Ch. 29
Electromagnetic Induction
Observations made during various induction
experiments (first performed by Michael
Faraday in the 1830’s:
When there is no current in the
electromagnet, so that B = 0, the
galvanometer shows no current.
 When the electromagnet is initially turned
on, there is a momentary current through
the meter as B increases.
 When B levels off at a steady value, the
current drops to zero, no matter how large
B is.

Further observations:
With the coil in a horizontal plane, we squeeze it
so as to decrease the cross-sectional area of the
coil. The meter detects current only during the
deformation, not before or after. When we
increase the area to return the coil to its original
shape, there is current in the opposite direction,
but only while the area of the coil is changing.
 If we rotate the coil a few degrees about a
horizontal axis, the meter detects current during
its rotation, in the same direction as when we
decreased the area. When we rotate the coil
back, there is a current in the opposite direction
during this rotation.

Even more observations:
If we jerk the coil out of the magnetic field, there is a
current during the motion, in the same direction as
when we decreased the area.
 If we decrease the number of turns in the coil by
unwinding one or more turns, there is a current
during the unwinding, in the same direction as when
we decreased the area. If we wind more turns onto
the coil, there is a current in the opposite direction
during the winding.
 When the magnet is turned off, there is a momentary
current in the direction opposite to the current when
it was turned on.

And even more observations:



The faster we carry out any of these
changes, the greater the current.
If all these experiments are repeated with a
coil that has the same shape but different
material and different resistance, the current
in each case is inversely proportional to the
total circuit resistance. This shows that the
induced emfs that are causing the current do
not depend on the material of the coil but
only on its shape and the magnetic field.
Young and Freeman, pg. 1107
In conclusion,
 In
reviewing these statements,
what is the common concept
that exists??
Faraday's Magnetic Field
Induction Experiment
When Michael Faraday made his discovery
of electromagnetic induction in 1831, he
hypothesized that a changing magnetic field
is necessary to induce a current in a nearby
circuit. To test his hypothesis he made a coil
by wrapping a paper cylinder with wire. He
connected the coil to a galvanometer, and
then moved a magnet back and forth inside
the cylinder.
 http://micro.magnet.fsu.edu/electromag/java/f
araday2/

Definition

Electromagnetic induction:
◦ A changing magnetic flux through a circuit
induces an emf and current in the circuit.
Faraday’s Law

The induced emf in a circuit is proportional
to the time rate of the change of magnetic
flux through the circuit.
dB
 
dt

Recall:

http://phet.colorado.edu/simulations/sims.ph
 B  NBA cos 
p?sim=Faradays_Electromagnetic_Lab
Examples of Faraday’s Law

A bar magnet is moved
through a loop of wire
that has a crosssectional area of 0.004
sq. m. The magnetic
field changes from 0.04
T to 0.07 T in 0.005 s.
Calculate the
magnitude of the
induced emf.
More Faraday’s Law Examples

Flux through coil
changes because bar
magnet is moved up
and down.

AC current in
bottom coil causes
changing B-field along
iron core.
Flux Changing by Changing Areas

Magnetic field doesn’t change; area
changes. The more quickly the loop is
stretched, the larger the induced emf.
Changing Magnetic Fields Cause
Changing Flux

As the magnet approaches the loop, the
more B-field lines penetrate the loop
causing the flux to increase.
In the opposite direction

As the magnet is moved away from the
loop, the number of B-field lines decrease
and the flux decreases.
Lenz’s Law

States that the polarity of the induced
emf is such that it tends to produce a
current that creates a magnetic flux to
oppose the change in magnetic flux
through the area enclosed by the current
loop, or in other words, the direction of
any magnetic induction effect is such as to
oppose the cause producing it.
Lenz’s Law
 As
the magnet is
brought closer,
increasing the
number of field line
penetrating the plane
of the loop.
Cause: Magnet moving to the
right
Effect: Coil becomes an
electromagnet to oppose
movement of bar.
Rule: "see counterclockwise, see
north"
---------------------------------------Another way to look at it:
Cause: More B-arrows
puncture plane
Effect: Induced electromagnet
creates its own B-field arrows
pointing in the opposite
direction, partially cancelling the
increase.
Lenz’s s Law

Magnet is taken away from the
loop, decreasing the number
of B-field penetrations of the
plane of the loop.
Cause: Magnet moving away, to
the left
Effect: Coil becomes an
electromagnet to attract back
the bar magnet.
Rule: "see clockwise, see south"
---------------------------------------Another way to look at it:
Cause: Fewer B-arrows
puncture plane
Effect: Induced electromagnet
creates its own B-field arrows
pointing in the same direction as
the bar magnet's field, partially
cancelling the loss of B arrows.
Lenz’s Law
Cause: Increase in flux
Effect: Induced current in loop
creates a magnetic field (not
shown) which partially cancels
flux
A second way to look at it:
The induced current as viewed
from the left
is clockwise, making the left face
of loop the
south pole, which is repelled by
the south pole
of the electromagnet.
(Effect opposes cause.)
---------------------------------------------A third way:
Growth of counter-clockwise
current is opposed by growth of
clockwise current
Lenz’s Law
Cause: Decrease in flux
Effect: Induced current in loop creates a
magnetic field (not shown) which partially
restores flux
Lenz’s Law
"See counterclockwise, see
north"
--------------------------------Ring on left acts like a
magnet with a north face
on top to repel the falling
magnet (effect opposing
cause)
As viewed from above is
current in ring clockwise,
or counter-clockwise?
--------------------------------What happens in the split
ring?
Lenz’s Law
Cause: bar magnet
moving away.
Effect: induced
electromagnet's
polarity will be such
that it will try to
attract the magnet
back.
What will be the
polarity, north, or
south, of the left face
of the induced
electromagnet?
Lenz’s Law

Current is suddenly established in wire at
bottom. What is the direction--clockwise,
or counter clockwise--in the loop?
Lenz’s Law

What will be the direction of the current
in the resistor when the switch is
closed? Hint: what will be the polarity of
the right face of the first magnet?
Faraday’s & Lenz’s Laws

An emf is generated only if the flux is
changing. Note that current is zero while
the loop is completely inside the magnetic
field. Why?
Motional emf
Charges at ends of rod
exert electrostatic
force on any charge q
in rod.
At equilibrium,
Fe = Fm
qE = Fm
qE = qvB
E = vB
Recall,
E = ΔV /Δs
ΔV= E Δs
= vBL
(induced emf)
ΔV = vBL
Magnetic force on induced current
Magnetic force to the left resists push to the right
by the hand.
Induced emf and Electric Fields
We have seen that a changing magnetic
flux induces an emf and a current in a
conducting loop. Therefore, we must
conclude that an electric field is
created in the conductor as a result
of the changing magnetic flux.
 The induced electric field is nonconservative and time varying.

Induced E-Field created by
increasing B-Field
The E-Field lines
form a vortex or
"eddy".
 An induced emf
exists in a circular
pattern.
 To move the charges
once around, the
work done is

q  qE (2 r )
Induced E-Fields
q  qE (2 r )

From Faraday’s law,

E
2 r
1 dB
1 d ( B r 2 )
E

2 r dt
2 r
dt
r dB
E
2 dt
Induced E-Fields
The negative sign indicates that the
induced electric field opposes the change
in the magnetic field.
 In general form, Faraday’s law of
induction,


dB
E  dl  
dt
Induced E-Fields

It is important to recognize that the
induced electric field is a nonconservative, time-varying field that
is generated by a changing magnetic
flux.
Motors



Convert electrical energy
into mechanical energy
As the coils turn in the
magnetic field, an induced
emf is created that
produces an induced
current in the reverse
direction.
This is known as the
‘generator effect.’
Generators



Convert mechanical energy
into electrical energy
Once there is a current in
the loop, there exists a
torque that acts on the
loop in the opposite
direction of the motion
This is known as the ‘motor
effect.’
Motors & Generators
Maxwell’s Equations

Four equations, formulated by James Clerk
Maxwell, that together form a complete
description of the production and interrelation of
electric and magnetic fields. The statements of
these four equations are (1) electric field diverges
from electric charge, (2) there are no isolated
magnetic poles, (3) electric fields are produced by
changing magnetic fields, and (4) circulating
magnetic fields are produced by changing electric
fields and by electric currents. Maxwell based his
description of electromagnetic fields on these
four statements.
Maxwell’s Equations

Gauss’s Law
Gauss’s Law for
Magnetism

 E  dA 
qenclosed
o
 B  dA  0
dB
E  dl  
dt

Faraday’s Law


Ampere’s Law
 B  dl
 o I enclosed