College Physics

Figure 23.5Rotation of a coil in a magnetic field produces an emf. This is the basic construction of a generator, where work done to turn the coil is converted to electric energy.

Note the generator is very similar in construction to a motor.

So we see that changing the magnitude or direction of a magnetic field produces an emf. Experiments revealed that there is a crucial quantity called

themagnetic flux,Φ, given by

Φ=BAcosθ, (23.1)

whereBis the magnetic field strength over an areaA, at an angleθwith the perpendicular to the area as shown inFigure 23.6.Any change in

magnetic fluxΦinduces an emf.This process is defined to beelectromagnetic induction. Units of magnetic fluxΦareT ⋅ m^2. As seen in

Figure 23.6,Bcosθ=B⊥, which is the component ofBperpendicular to the areaA. Thus magnetic flux isΦ=B⊥A, the product of the area

and the component of the magnetic field perpendicular to it.

Figure 23.6Magnetic fluxΦis related to the magnetic field and the area over which it exists. The fluxΦ=BAcosθis related to induction; any change inΦinduces

an emf.

All induction, including the examples given so far, arises from some change in magnetic fluxΦ. For example, Faraday changedBand henceΦ

when opening and closing the switch in his apparatus (shown inFigure 23.3). This is also true for the bar magnet and coil shown inFigure 23.4.

When rotating the coil of a generator, the angleθand, hence,Φis changed. Just how great an emf and what direction it takes depend on the

change inΦand how rapidly the change is made, as examined in the next section.

23.2 Faraday’s Law of Induction: Lenz’s Law

Faraday’s and Lenz’s Law

Faraday’s experiments showed that the emf induced by a change in magnetic flux depends on only a few factors. First, emf is directly proportional to

the change in fluxΔΦ. Second, emf is greatest when the change in timeΔtis smallest—that is, emf is inversely proportional toΔt. Finally, if a

816 CHAPTER 23 | ELECTROMAGNETIC INDUCTION, AC CIRCUITS, AND ELECTRICAL TECHNOLOGIES

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