Chapter 22
Induction
Induced emf
n
A current can be produced by a changing
magnetic field
n
First shown in an experiment by Michael Faraday
n
n
A primary coil is connected to a battery
A secondary coil is connected to an ammeter
Faraday’s Experiment
n
n
n
n
The purpose of the secondary circuit is to
detect current that might be produced by the
magnetic field
When the switch is closed, the ammeter
deflects in one direction and then returns to
zero
When the switch is opened, the ammeter
deflects in the opposite direction and then
returns to zero
When there is a steady current in the primary
circuit, the ammeter reads zero
Faraday’s Conclusions
n An
electrical current is produced by a
changing magnetic field
n The secondary circuit acts as if a source
of emf were connected to it for a short
time
n It is customary to say that an induced
emf is produced in the secondary circuit
by the changing magnetic field
Magnetic Flux
n
n
n
The emf is actually induced by a change in
the quantity called the magnetic flux rather
than simply by a change in the magnetic field
Magnetic flux is defined in a manner similar
to that of electrical flux
Magnetic flux is proportional to both the
strength of the magnetic field passing
through the plane of a loop of wire and the
area of the loop
Magnetic Flux, 2
n
n
n
n
You are given a loop of
wire
The wire is in a uniform
magnetic field B
The loop has an area A
The flux is defined as
n
ΦB = B^A = B A cos θ
n
θ is the angle between
B and the normal to the
plane
Magnetic Flux, 3
n
n
When the field is perpendicular to the plane of the
loop, as in a, θ = 0 and ΦB = ΦB, max = BA
When the field is parallel to the plane of the loop, as
in b, θ = 90° and ΦB = 0
n
n
The flux can be negative, for example if θ = 180°
SI units of flux are T m² = Wb (Weber)
Magnetic Flux, final
n
The flux can be visualized with respect to
magnetic field lines
n
n
n
The value of the magnetic flux is proportional to
the total number of lines passing through the loop
When the area is perpendicular to the lines,
the maximum number of lines pass through
the area and the flux is a maximum
When the area is parallel to the lines, no lines
pass through the area and the flux is 0
Electromagnetic Induction –
An Experiment
n
n
n
n
When a magnet moves
toward a loop of wire, the
ammeter shows the
presence of a current (a)
When the magnet is held
stationary, there is no
current (b)
When the magnet moves
away from the loop, the
ammeter shows a current
in the opposite direction (c)
If the loop is moved
instead of the magnet, a
current is also detected
Electromagnetic Induction –
Results of the Experiment
nA
current is set up in the circuit as long
as there is relative motion between the
magnet and the loop
n
The same experimental results are found
whether the loop moves or the magnet
moves
current is called an induced current
because is it produced by an induced
emf
n The
Faraday’s Law and
Electromagnetic Induction
The instantaneous emf induced in a circuit
equals the time rate of change of
magnetic flux through the circuit
n If a circuit contains N tightly wound loops
and the flux changes by ΔΦ during a time
interval Δt, the average emf induced is
given by Faraday’s Law:
n
DF B
e = -N
Dt
Faraday’s Law and Lenz’ Law
n
The change in the flux, ΔΦ, can be produced
by a change in B, A or θ
n
n
Since ΦB = B A cos θ
The negative sign in Faraday’s Law is included to
indicate the polarity of the induced emf, which is
found by Lenz’ Law
n
n
The polarity of the induced emf is such that it produces
a current whose magnetic field opposes the change in
magnetic flux through the loop
That is, the induced current tends to maintain the
original flux through the circuit
Application of Faraday’s Law –
Motional emf
n
n
A straight conductor of
length ℓ moves
perpendicularly with
constant velocity
through a uniform field
The electrons in the
conductor experience a
magnetic force
n
n
F=qvB
The electrons tend to
move to the lower end
of the conductor
Motional emf in a Circuit
Assume the moving bar
has zero resistance
n As the bar is pulled to the
right with velocity v under
the influence of an applied
force, F, the free charges
experience a magnetic
force along the length of
the bar
n This force sets up an
induced current because
the charges are free to
move in the closed path
n
Lenz’ Law Revisited – Moving
Bar Example
As the bar moves to the
right, the magnetic flux
through the circuit
increases with time
because the area of the
loop increases
n The induced current must
in a direction such that it
opposes the change in the
external magnetic flux
n
Lenz’ Law, Bar Example, cont
n
n
n
The flux due to the external field in increasing
into the page
The flux due to the induced current must be
out of the page
Therefore the current must be
counterclockwise when the bar moves to the
right
Lenz’ Law, Bar Example, final
n
n
n
The bar is moving
toward the left
The magnetic flux
through the loop is
decreasing with time
The induced current
must be clockwise to
to produce its own
flux into the page
Lenz’ Law Revisited,
Conservation of Energy
n
n
Assume the bar is moving to the right
Assume the induced current is clockwise
n
n
n
n
The magnetic force on the bar would be to the
right
The force would cause an acceleration and the
velocity would increase
This would cause the flux to increase and the
current to increase and the velocity to increase…
This would violate Conservation of Energy
and so therefore, the current must be
counterclockwise
Lenz’ Law, Moving Magnet
Example
n
A bar magnet is moved to the right toward a
stationary loop of wire (a)
n
n
As the magnet moves, the magnetic flux increases with time
The induced current produces a flux to the left, so
the current is in the direction shown (b)
Lenz’ Law, Final Note
applying Lenz’ Law, there are two
magnetic fields to consider
n When
The external changing magnetic field that
induces the current in the loop
n The magnetic field produced by the current
in the loop
n
Generators
n Alternating
Current (AC) generator
Converts mechanical energy to electrical
energy
n Consists of a wire loop rotated by some
external means
n There are a variety of sources that can
supply the energy to rotate the loop
n
n
These may include falling water, heat by
burning coal to produce steam
AC Generators, cont
n
Basic operation of the
generator
n
n
n
n
As the loop rotates, the
magnetic flux through it
changes with time
This induces an emf and a
current in the external
circuit
The ends of the loop are
connected to slip rings that
rotate with the loop
Connections to the external
circuit are made by
stationary brushed in
contact with the slip rings
AC Generators, final
n
The emf generated by the
rotating loop can be found
by
ε =2 B ℓ v^=2 B ℓ sin θ
n
If the loop rotates with a
constant angular speed, ω,
and N turns
ε = N B A ω sin ω t
ε = εmax when loop is parallel
to the field
n ε = 0 when when the loop is
perpendicular to the field
n
DC Generators
n
n
Components are
essentially the same
as that of an ac
generator
The major difference
is the contacts to
the rotating loop are
made by a split ring,
or commutator
DC Generators, cont
The output voltage always
has the same polarity
n The current is a pulsing
current
n To produce a steady
current, many loops and
commutators around the
axis of rotation are used
n
n
The multiple outputs are
superimposed and the
output is almost free of
fluctuations
Chapter 23
Electromagnetic waves
Electromagnetic Waves
Produced by an Antenna
n
When a charged particle undergoes an
acceleration, it must radiate energy
n
n
n
If currents in an ac circuit change rapidly, some
energy is lost in the form of em waves
EM waves are radiated by any circuit carrying
alternating current
An alternating voltage applied to the wires of
an antenna forces the electric charge in the
antenna to oscillate
EM Waves by an Antenna,
cont
Two rods are connected to an ac source, charges oscillate
between the rods (a)
n As oscillations continue, the rods become less charged,
the field near the charges decreases and the field
produced at t = 0 moves away from the rod (b)
n The charges and field reverse (c)
n The oscillations continue (d)
n
EM Waves by an Antenna,
final
n
n
Because the
oscillating charges in
the rod produce a
current, there is also
a magnetic field
generated
As the current
changes, the
magnetic field
spreads out from
the antenna
Charges and Fields, Summary
n Stationary
charges produce only electric
fields
n Charges in uniform motion (constant
velocity) produce electric and magnetic
fields
n Charges that are accelerated produce
electric and magnetic fields and
electromagnetic waves
Electromagnetic Waves,
Summary
nA
changing magnetic field produces an
electric field
n A changing electric field produces a
magnetic field
n These fields are in phase
n
At any point, both fields reach their
maximum value at the same time
Electromagnetic Waves are
Transverse Waves
n
n
The E and B fields
are perpendicular to
each other
Both fields are
perpendicular to the
direction of motion
n
Therefore, em
waves are
transverse waves
Properties of EM Waves
n
n
Electromagnetic waves are transverse waves
Electromagnetic waves travel at the speed of
light
1
c=
moeo
n
Because em waves travel at a speed that is
precisely the speed of light, light is an
electromagnetic wave
Properties of EM Waves, 2
n
The ratio of the electric field to the magnetic
field is equal to the speed of light
E
c=
B
n
Electromagnetic waves carry energy as they
travel through space, and this energy can be
transferred to objects placed in their path
Properties of EM Waves, 3
n Energy
carried by em waves is shared
equally by the electric and magnetic
fields
Average power per unit area =
2
2
EmaxBmax Emax
c Bmax
=
=
2m o
2m oc
2m o
Properties of EM Waves, final
n Electromagnetic
waves transport linear
momentum as well as energy
For complete absorption of energy U,
p=U/c
n For complete reflection of energy U,
p=(2U)/c
n
n Radiation
pressures can be determined
experimentally
The Spectrum of EM Waves
n Forms
of electromagnetic waves exist
that are distinguished by their
frequencies and wavelengths
n
c = ƒλ
n Wavelengths
for visible light range from
400 nm to 700 nm
n There is no sharp division between one
kind of em wave and the next
The EM
Spectrum
n
n
n
Note the overlap
between types of
waves
Visible light is a
small portion of
the spectrum
Types are
distinguished by
frequency or
wavelength
Notes on The EM Spectrum
n Radio
n
Waves
Used in radio and television communication
systems
n Microwaves
Wavelengths from about 1 mm to 30 cm
n Well suited for radar systems
n Microwave ovens are an application
n
Notes on the EM Spectrum, 2
n Infrared
waves
Incorrectly called “heat waves”
n Produced by hot objects and molecules
n Readily absorbed by most materials
n
n Visible
light
Part of the spectrum detected by the
human eye
n Most sensitive at about 560 nm (yellowgreen)
n
Notes on the EM Spectrum, 3
n
Ultraviolet light
n
n
n
n
Covers about 400 nm to 0.6 nm
Sun is an important source of uv light
Most uv light from the sun is absorbed in the
stratosphere by ozone
X-rays
n
n
Most common source is acceleration of highenergy electrons striking a metal target
Used as a diagnostic tool in medicine
Notes on the EM Spectrum,
final
n Gamma
rays
Emitted by radioactive nuclei
n Highly penetrating and cause serious
damage when absorbed by living tissue
n
n Looking
at objects in different portions
of the spectrum can produce different
information