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Electromagnetic
Induction
Taking It To The Maxwell
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Michael Faraday
(1791 – 1867)
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Introduction
We’ve discussed two ways in which electricity and
magnetism are related:
(1) an electric current produces a magnetic field.
(2) a magnetic field exerts a force on an current
carrying wire or moving electric charge.
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Introduction
These discoveries were made in 1820 – 1821.
Scientists wondered: If electric currents
produce a magnetic field, does a magnetic
field produce electric currents?
Joseph Henry (1797 – 1878) and Michael Faraday
(1791 – 1867) independently found, ten years
later, that this is so.
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Hey Mikey!
Faraday found that changing a magnetic field
produces a current.
Such a current is called an induced current.
To move charges requires a force and this force is
Called the ELECTROMAGNETIC FORCE,
EMF for short.
You know it as VOLTS of potential.
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Induced Current
Faraday suspected that a magnetic field would induce a
current, just like a current produces a magnet field.
Mikey found that a steady current in X produced no
current in Y. Only when the current in X was starting or
stopping (i.e., changing) was a current produced in Y.
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The Big Idea
To induce a current in a wire ….
The MAGNETIC FIELD MUST BE
CHANGING WITH RESPECT TO TIME
There are a number of differential equations to
describe this, but why complicate things?
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Since there is no change
in the magnetic flux, no
current is induced.
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The Status Quo
I. Distance between coil and
magnet decreases.
So the magnetic field (therefore
the flux) through the coil
increases.
III. Current is
induced.
II. To oppose this
upward increase in the
magnetic filed (flux),
the field produced by
the induced current
points downward.
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I. Distance between magnet
and coil increases.
III. Current is
So the magnetic field (and
therefore the flux) decreases.
induced in the
opposite direction
as the previous
case.
II. To oppose the decrease
in the upward magnetic
field (flux), the induced
current produces an
upward magnetic field,
trying to maintain the
“status quo.”
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The Big Idea!
The induced current moves such that its magnetic
field tends to oppose and resist the bar magnet’s
moving field.
Essentially it wants to DAMPEN the other field.
Nature wants the two fields to be in harmony.
This is LENZ’S LAW and it explains why the
magnet falls slowly through the copper pipe!
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Lenz’s Law
An induced emf always gives rise to a current
whose magnetic field opposes the original
change in flux.
An induced emf is always in a direction that
opposes the original change in flux that
caused it.
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The Flux Capacitor
The measure of how the field changes has to do
with an amount, or area, of coil or loop of wire
exposed to the field.
It doesn’t matter if the field is in motion, changing
in intensity, or if the coil is moving.
So long as – FROM THE POINT OF VIEW OF
THE WIRE - the B field appears to be changing
with respect to time.
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The Flux Capacitor
Magnetic flux is a measure of field strength B over
an area measured in m2.
Think of it this way. The absolute amount of rain
fall is 2” per hour over the entire state.
We only care about a small part, namely a square
foot.
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The Flux Capacitor
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Phi, Fi, Pho, Phum?
The unit of flux is the Henry, named for Joseph
Henry. The symbol is the capitol Greek letter
Phi….
Φ=BXA
Φ = B A cosθ
Henry = Tesla • m2
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Case 1
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Motion
A current can be induced by changing the area of the
field exposed to the coil. Here the area depends on
moving the coil into the field.
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Case 2
Area through the coil decreases
Therefore
A current can be induced by changing the area of the
coil exposed to the field by collapsing the coil. Here,
the area is changed by shrinking the ring.
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Case 3 – A Generator
This side is coming toward you
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A current can be induced by changing the area of the
coil exposed to the field. Here, the area is
changed by rotating with respect to the field.
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How to Induce an EMF
An emf can be induced whenever there is a change
in flux.
Since B = BA cos  an emf can be induced in
three ways:
by a changing magnetic field B
by changing the area of the loop in the field
by changing the loop’s orientation  with respect
to the field.
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Fleming’s LHR Revisited
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I
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Area has increased
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dx =
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I
F
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Umm….Sorry
But we simply have to have a differential equation.
Emf = change in Flux = B Field x Change in Area
change in time
change in time
Emf = B Field x length x velocity x change in time
change in time
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EMF Induced in a Moving
Conductor
dB B dA Blv dt
 = dt = dt = dt = Blv
This equation is valid as long as B, l, and v are
mutually perpendicular.
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F = qv x B is the force on the
charges in the wire that
produces a current.
Rotating clockwise
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Faraday’s Law of Induction
N = Number of
loops of wire

Induced emf
Lenz’s law
dB
= N
dt
Faraday found, experimentally, that the magnitude of
the induced emf is proportional to the:
rate of change of magnetic flux.
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Example 29-5
An ac generator.
The armature of a 60-Hz ac generator rotates in
a 0.15-T magnetic field. If the area of the coil is
2.0 x 10-2 m2, how many loops must the coil
contain if the peak output is to be 0 = 170 V?
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DC Generator
A dc generator is much like an ac generator or
alternator, except the slip rings are replaced by
split-ring commutators, just as in a dc motor.
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29-6 Transformers and the
Transmission of Power


A transformer is a device for increasing or
decreasing an ac voltage.
It consists of two coils of wire known as the
primary and secondary coils.
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29-6 Transformers and the
Transmission of Power



A transformer is a device for increasing or
decreasing an ac voltage.
A transformer may be a step-up transformer
(increasing voltage) or a step-down
transformer (decreasing voltage).
A transformer consists of two coils of wire
known as primary (voltage input) and
secondary
(voltage output) coils.
Transformer
equation:
VS
VP
=
NS
NP
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Example 29-8
Portable radio transformer.
A transformer for home use of a portable radio
reduces 120-V ac to 9.0-V ac. The secondary
contains 30 turns and the radio draws 400 mA.
Calculate (a) the number of turns in the primary;
(b) the current in the primary; and (c) the power
transformed.
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Example 29-9
Transmission lines.
An average of 120 kW of electric power is sent
to a small town from a power plant 10 km away.
The transmission lines have a total resistance of
0.40 . Calculate the power loss if the power is
transmitted at (a) 240 V and (b) 24,000 V.
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29-7 Changing Magnetic Flux
Produces an Electric Field
A changing magnetic flux induces an emf
and a current in a conducting loop.
Therefore, it produces an electric field.
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Changing Magnetic Flux Produces
an Electric Field



Changing magnetic flux induces current-emfelectric field.
An electric field is always generated by a
changing magnetic flux, even in free space where
no charges are present
Flux-induced field has properties different
from electrostatic electric field produced by
stationary charges.
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Faraday’s Law – General Form

dB

E dl =dt
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Forces Due to Changing B are
Nonconservative




An electric field is induced by a changing
magnetic field, even in the absence of a
conductor.
The induced electric field E that appears in the
in the previous equation, is a nonconservative,
time-varying field produced by a changing
magnetic field.
Electric field lines produced by static charges
stop and end on charges.
Electric field lines produced by a changing
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Electrostatic E Field
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Forces Due to Changing B are
Nonconservative



The fact that the integral of E dl around a
closed path is zero follows from the fact that
electro static force is a conservative force, and
so a potential energy function could be defined.
The above tells us that the work done per unit
charge around any closed path is zero.
That is the work done between any two points is
independent of the path, which is a property of
a conservative force.
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Forces Due to Changing B are
Nonconservative



But the generalized form of Faraday’s law tells
us that the integral around a closed path is not
zero.
Thus we are unable to define a potential energy
function.
Thus we conclude that when the electric force is
produced by a changing magnetic field the
forces are not conservative.
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Example 29-10
E produced by changing B.
A magnetic filed B between the pole faces of an
electromagnetic is nearly uniform at any instance
over a circular area of radius r0. The current in
the windings of the electromagnet is increasing
in time so that B changes in time at a constant
rate dB/dt at each point. Beyond the circular
region (r > r0), we assume B = 0 at all times.
Determine the electric field E at any point P a
distance r from the center of the circular area.
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Changing Magnetic Flux Produces
an Electric Field



Electrons in the moving conductor must feel a
force since there is a current.
A force implies that there is an electric field in
the conductor.
Therefore, we conclude that a changing
magnetic flux produces an electric field.
F qvB
E = q = q = vB
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FB
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Fext = ?
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FB
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Fext = ?
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