CK-12-Physics - Intermediate

19.1. Electromagnetic Induction http://www.ck12.org

FIGURE 19.5

Wilhelm E. Weber.

FIGURE 19.6

Faraday’s discovery is called the law of induction, which we give below:

Faraday’s law of induction applied to a coil ofNturns: The average induced voltage in a coil is equal to the product

of the number of loopsN(or the number of turns) in the coil, and the time rate of change in the magnetic flux

∆Φ

∆tthrough the coil.

V=−N∆Φ∆t

The negative sign indicates that the induced voltage produces a current whose magnetic field opposes the direction

of the original change in the magnetic flux.This statement is known as Lenz’s law.

For more information on Faraday’s law of induction, follow the links below.

http://demonstrations.wolfram.com/ShowingFaradaysLawWithAnOscilloscope/

http://phet.colorado.edu/en/simulation/faraday

Lenz’s law

Lenz’s law is named for the 19th century physicist Heinrich Lenz (1804-1865). In order to understand Lenz’s law,

considerFigure19.1. As the north pole of the magnet is inserted into the loop, the induced current in the loop

produces a magnetic field. The magnetic field (as indicated by the right-hand rule) must be equivalent to the field

produced by a magnet with its north pole facing the incoming north pole of the magnet. Two north poles will, of

course, repel. Thus, the induced current has set up a magnetic field to oppose the motion of the magnet. What if the

reverse occurred? If the induced current were to set up a magnetic field that attracted the magnet, the flux through

the loop would increase, and therefore the induced voltage would increase. But a larger voltage would produce yet

a larger induced current and an even larger flux. Such a process would lead to ever-increasing induced voltages and

currents, violating the law of conservation of energy. The smallest work done in pushing the magnet toward (or away

from) the loop would result in more and more energy generated within the system. Instead, Lenz’s law ensures that

the induced current always acts to keep the flux constant by opposing whatever change in the magnetic flux that has

brought the induced current to life. If the magnetic flux decreases, the induced current produces a magnetic field to

increase the flux, and vice versa.