This is the Nearest One Head
P U Z Z L E R
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
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
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
FARADAY’S LAW OF INDUCTION
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....