phy1020.DVI

Chapter 36

Faraday’s Law

The fundamental equations of classical electricity and magnetism are four equations calledMaxwell’s equa-
tions. The four equations are:

1. Gauss’s law(Chapter 16) describes the electric field created by electric charges.


2. Gauss’s law for magnetism(Chapter 31) states that there are no magnetic monopoles.


3. Amp`ere’s law(Chapter 35) describes how a time-varying electric field creates a magnetic field.


4. Faraday’s lawdescribes how a time-varying magnetic field creates an electric field.
   In this chapter we’ll look at the fourth of these equations, Faraday’s law. Mathematically, Faraday’s law
   states that if the magnetic fluxˆBthrough a closed loop of wire changes with time, then there will be an
   electromotive forceE(i.e. a voltage) induced in the wire given by

EDN

ˆB

t

(36.1)

HereEis the induced electromotive force,Nis the number of turns of wire in the loop, andˆBis the
change in magnetic flux in timet. (Recall that the magnetic flux is given byˆBDBA.
The magnetic flux through the loop(s) of wire can be changed in several ways: the magnetic fieldB
can change in magnitude with time; the magnetic field can change direction with time; the loop of wire can
change its orientation with time; the area of the loop can change with time; or some combination of these.
Faraday’s law forms the basis of theelectric generator, which is responsible for producing most of the
electricity we use every day (except for electricity produced by batteries or solar arrays). Loops of wires are
turned inside a stationary magnetic field (or magnets may be turned inside stationary wires); this causes the
magnetic flux through the wires to change with time, creating an electric current. The turning motion may be
created by a water wheel, by geothermal steam, by steam created from burning coal or oil, or by steam created
by heat from a nuclear reaction. In effect, an electric generator converts mechanical motion into electrical
energy.
Faraday’s law may also be used in reverse: electrical energy may be converted into mechanical motion.
This creates anelectric motor, a device that is familiar in such household appliances as vacuum cleaners and
electric dryers.

36.1 Lenz’s Law

Faraday’s law gives the magnitude of the induced electromagnetic force (emf) created by a changing magnetic
field. Thedirectionof the induced electromotive force and current may be found from a statement known a