Chapter 21
Magnetic Induction
Magnetic Induction
 Electric and magnetic forces both act only on
particles carrying an electric charge
 Moving electric charges create a magnetic field
 A changing magnetic field created an electric field
 This effect is called magnetic induction
 This links electricity and magnetism in a fundamental
way
 Magnetic induction is also the key to many practical
applications
Electromagnetism
 Electric and magnetic phenomena were connected
by Ørsted in 1820
 He discovered an electric current in a wire can exert a
force on a compass needle
 Indicated a electric field can lead to a force on a
magnet
 He concluded an electric field can produce a magnetic
field
 Did a magnetic field produce an electric field?
 Experiments were done by Michael Faraday
Section 21.1
Faraday’s Experiment
 Faraday attempted to
observe an induced
electric field
 He didn’t use a lightbulb
 If the bar magnet was in
motion, a current was
observed
 If the magnet is stationary,
the current and the
electric field are both zero
Section 21.1
Another Faraday Experiment
 A solenoid is positioned near a loop of wire with the lightbulb
 He passed a current through the solenoid by connecting it to a
battery
 When the current through the solenoid is constant, there is no
current in the wire
 When the switch is opened or closed, the bulb does light up
Section 21.1
Conclusions from Experiments
 An electric current is produced during those
instances when the current through the solenoid is
changing
 Faraday’s experiments show that an electric current
is produced in the wire loop only when the magnetic
field at the loop is changing
 A changing magnetic field produces an electric field
 An electric field produced in this way is called an
induced electric field
 The phenomena is called electromagnetic induction
Section 21.1
Magnetic Flux
 Faraday developed a quantitative theory of induction
now called Faraday’s Law
 The law shows how to calculate the induced electric
field in different situations
 Faraday’s Law uses the concept of magnetic flux
 Magnetic flux is similar to the concept of electric flux
 Let A be an area of a surface with a magnetic field
passing through it
 The flux is ΦB = B A cos θ
Section 21.2
Magnetic Flux, cont.
 If the field is perpendicular to the surface, ΦB = B A
 If the field makes an angle θ with the normal to the
surface, ΦB = B A cos θ
 If the field is parallel to the surface, ΦB = 0
Section 21.2
Magnetic Flux, final
 The magnetic flux can be defined for any surface
 A complicated surface can be broken into small
regions and the definition of flux applied
 The total flux is the sum of the fluxes through all the
individual pieces of the surface
 The unit of magnetic flux is the Weber (Wb)
 1 Wb = 1 T . m2
Section 21.2
Faraday’s Law
 Faraday’s Law indicates how to calculate the
potential difference that produces the induced
current
 Written in terms of the electromotive force induced in
the wire loop
!" B
å= #
!t
 The magnitude of the induced emf equals the rate of
change of the magnetic flux
 The negative sign is Lenz’s Law
Section 21.2
Applying Faraday’s
Law
 The ε is the induced
emf in the wire loop
 Its value will be
indicated on the
voltmeter
 It is related to the
electric field directly
along and inside the
wire loop
 The induced potential
difference produces the
current
Applying Faraday’s Law, cont.
 The emf is produced by changes in the magnetic flux
through the circuit
 A constant flux does not produce an induced voltage
 The flux can change due to
 Changes in the magnetic field
 Changes in the area
 Changes in the angle
 The voltmeter will indicate the direction of the
induced emf and induced current and electric field
Section 21.2
Flux Though a
Changing Area
 A magnetic field is
constant and in a direction
perpendicular to the plane
of the rails and the bar
 Assume the bar moves at
a constant speed
 The magnitude of the
induced emf is ε = B L v
 The current leads to
power dissipation in the
circuit
Section 21.2
Conservation of Energy
 The mechanical power put into the bar by the
external agent is equal to the electrical power
delivered to the resistor
 Energy is converted from mechanical to electrical,
but the total energy remains the same
 Conservation of energy is obeyed by
electromagnetic phenomena
Section 21.2
Electrical Generator
 Need to make the rate
of change of the flux
large enough to give a
useful emf
 Use rotational motion
instead of linear motion
 A permanent magnet
produces a constant
magnetic field in the
region between its poles
Section 21.2
Generator, cont.
 A wire loop is located in the region
of the field
 The loop has a fixed area, but is
mounted on a rotating shaft
 The angle between the field and
the plane of the loop changes as
the loop rotates
 If the shaft rotates with a constant
angular velocity, the flux varies
sinusoidally with time
 This basic design could generate
about 70 V so it is a practical
design
Section 21.2
Changing a Magnetic Flux,
Summary
 A change in magnetic flux and therefore an induced
current can be produced in four ways
 If the magnitude of the magnetic field changes with
time
 If the area changes with time
 If the loop rotates so that the angle changes with time
 If the loop moves from one region to another and the
magnitude of the field is different in the two regions
Section 21.2
Lenz’s Law
 Lenz’s Law gives an
easy way to determine
the sign of the induced
emf
 Lenz’s Law states the
magnetic field produced
by an induced current
always opposes any
changes in the magnetic
flux
Section 21.3
Lenz’s Law, Example 1
 Assume a metal loop in which the magnetic field passes upward
through it
 Assume the magnetic flux increases with time
 The magnetic field produced by the induced emf must oppose the
change in flux
 Therefore, the induced magnetic field must be downward and the
induced current will be clockwise
Section 21.3
Lenz’s Law, Example 2
 Assume a metal loop in which the magnetic field passes upward
through it
 Assume the magnetic flux decreases with time
 The magnetic field produced by the induced emf must oppose the
change in flux
 Therefore, the induced magnetic field must be downward and the
induced current will be counterclockwise
Section 21.3