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Lecture Topics
Sources of magnetic fields
Magnetization M
B, H, and M relationship
Diamagnetic materials
Paramagnetic materials
Ferromagnetic materials
ELEC 3105 Basic EM and Power Engineering
2
Sources of magnetic fields
From postulate 2: Currents in wires
produce magnetic fields.
26
MagnetostaticsPOSTULATE POSTULATE 22FOR THE MAGNETIC FIELDFOR THE MAGNETIC FIELD
A current element produces a magnetic field which at a distance Ris given by:
d
R
RIBd o
2
ˆ
4
dI
B
Bd
Units of {T,G,Wb/m2}
5
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 bar magnet.
Sources of magnetic fields
6
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.
Sources of magnetic fields
Equivalent views of the bar magnet
Sources of magnetic fields
The magnetization M of the bar can be interpreted through the two points of view.
8
Magnetization M 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)
The magnetization is defined as the average dipole moment per unit volume:
M
v
mM
The units of {M} are Amperes per meter.
m
A
v is a small volume that contains many atomic dipoles.
Knowing implies that we not concern ourselves with the individual atomic dipole moments.
M
Recallv
pP
for polarization
Magnetization M
Equivalent charge formulism
Equivalent current formulism
sm Magnetic surface charge density
mK Magnetic surface current density
Magnetization M
13
B, H, and M relationship
MHBoo
H
o
This term gives the contribution to the flux density due to the real current I in the windings of the toroid.
B
Mo
This term gives the additional contribution to the flux density due to the induced magnetization in the core material.
B
M
B, H, and M relationship and permeability
14
For an air core toroid we have: 0M
Thus MHBoo
becomes HB
o
When we can rewrite
in a similar linear relationship
0M
MHBoo
HB
1
2
1 2
FROM
we can obtain:
H
Mo
1
15
B, H, and M relationship and permeability
Introducing the relative permeability:
Thus
H
Mo
1
H
Mr
1
Then
or
4
M a g n e t o s t a t ic sP e r m e a b i l i t yP e r m e a b i l i t y
or P e r m e a b i l i t y o f f r e e s p a c e
R e l a t i v e p e r m e a b i l i t y f o r a m e d i u m
P e r m e a b i l i t y o f t h e m e d i u m
m
Ho
7104
m
Wb
m
HE x a c t c o n s t a n t
16
B, H, and M relationship
We will now examine the nature of the magnetization M
The three classes of magnetic materials are:
DIAMAGNETICPARAMAGNETIC
FERROMAGNETICThe 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 which are non-magnetic o
17
B, H, and M relationship
When no magnetic material is introduced in the solenoid the magnetic field at the point P is Bo.
P
Introducing various cores in the solenoid we observe that Bo changes to B
DIAMAGNETIC
PARAMAGNETIC
FERROMAGNETIC
1o
B
B
1o
B
B
1o
B
B
19
*Diamagnetic materials
HMm
HMr
1
Diamagnetic materials display no permanent magnetization. That is, when H is removed M vanishes.
Linear function
.0m
20
*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.
21
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.
1o
B
B Bo appliedB measured in material
Diamagnetic materials
A diamagnetic material placed in a magnetic field is repelled, pushed out of the magnetic field region. The effect is very small.
2IF
F is greatest where B is greatest.
IB
Im
since
24
Diamagnetism
Push me a grape.
Material
• Two large grapes
• Drinking straw
• Film canister with lid
• Push pin
• Small knife or razor blade
• Neodymium magnet
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.
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.
25
Diamagnetism
The grape will be repelled by the magnet and begin to move slowly away from the magnet. Pull the magnet away and let the grape stop its motion. Turn the magnet over and bring the other pole near the grape. The grape will also be repelled by the other pole; the grape is repelled by both poles of the magnet.
Bring one pole of the magnet near the grape. Do not touch the grape with the magnet.
26
DiamagnetismFerromagnetic materials, such as iron, are strongly attracted to both poles of a magnet. Paramagnetic materials, such as aluminum, are weakly attracted to both poles of a magnet. Diamagnetic materials, however, are repelled by both poles of a magnet. The diamagnetic force of repulsion is very weak (a hundred thousand times weaker than the ferromagnetic force of attraction). Water, the main component of grapes, is diamagnetic.
When an electric charge moves, a magnetic field is created. Every electron is therefore a very tiny magnet, because electrons carry charge and they spin. Additionally, the motion of an orbital electron is an electric current, with an accompanying magnetic field. In atoms of iron, cobalt, and nickel, electrons in one atom will align with electrons in neighboring atoms, making regions called domains, with very strong magnetization. These materials are ferromagnetic, and are strongly attracted to magnetic poles.
Atoms and molecules that have single, unpaired electrons are paramagnetic. Electrons in these materials orient in a magnetic field so that they will be weakly attracted to magnetic poles. Hydrogen, lithium, and liquid oxygen are examples of paramagnetic substances. Atoms and molecules in which all of the electrons are paired with electrons of opposite spin, and in which the orbital currents are zero, are diamagnetic. Helium, bismuth, and water are examples of diamagnetic substances.
If a magnet is brought toward a diamagnetic material, it will generate orbital electric currents in the atoms and molecules of the material. The magnetic fields associated with these orbital currents will be oriented such that they repelled by the approaching magnet.
This behavior is predicted by a law of physics known as Lenz's Law. This law states that when a current is induced by a change in magnetic field (the orbital currents in the grape created by the magnet approaching the grape), the magnetic field produced by the induced current will oppose the change.
What’s going on
27
Paramagnetic materials
HMm
HMr
1
Paramagnetic materials display no permanent magnetization. That is, when H is removed M vanishes.
Linear function
.0m
28
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.
oB
29
A paramagnetic material placed in a magnetic field is attracted into the higher magnetic field regions. The effect is very small.
2IF
F is greatest where B is greatest.
IB
Im
since
Paramagnetic materials
AluminumNS
30
Paramagnetic materials HMm
HMr
1 Linear function
.0m
Temperature dependence of M
mB
kT
kT
mBNmM )coth(
Temperature dependence of m
kT
Nmo
m 3
2
Ferromagnetic materials
HHMm
HHMr
1 H
r Are functions of the
applied magnetic field H. Hm
Tc = Currie temperature
Ferromagnetic region
Paramagnetic region
32
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.
33
Ferromagnetic materials WHY?
• 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.
What happens when a magnetic field is applied.
Ferromagnetic materials show hysteresis in the B versus H curve.
Ferromagnetic materials
SOFT and HARD Ferromagnetic materials
Soft ::: transformer cores, solenoids, ….Hard :: permanent magnets
Area of hysteresis loop is equivalent to energy lost in one cycle. (Proof found in transformer loss mechanisms)
Ferromagnetic materials
A ferromagnetic material placed in a magnetic field is strongly attracted towards the regions of higher magnetic field.
IF
F is greatest where B is greatest.
IB
m
constant
since
40
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.
Note Radio Shack is now “The Source”
41
Assembly
(15 minutes or less)
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. To do and notice
(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.
Curie Point
42
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.
Curie Point