Chapter2 Magnet

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SEE 2053 Teknologi Elektrik

Chapter 2

Electromagnetism


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Electromagnetism

1. Understand magnetic fields and theirinteractions with moving charges.

2.

Use the right-hand rule to determine thedirection of the magnetic field around acurrent-carrying wire or coil.


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Electromagnetism

3. Calculate forces on moving charges andcurrent carrying wires due to magneticfields.

4. Calculate the voltage induced in a coil by achanging magnetic flux or in a conductor

cutting through a magnetic field.5. Use Lenzs law to determine the polarities

of induced voltages.


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Electromagnetism

6.

Apply magnetic-circuit concepts todetermine the magnetic fields in practicaldevices.

7. Determine the inductance and mutualinductance of coils given their physicalparameters.

8. Understand hysteresis, saturation, coreloss, and eddy currents in cores composedof magnetic materials such as iron.


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Electromagnetism

Magnetism is a force field that acts onsome materials (magnetic materials)but not on other materials (nonmagnetic materials).

Magnetic field around a bar magnet Two poles dictated by direction of the

field

Opposite poles attract (aligned

magnetic field) Same poles repel (opposing magnetic

field)


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By convention, flux lines leave the north-seeking end (N) of a magnet and enter itssouth-seeking end (S).

Electromagnetism


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Magnetic flux lines form closed paths that areclose together where the field is strong andfarther apart where the field is weak.

Electromagnetism

N N

SS

Strong field weak field


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Magnetic materials (ferromagmagnetic): iron,

steel, cobalt, nickel and some of their alloys.

Non magnetic materials: water, wood, air,quartz, silver, copper etc.

Electromagnetism


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The basic source of the magnetic field is electrical chargein motion. In magnetic materials, fields are created bythe spin of electrons in atoms. These fields aid oneanother, producing the net external field that we observe.

In most other materials (non magnetic materials), themagnetic fields of electrons tend to cancel one another.

In a current-carrying wire, the moving electrons in the wire

create magnetic fields around the wire.

Electromagnetism


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Electromagnetism

Iron bar

Magnetic molecules

In an unmagnetised state, the molecular magnets lie inrandom manner, hence there is no resultant externalmagnetism exhibited by the iron bar.

wood

Non-magnetic molecules


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Electromagnetism

Iron bar

Magnetic molecules

When the iron bar is placed in a magnetic field or underthe influence of a magnetising force, then these molecularmagnets start turning their axes and orientate themselvesmore or less along a straight lines.

S N

SN


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Electromagnetism

Iron barMagnetic molecules

When the iron bar is placed in a very strong magneticfield, all these molecular magnets orientate themselvesalong a straight lines (saturated).

S N

NS


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Electromagnetism


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Field Detector

Can use a compass to mapout magnetic field

Field forms closed fluxlines around the magnet(lines of magnetic fluxnever intersect)

Magnetic flux measured inWebers (Wb)

Symbol *


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Magnetic Flux

Magnetic flux lines are assumed to have the followingproperties:

Leave the north pole (N) and enter the south pole (S) ofa magnet.

Like magnetic poles repel each other. Unlike magnetic poles create a force of attraction.

Magnetic lines of force (flux) are assumed to becontinuous loops.


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Magnetic Field Conductor

Magnetic fields alsoexist in the spacearound wires thatcarry current.

Field can bedescribed using righthand screw rule


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Right Hand Rule

Thumb indicatesdirection ofcurrent flow

Finger curlindicates thedirection of field


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Right-HandRule


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Wire Coil

Notice that acarrying-currentcoil of wire willproduce aperpendicularfield


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Magnetic Field: Coil

A series of coils produces a fieldsimilar to a bar magnet but weaker!


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Magnetic Field

*Flux can be increased byincreasing the currentI,

I

I


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Magnetic Field

*Flux can be increased byincreasing the number of turns N,

I

N

N


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Magnetic Field

*Flux can be increased byincreasing the cross-sectionarea of coil A,

I

A

N

A


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Magnetic Field

* Flux can be increased byincreasing the cross-sectionarea of coil A,

I

A

N

A


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Magnetic Field

* Flux is decreased byincreasing the length of coil l,

I

N

A

1

ll


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Magnetic Field

* Therefore we can write anequation for flux as,

I

N

A

NIA

ll

or

=

0NIA

l


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Where 0 is vacuum or non-magnetic materialpermeability

0= 4 x 10-7 H/m

Magnetic Field

=

0NIA

l


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Placing a ferrous materialinside the coil increases themagnetic field

Acts to concentrate the fieldalso notice field lines areparallel inside ferrous element

flux density has increased


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Magnetic Field

* By placing a magnetic materialinside the coil,

I

N

A

l =

NIA

l

Where is thepermeability of themagnetic material(core).


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Magnetic Field

* By placing a magnetic materialinside the coil,

I

N

A

l =

NIA

l

Where is thepermeability of themagnetic material(core).


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Flux Density


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Permeability

Permeability is a measure of the ease bywhich a magnetic flux can pass through amaterial (Wb/Am)

Permeability of free space o = 4 x 10-7(Wb/Am)

Relative permeability:


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Reluctance

Reluctance: resistance toflow of magnetic flux

Associated with magneticcircuit flux equivalent to

current Whats equivalent of voltage?


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Magnetomotive Force, F

Coil generates magneticfield in ferrous torroid

Driving force Fneededto overcome torroidreluctance

Magnetic equivalent ofohms law


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Circuit Analogy


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Magnetomotive Force

The MMF is generated by the coil Strength related to number of turns

and current, measured in Ampereturns (At)


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Field Intensity

The longer the magnetic path the greaterthe MMF required to drive the flux

Magnetomotive force per unit length is

known as the magnetizing force H

Magnetizing force and flux density relatedby:


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Electric circuit:

Emf = V = I x R

Magnetic circuit:

mmf = F = x

= (B x A) x

l

A= (B x A) x

l

= B x = H x l

= H x l


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Hysteresis

The relationship between Band Hiscomplicated by non-linearity andhysteresis


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= x

l

A=

0.16

1.818 x 10-3 x 2 x 10-3=

= 44004.4


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= x

= x

= 4 x 10-4 x 44004.4

= 17.6

I=F

N

=17.6

400= 44 mA


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Circuit Analogy


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Leakage Flux and Fringing

Leakage

flux

fringing


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Leakage Flux

It is found that it is impossible to confine all theflux to the iron path only. Some of the fluxleaks through air surrounding the iron ring.

Leakage coefficient =Total flux produced

Useful flux available


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Fringing

Spreading of lines of flux at the edges of theair-gap. Reduces the flux density in the air-gap.


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Forceson Charges Moving

in MagneticFields


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Forceson Charges Moving

in MagneticFields

Buf v! q

UsinquBf!


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Forceson Current-Carrying

Wires

Blfv!

idd

sinilBf!

Force on a current carrying


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Force on a current-carryingconductor

It is found that whenever a current-carryingconductor is placed in a magnetic field, itexperiences a force which acts in a directionperpendicular both to the direction of the current

and the field.

N

S



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It is found that whenever a current-carryingconductor is placed in a magnetic field, itexperiences a force which acts in a directionperpendicular both to the direction of the currentand the field.

N

S



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It is found that whenever a current-carryingconductor is placed in a magnetic field, itexperiences a force which acts in a directionperpendicular both to the direction of the currentand the field.

N

S

On the left hand side,the two fields in the

same direction

On the right handside, the two fields inthe opposition



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Hence, the combined effect is to strengthen themagnetic field on the left hand side and weaken iton the right hand side,

N

S


same direction




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Hence, the combined effect is to strengthen themagnetic field on the left hand side and weaken iton the right hand side, thus giving the distributionshown below.

N

S


same direction




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This distorted flux acts like stretched elastic cordsbend out of the straight , the line of the flux try toreturn to the shortest paths, thereby exerting aforce Furging the conductor out of the way.

N

S


same direction

On the right handside, the two fields inthe oppositionF


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Faradays Law

First Law.

Whenever the magnetic flux linked with acoil changes, an emf (voltage) is always

induced in it.Or

Whenever a conductor cuts magnetic flux,an emf (voltage) is induced in that

conductor.


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Faradays Law

Second Law.

The magnitude of the induced emf(voltage) is equal to the rate of change of

flux-linkages.

dt

de

P!

JP N!where

dt

Nd

dt

Nde

JJ!!

)(


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Direction of Induced emf

The direction (polarity) of induced emf(voltage) can be determined by applyingLenzs Law.

Lenzs law is equivalent toNewtons law.


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Lenzslawstates that the polarity ofthe induced voltage is such that thevoltage

would produce a current that opposesthe change in flux linkagesresponsible for inducing that emf.

LenzsLaw


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N S

I


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SELF INDUCTANCE,L

i

e

From Faradays Law:

dt

d

Ne

J

!

By substituting

=

NIA

l

v


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SELF INDUCTANCE,L

i

e

Rearrange theequation, yield

dt

l

NId

Ne

!

Q

dt

di

l

ANe

2Q

!

v


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SELF INDUCTANCE,L

i

e

dt

di

l

ANe

2Q!

dt

diLe !

or

where

l

ANL

2Q

!

v


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MUTUAL INDUCTANCE, M

i

e1

From Faradays Law:

v1 v2

e2

dtdNe J22 !

=

N1i1A

l

substituting


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i

e1

v1 v2

e2

rearrange

dt

l

AiNd

Ne

!

11

22

Q

dt

di

l

ANNe

1

122

! Q


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i

e1

v1 v2

e2

or

dt

di

l

ANNe

1

122

! Q

dt

diMe

1

2!

where

!

l

ANNM

12Q


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!

l

ANNM

12Q

ForM2,2

2

1

2

2

22

!

l

ANNM Q

!l

ANM

2

1

2Q

vl

AN

2

2Q = L1 x L2


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M2 = L1 x L2

M = (L1 x L2)

or

M = k(L1 x L2)

k = coupling coeeficient (0 --- 1)


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Dot Convention

Aiding fluxes are produced by currentsentering like marked terminals.

H t i L


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Hysteresis Loss

Hysteresis loopUniform distribution

From Faraday's law

WhereA is the cross section area

H t i L


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Hysteresis Loss

Field energyInput power :

Input energy from t1

to t2

where Vcore

is the volume of thecore

H t i L


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Hysteresis Loss

One cycle energy loss

where is the closed area ofB

-Hhysteresis loop Hysteresis power loss

where fis the operatingfrequency and Tis the period

H t i L


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Hysteresis Loss

Empirical equation

Summary : Hysteresis loss is proportional to fandABH

Edd C t L


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Eddy Current Loss

Eddy currentAlong the closed path, apply Faraday's law

whereA is the closed area

Changes in B = BA changes

induce emf along the closed pathproduce circulating circuit (eddy current) in the core

Eddy current losswhere R is the equivalent resistance along theclosed path

*

Edd C t L


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Eddy Current Loss

How to reduce Eddy current loss Use high resistivity core material

e.g. silicon steel, ferrite core (semiconductor)

Use laminated core

To decrease the area closedby closed path

Lamination thickness0.5~5mm for machines, transformers at line frequency

0.01~0.5mm for high frequency devices

Edd C t L


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Eddy Current Loss

Calculation of eddy current loss Finite element analysis

Use software: Ansys, Maxwell, Femlab, etc

Empirical equation

C L


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Core Loss

Core Loss

losscurrenteddyP

losshysteresisPwhere

PPP

e

h

ehc

!

!

!

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Chapter2 Magnet

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