Lecture Topics Sources of magnetic fields Magnetization M B, H, and M relationship Diamagnetic...

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


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}

3


4


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.


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.


Equivalent views of the bar magnet


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

11


12


MHBoo

B

H

M

Magnetization

Mag. Flux density.

Mag. Field strength

13


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


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


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

18


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.


• 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


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

23


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


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.


• 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


IB

Im

since


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


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.


33


• 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.


What happens when we cycle the applied magnetic field.


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)

36


37


38


no domains remain

Behaves as a paramagnetic material


A ferromagnetic material placed in a magnetic field is strongly attracted towards the regions of higher magnetic field.

IF


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

Lecture Topics Sources of magnetic fields Magnetization M B, H, and M relationship Diamagnetic...

Documents

Transcript of Lecture Topics Sources of magnetic fields Magnetization M B, H, and M relationship Diamagnetic...