Chapter 4 Magnetic Circuits Part A

7/27/2019 Chapter 4 Magnetic Circuits Part A

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Chapter 4 Magnetic Circuits

Part A


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Course Contents

Magnetic materials: diamagnetic material,

paramagnetic material,

ferromagnetic material.

Hysteresis loss and eddy current loss, reluctanceand permeance.

Analysis of linear magnetic circuits (with air-gapproblems).

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Magnetic Materials

All materials are composed of atoms, each with a positively chargednucleus and a number of orbiting negatively charged electrons.

Magnetization describes to what extent they are affected bymagnetic fields, and also determines the magnetic field that thematerial itself creates.

Magnetizationin a material is mostly due to the magnetic moment ofelectrons, generated by two principal mechanisms:

(1) orbital motionof the electrons, mo

(2) spinning motionsof the electrons, ms

Orbiting electron Spinning electron

nucleus

(2)Spinning electron(1)Orbiting electron

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Magnetic Moment

Magnetic moment, m = loop areaAcurrent I.

T = time for one revolution =

u = velocity of the electron

Le= angular momentum = meur

meis electron mass

Orbital magnetic moment,

Spin magnetic moment,

= h/2,

h is Plancks constant

Le= 0, ,2,

u

r2

r

eu

T

eI

2

e

e

Lm

em

eur

rr

eu

IAm

2

2

2

0

2

0

em

em

20

e

s

m

em

2

4

sJ106.626-34

h


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Magnetic Permeability Magnetization vector M= vector sum of magnetic dipole momentsof

the atoms contained in a unit volumeof the material. (Unit= (A xm2)/m3= A/m)

Total Magnetic flux density,

B= 0H + 0M = 0(H+M)

M= mH where mis magnetic susceptibility constant.

m - Degree of magnetization of a material in response to an applied magnetic field B = 0 (H+ mH) = 0(1 + m)H

B = H

= 0 (1 + m) , r =/0 =1 + m

Permeability, : Degree of magnetization of a material that responds

linearly to applied magnetic field.

External appliedmagnetic field

Magnetization ofthe material

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Diamagnetism In this material, all the orbital moments pair off.

When His applied, electrons in this material rearrangetheir orbital motionand the magnetic moment will opposeH.

Diamagnetic materials have a very weak and negativesusceptibility (m) to external magnetic fields.

Fig: Orbital diagram forNeon (1s22s22p6)- 10 electrons

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Diamagnetism

Diamagnetic materials do not exhibit permanentmagnetism, and the induced magnetic momentdisappears when the applied field is withdrawn.

Ex.: hydrogen, copper, gold, silicon, germanium,graphite, bismuth, helium, sulfur.

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Paramagnetism

Paramagnetic materials have some unpaired electrons that producethe net spin magnetic momentswhich tend to alignthemselves in thedirection of the external magnetic field.

They are weakly attracted to magnets and have a small positivesusceptibility (m) to magnetic fields.

Paramagnetism is temperature dependent:It becomes more magnetic when its temperature reduces.

It becomes less magnetic when its temperature increases.

Ex.: Aluminum, Platinum, air, potassium, tungsten, liquid oxygen.

Fig: Orbital diagram forAluminium

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Ferromagnetism

In these materials strong interactions between atomicmagnetic momentscause them to line up parallel to eachother in regions called magnetic domains.

When there is no externally applied field, the orientationsof the domain magnetizations are random.

But when H field is applied, they tend to orientthemselves parallel to the field. The domain boundariesalso shift, the domains magnetized in the field directiongrow (A), and those magnetized in other directions shrink

(C).

Fig: Domaintheory

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Ferromagnetism

Ferromagnetic materials have a large andpositive susceptibility to an external magneticfield.

Ferromagnetic materials lose all their magneticproperties if they are heated to a high enough

temperature, due to the magnetized domains willorganize themselves randomly after their atomsare being heated.

The temperature at which a ferromagneticmaterial loses its magnetism is called the Curie

temperatureand it is different for every metal.

Ex: cobalt, nickel, iron are usually used tofabricate permanent magnets due to the abilityto retain their magnetism properties for longtime.

Fig: Curie point

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Ferromagnetism

Experiment of CurieTemp.: Nickel-iron asferromagnetic.

Domains of electronsalign causing thesample to be attracted

to the magnet. Heating the sample

scrambles thealignment of theelectrons.

The sample is no

longer attracted to themagnet.

After the sample hascooled down, theelectrons realign andthe ferromagnetismreturns.

After 25 seconds

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Properties of Magnetic Materials

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Documents

Chapter 4 Magnetic Circuits Part A