Transcript Sources of magnetic fields

ELEC 3105 Basic EM and Power Engineering
Lecture Topics
Sources of magnetic fields
Magnetization M
B, H, and M relationship
Diamagnetic materials
Paramagnetic materials
Ferromagnetic materials
Magnetostatics
POSTULATE 2 FOR THE MAGNETIC FIELD

A current
element I d produces a magnetic

field B which at a distance R is given by:
From postulate 2:
Currents in wires
produce magnetic fields.

  o I  Rˆ
dB 
d
4 R 2

dB
Units of {T,G,Wb/m2}
2
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3
4
Qm is considered as an equivalent magnetic charge.
Magnetic charges do not exist but some times it is easier
to think that they do in order to visualize cause and effect
in magnetic field situations. Qm would be for the entire
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bar magnet.
qm is considered as an equivalent magnetic charge that produces
the same magnetic field as a current loop of current I. qm would
be for a single current loop. Note that
the loop can be formed by a single
spinning electron about the nucleus.
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Equivalent
views of the
bar magnet
The magnetization M of the bar can be interpreted through
the two points of view.
The tiny magnets produced by
electrons spinning about the nucleus
are the source of the magnetic field
produced by a bar magnet and
magnetizable materials.
This can be formalized by
introducing the
magnetization. (Describes
the MAGNET in the
macroscopic domain)
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
The magnetization M is defined as the average
dipole moment per unit volume:

 m
M
v
The units of {M} are Amperes per meter.
v
 A
 
m 
is a small volume that contains many atomic dipoles.

Knowing M implies that we not concern ourselves with the
individual atomic dipole moments.
Recall
 p
P
v
for polarization
Equivalent charge formulism

sm
Magnetic surface charge density
Equivalent current formulism
K
Magnetic surface current density
m
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


B H  M
o
o

B

H

M
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Mag. Flux density.
Mag. Field strength
Magnetization

H



B H  M
o
o
o
This term gives the contribution

to the flux density B due to the
real current I in the windings of
the toroid.

M
o
This term gives the additional 
contribution to the flux density B 
due to the induced magnetization M
in the core material.
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
For an air core toroid we have: M  0
Thus



B H  M
o
o
becomes


B H
o




When M  0 we can rewrite B   o H   o M
1
in a similar linear relationship
2
FROM
1
2
we can obtain:


B  H
 M
   1  
 H
o
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 M
   1  
Thus
 H
Introducing the relative permeability:
o
 M
  1  
 H
r
Magnetostatics
Then
Permeability
  r o
 
r
Permeability of free space
Relative permeability for a medium
o
H 

m
 o  4 107 
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Exact constant
Permeability of the medium
H 
Wb 
  
m
m
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We will now examine the nature of the magnetization M
The three classes of magnetic materials are:
DIAMAGNETIC
PARAMAGNETIC
FERROMAGNETIC
The material is characterized by the
effect they have on the magnetic
field. In the case chosen we will
examine the magnetic field of a
solenoid.
Of course you have materials which16are non-magnetic
 
o
P
When no magnetic
material is introduced in
the solenoid the magnetic
field at the point P is Bo.
Introducing various cores in the solenoid we observe that Bo changes to B
DIAMAGNETIC
B
1
B
o
PARAMAGNETIC
B
1
B
o
FERROMAGNETIC
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B
 1
B
o
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* Diamagnetic materials
M    1H
r
Linear function
Diamagnetic materials
display no permanent
magnetization. That is, when
H is removed M vanishes.
M  H
m
 m  0.
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* Diamagnetic materials WHY?
• Results from the orbital motion of the electrons
• Each circulating electron acts as a current loop producing a magnetic field
• Two electrons travel in each orbit and in opposite direction
• The magnetic moment produced my each electron of the orbit cancel.
• This explains why diamagnetic materials have no residual magnetization.
What happens when a magnetic field is applied.
• One electron in the orbit will speed up
• One electron in the orbit will slow down.
• Effect is such that net magnetic moment is opposite to the applied field.
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Diamagnetic materials WHY?
• Results from the orbital motion of the electrons
• Each circulating electron acts as a current loop producing a magnetic field
• Two electrons travel in each orbit and in opposite direction
• The magnetic moment produced my each electron of the orbit cancel.
• This explains why diamagnetic materials have no residual magnetization.
What happens when a magnetic field is applied.
• One electron in the orbit will speed up
• One electron in the orbit will slow down.
• Effect is such that net magnetic moment is opposite to the applied field.
There is a reduction in the magnetic flux density.
B
1
B
Bo applied
B measured in material
o
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Diamagnetic materials
A diamagnetic material placed in a
magnetic field is repelled, pushed
out of the magnetic field region. The
effect is very small.
FI
since
F is greatest where B is greatest.
2

 m  I
 B  I
Diamagnetic materials
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Diamagnetism
Push me a grape.
A grape is repelled by both the north and
south poles of a strong rare-earth magnet. The
grape is repelled because it contains water,
which is diamagnetic. Diamagnetic materials
are repelled by magnetic poles.
Material
• Two large grapes
• Drinking straw
• Film canister with lid
• Push pin
• Small knife or razor blade
• Neodymium magnet
Assembly
Insert the push pin through the underside of the film
canister lid and put the lid on the canister so that the
point of the pin is sticking out.
Find the center of the drinking straw and use the knife to
cut a small hole, approximately 0.5 cm x 1 cm. (You can
also use the hot tip of a soldering gun to melt a hole.)
Push one grape onto each end of the straw. Balance the
straw with the grapes on the point of the push pin; the
point of the pin goes through the small hole on the straw.
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Paramagnetic materials
M    1H
r
Linear function
Paramagnetic materials
display no permanent
magnetization. That is, when
H is removed M vanishes.
M  H
m
 m  0.
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Paramagnetic materials WHY?
• Results from the spin motion of the electron
• Each electron has an magnetic moment
• Thermal motion randomly orients the associated magnetic moments
• This explains why paramagnetic materials have no residual magnetization.
What happens when a magnetic field is applied.
• The axis of the spins for the electrons align in the direction of the field
• Magnetic dipoles tend to align with the magnetic field
• Alignment is only partial due to thermal effects.

B
o
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Paramagnetic materials
N
S
Aluminum
A paramagnetic material placed in a
magnetic field is attracted into the
higher magnetic field regions. The
effect is very small.
FI
since
F is greatest where B is greatest.
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2

 m  I
 B  I
Paramagnetic materials
M    1H
r
M  H
m
Linear function
Temperature dependence of M
mB kT 

M  Nmcoth( ) 

kT
mB 

Temperature dependence of m
Nm 
 
3kT
2
o
m
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 m  0.
Ferromagnetic materials
M   H   1H
r
 H 
 H 
r
Are functions of the
applied magnetic field H.
m
Ferromagnetic region
M   H H
m
Tc = Currie temperature
Paramagnetic region
Ferromagnetic materials WHY?
• Results from the spin motion of the electron
• Strong inter molecular fields are present which act on individual electron spins
• Spins of the molecules align over small regions called domains
• No external field is required to align spins within a domain
• No net magnetization observed since domain moments point in random directions.
What happens when a magnetic field is applied.
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Ferromagnetic materials WHY?
What happens when a magnetic field is applied.
• As the magnetic filed is increased, the domain which is most closely
aligned with the applied magnetic field will grow. This growth is at the
expense of those domains not in alignment with the applied magnetic field.
• Domain growth continues until the entire material consist of one domain.
• Domain rotation will then occur in order to complete the alignment of the
magnetic moment with the applied filed, saturating the effect.
Ferromagnetic materials show
hysteresis in the B versus H curve.
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Ferromagnetic materials WHY?
What happens when we cycle the applied magnetic field.
Ferromagnetic materials
SOFT and HARD Ferromagnetic materials
Area of hysteresis loop
is equivalent to energy
lost in one cycle. (Proof
Soft ::: transformer cores, solenoids, ….
Hard :: permanent magnets
found in transformer loss mechanisms)
Ferromagnetic materials
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Ferromagnetic materials
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Ferromagnetic materials
no domains remain
Behaves as a paramagnetic material
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Ferromagnetic materials
A ferromagnetic material placed in a
magnetic field is strongly attracted
towards the regions of higher
magnetic field.
FI
since
F is greatest where B is greatest.

 m  constant
 B  I
Curie Point
When a piece of iron gets too hot, it is no longer attracted to a
magnet.
A piece of iron will ordinarily be attracted to a magnet,
but when you heat the iron to a high enough temperature
(called the Curie point), it loses its ability to be
magnetized. Heat energy scrambles the iron atoms so that
they can't line up and create a magnetic field. Here is a
simple demonstration of this effect
Material
A small magnet. (Radio Shack's disk magnets work fine.)
A stand to hold the magnet pendulum and wire. (The stand can be easily made from
Tinkertoys™ or pieces of wood.)
One 6-volt lantern battery (or other 6-volt power supply).
2 electrical lead wires with alligator clips at both ends (available at Radio Shack).
One 3-inch (8 cm) length of thin iron wire, obtainable by separating one strand from
braided picture-hanging wire.
String, about 1 foot (30 cm) long.
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Note Radio Shack is now “The Source”
Curie Point
Assembly
(15 minutes or less)
To do and notice
Make a stand from Tinkertoys™ or other wood
as shown in the diagrams. Suspend the magnet
from the top of the stand with a string. Make a
pendulum at least 4 inches (10 cm) long. Stretch
the iron wire between two posts so that, at its
closest, the wire is 1 inch (2.5 cm) from the
magnet.
(15 minutes or more)
Touch the magnet to the iron wire. It should magnetically attract and stick to the wire.
Connect the clip leads to the terminals of the lantern battery. Connect one clip lead to one side of the
iron wire, and touch the other clip lead to the iron wire on the opposite side of the magnet. Current
will flow through the iron wire, causing the wire to heat up. (CAUTION: The wire will get hot!) As
the iron heats up and begins to glow, the magnet will fall away from the wire. Take a clip lead away
from the iron wire. Let the iron wire cool. When the iron wire is cool, notice that the magnet will
stick to it once again.
If the wire does not heat up enough to glow red, move the clip leads closer together.
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Curie Point
What’s going on:
The iron wire is made of atoms that act like tiny magnets, each one having a north
and south pole of its own. These iron atoms usually point in all different directions,
so the iron has no net magnetic field. But when you hold a magnet up to the iron, the
magnet makes the iron atoms line up. These lined-up atomic magnets turn the iron
into a magnet. The iron is then attracted to the original magnet.
High temperatures can disturb this process of magnetization. Thermal energy makes
the iron atoms jiggle back and forth, disturbing their magnetic alignment. When the
vibration of the atoms becomes too great, the atomic magnets do not line up as well,
and the iron loses its magnetism. The temperature at which this occurs is called the
Curie point
Inside the earth, there is a core of molten iron. This iron is at a
temperature above the Curie point and therefore can't be
magnetized. Yet the earth is magnetized, with a north and a south
magnetic pole. The magnetic field of the earth comes from an
electromagnet, that is, from electrical currents flowing inside the
liquid metal core.
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