraday in England in 1831 and independently by Joseph Henry in the United States that same year showed that an emf can be induced in a circuit by a changing magnetic field. As we shall see, an emf (and therefore a current as well) can be induced in many ways — for instance, by moving a closed loop of wire into a region where a magnetic field exists. The results of these experiments led to a very basic and important law of electromagnetism known as Faraday’s law of induction. This law states that the magnitude of the emf induced in a circuit equals the time rate of change of the magnetic flux through the circuit. With the treatment of Faraday’s law, we complete our introduction to the fundamental laws of electromagnetism. These laws can be summarized in a set of four equations called Maxwell’s equations. Together with the Lorentz force law, which we discuss briefly, they represent a complete theory for describing the interaction of charged objects. Maxwell’s equations relate electric and magnetic fields to each other and to their ultimate source, namely, electric charges.

12.6 & 12.7


A demonstration of electromagnetic induction. A changing potential difference is applied to the lower coil. An emf is induced in the upper coil as indicated by the illuminated lamp. What happens to the lamp’s intensity as the upper coil is moved over the vertical tube? (Courtesy of Central Scientific Company)

To see how an emf can be induced by a changing magnetic field, let us consider a loop of wire connected to a galvanometer, as illustrated in Figure 31.1. When a magnet is moved toward the loop, the galvanometer needle deflects in one direction, arbitrarily shown to the right in Figure 31.1a. When the magnet is moved away from the loop, the needle deflects in the opposite direction, as shown in Figure 31.1c. When the magnet is held stationary relative to the loop (Fig. 31.1b), no deflection is observed. Finally, if the magnet is held stationary and the loop is moved either toward or away from it, the needle deflects. From these observations, we conclude that the loop “knows” that the magnet is moving relative to it because it experiences a change in magnetic field. Thus, it seems that a relationship exists between current and changing magnetic field. These results are quite remarkable in view of the fact that a current is set up even though no batteries are present in the circuit! We call such a current an induced current and say that it is produced by an induced emf. Now let us describe an experiment conducted by Faraday 1 and illustrated in Figure 31.2. A primary coil is connected to a switch and a battery. The coil is wrapped around a ring, and a current in the coil produces a magnetic field when the switch is closed. A secondary coil also is wrapped around the ring and is connected to a galvanometer. No battery is present in the secondary circuit, and the secondary coil is not connected to the primary coil. Any current detected in the secondary circuit must be induced by some external agent....
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