Chapter 20
Electromagnetic Induction
and Waves
Units of Chapter 20
Induced emf: Faraday’s Law and Lenz’s Law
Electric Generators and Back emf
Transformers and Power Transmission
Electromagnetic Waves
20.1 Induced emf: Faraday’s Law
and Lenz’s Law
We observe that, when a magnet is moved
near a conducting loop, a current is induced.
When the motion stops, the current stops.
20.1 Induced emf: Faraday’s Law
and Lenz’s Law
On the other hand, when a loop moves
parallel to a magnetic field, no current is
induced.
20.1 Induced emf: Faraday’s Law
and Lenz’s Law
We conclude that current is induced only
when the magnetic field through the loop
changes.
An induced emf is produced in a loop or complete
circuit whenever the number of magnetic field lines
passing through the plane of the loop or circuit
changes.
ANIMATION: Faraday’s Law
20.1 Induced emf: Faraday’s Law
and Lenz’s Law
Changing current in one
loop can induce a current
in a second loop.
20.1 Induced emf: Faraday’s Law
and Lenz’s Law
In order to measure the change in the magnetic
field through a loop, we define the magnetic
flux:
SI unit of magnetic flux: the weber, Wb
20.1 Induced emf: Faraday’s Law
and Lenz’s Law
Faraday’s law for the induced emf:
The minus sign indicates the direction of
the induced emf, which is given by Lenz’s
law.
20.1 Induced emf: Faraday’s Law
and Lenz’s Law
Lenz’s law:
ANIMATION: Lenz’s Law
An induced emf in a wire loop or coil has a direction
such that the current it creates produces its own
magnetic field that opposes the change in magnetic
flux through that loop or coil.
So if the magnetic field is increasing, the
induced current will produce a field in the
opposite direction, tending to decrease the
field.
20.1 Induced emf: Faraday’s Law
and Lenz’s Law
The direction of the induced current is given by
a right-hand rule.
With the thumb of the right hand pointing in the
direction of the induced field, the fingers curl in the
direction of the induced current.
20.1 Induced emf: Faraday’s Law
and Lenz’s Law
Lenz’s law is a
consequence of the
conservation of energy.
Another way of viewing
Lenz’s law is that the
induced current is such
that the flux through the
loop tends to remain
constant.
20.2 Electric Generators and Back emf
One way of changing the
flux through a loop is to
change its orientation with
respect to the field. If this is
done via some mechanical
means, electricity can be
generated.
20.2 Electric Generators and Back emf
The induced emf is then:
Such a generator is also called an
alternator.
The emf as a function of time:
20.2 Electric Generators and Back emf
In common usage, we refer to the frequency
rather than the angular frequency:
20.2 Electric Generators and Back emf
An electric motor has a loop rotating in a
magnetic field, and will also create an induced
emf.
This back emf is given
by:
It limits the current in
a motor and can help
protect it.
20.3 Transformers and Power
Transmission
A transformer can be used to reduce current
while keeping power constant; this is useful in
transmission lines, where losses depend on
the current.
Since P = IV, reducing the current while the
power remains unchanged means increasing
the voltage.
20.3 Transformers and Power
Transmission
A transformer works by
induction—an ac current in
the primary coil induces a
current in the secondary
coil. The voltage ratio
depends on the number of
loops in each coil.
ANIMATION: Transformers
20.3 Transformers and Power
Transmission
The voltage ratio can be derived by looking
at the induced emf.
Constant power means that
Therefore,
20.3 Transformers and Power
Transmission
In reality, there is always some power loss
between the primary and secondary coils, due
to resistance, flux leakage, and self-induction.
Currents can also be induced in the bulk of
the material itself; these are called eddy
currents.
20.3 Transformers and Power
Transmission
Eddy currents can function as powerful brakes
for a solid conductor moving in a magnetic field.
Braking can be reduced by shaping the
conductor to make current loops difficult to form.
20.4 Electromagnetic Waves
James Clerk Maxwell showed how the electric
and magnetic fields could be viewed as a single
electromagnetic field, with the following
properties:
A time-varying magnetic field produces a time-varying
electric field.
A time-varying electric field produces a time-varying
magnetic field.
We have studied the first, but the second is new.
We will not study it in detail, but will use its
consequences.
20.4 Electromagnetic Waves
An accelerating charge produces an
electromagnetic wave. The electric and
magnetic fields are perpendicular to each other
and to the direction of propagation of the wave.
20.4 Electromagnetic Waves
All electromagnetic waves travel at the
same speed in vacuum:
In a vacuum, all electromagnetic waves, regardless
of frequency or wavelength, travel at the same
speed, c = 3.00 × 108 m/s.
This finite speed of electromagnetic waves
leads to delays in transmitting signals over
long distances, such as to spacecraft.
20.4 Electromagnetic Waves
An electromagnetic wave
transmits energy; its electric
and magnetic fields are
capable of accelerating
charged particles. It will exert
a force on any surface it
intercepts; this phenomenon
is called radiation pressure. It
is negligible in everyday
experience, but could be
used to power “solar sails”
for interplanetary travel.
20.4 Electromagnetic Waves
Electromagnetic waves can have any
frequency. Different frequencies have been
given different labels.
20.4 Electromagnetic Waves
Waves of different frequencies have different
sources.
Review of Chapter 20
Magnetic flux:
Faraday’s law of induction:
Lenz’s law: Induced emf tends to oppose
the change that induced it.
AC generator:
Review of Chapter 20
A transformer uses induction to reduce or
increase current in a secondary coil.
An electromagnetic wave consists of timevarying electric and magnetic waves,
perpendicular to each other and to the
direction of propagation, and traveling with
a speed of 3.00 × 108 m/s in vacuum.