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
0
