SEE 2053 Teknologi Elektrik Chapter 2 Electromagnetism.

SEE 2053 Teknologi Elektrik

Chapter 2 Electromagnetism

Electromagnetism

1. Understand magnetic fields and their interactions with moving charges.

2. Use the right-hand rule to determine the direction of the magnetic field around a current-carrying wire or coil.

Electromagnetism

3. Calculate forces on moving charges and current carrying wires due to magnetic fields.

4. Calculate the voltage induced in a coil by a changing magnetic flux or in a conductor cutting through a magnetic field.

5. Use Lenz’s law to determine the polarities of induced voltages.

Electromagnetism6. Apply magnetic-circuit concepts to

determine the magnetic fields in practical devices.

7. Determine the inductance and mutual inductance of coils given their physical parameters.

8. Understand hysteresis, saturation, core loss, and eddy currents in cores composed of magnetic materials such as iron.

Electromagnetism

• Magnetism is a force field that acts on some materials (magnetic materials) but not on other materials (non magnetic 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)

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

Electromagnetism

Magnetic flux lines form closed paths that are close together where the field is strong and farther apart where the field is weak.

Electromagnetism

N N

SS

Strong field weak field

Magnetic materials (ferromagmagnetic): iron, steel, cobalt, nickel and some of their alloys.

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

Electromagnetism

The basic source of the magnetic field is electrical charge in motion. In magnetic materials, fields are created by the spin of electrons in atoms. These fields aid one another, producing the net external field that we observe. In most other materials (non magnetic materials), the magnetic 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

Electromagnetism

Iron bar

Magnetic molecules

In an unmagnetised state, the molecular magnets lie in random manner, hence there is no resultant external magnetism exhibited by the iron bar.

wood

Non-magnetic molecules

Electromagnetism

Iron bar

Magnetic molecules

When the iron bar is placed in a magnetic field or under the influence of a magnetising force, then these molecular magnets start turning their axes and orientate themselves more or less along a straight lines.

S N

SN

Electromagnetism

Iron barMagnetic molecules

When the iron bar is placed in a very strong magnetic field, all these molecular magnets orientate themselves along a straight lines (saturated).

S N

N S

Electromagnetism

Field Detector

• Can use a compass to map out magnetic field

• Field forms closed “flux lines” around the magnet (lines of magnetic flux never intersect)

• Magnetic flux measured in Webers (Wb)

• Symbol

Magnetic Flux

Magnetic flux lines are assumed to have the following properties:

• Leave the north pole (N) and enter the south pole (S) of a magnet.

• Like magnetic poles repel each other.• Unlike magnetic poles create a force of attraction.• Magnetic lines of force (flux) are assumed to be

continuous loops.

Magnetic Field Conductor

• Magnetic fields also exist in the space around wires that carry current.

• Field can be described using “right hand screw rule”

Right Hand Rule

• Thumb indicates direction of current flow

• Finger curl indicates the direction of field

Right-Hand Rule

Wire Coil

• Notice that a carrying-current coil of wire will produce a perpendicular field

Magnetic Field: Coil

• A series of coils produces a field similar to a bar magnet – but weaker!

Magnetic Field

Flux Ф can be increased by increasing the current I,

I

Ф I

Magnetic Field

Flux Ф can be increased by increasing the number of turns N,

I

Ф N

N

Magnetic Field

Flux Ф can be increased by increasing the cross-section area of coil A,

I

Ф A

N

A

Magnetic Field

Flux Ф is decreased by increasing the length of coil l,

I

Ф

N

A

1l

l

Magnetic Field

Therefore we can write an equation for flux Ф as,

I

Ф

N

A

NIAl

l

or

Ф =μ0 NIA

l

Where μ0 is vacuum or non-magnetic material permeability

μ0 = 4π x 10-7 H/m

Magnetic Field

Ф =μ0 NIA

l


• Placing a ferrous material inside the coil increases the magnetic field

• Acts to concentrate the field also notice field lines are parallel inside ferrous element

• ‘flux density’ has increased

Magnetic Field

By placing a magnetic material inside the coil,

I

N

A

lФ =

μ NIA

l

Where μ is the permeability of the magnetic material (core).

Flux Density

Permeability

• Permeability μ is a measure of the ease by which a magnetic flux can pass through a material (Wb/Am)

• Permeability of free space μo = 4π x 10-7 (Wb/Am)

• Relative permeability:

Reluctance• Reluctance: “resistance” to flow

of magnetic flux

Associated with “magnetic circuit” – flux equivalent to current

• What’s equivalent of voltage?

Magnetomotive Force, F

• Coil generates magnetic field in ferrous torroid

• Driving force F needed to overcome torroid reluctance

• Magnetic equivalent of ohms law

Circuit Analogy

Magnetomotive Force

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

current, measured in Ampere turns (At)

Field Intensity

• The longer the magnetic path the greater the MMF required to drive the flux

• Magnetomotive force per unit length is known as the “magnetizing force” H

• Magnetizing force and flux density related by:

Electric circuit:

Emf = V = I x R

Magnetic circuit:

mmf = F = Φ x

= (B x A) x

l

μ A= (B x A) x

l

μ= B x = H x l

= H x l

Hysteresis

• The relationship between B and H is complicated by non-linearity and “hysteresis”

= Φ x

l

μ A=

0.16

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

= 44004.4

= Φ x

= Φ x

= 4 x 10-4 x 44004.4

= 17.6

I = F

N =

17.6

400= 44 mA

Circuit Analogy

Leakage Flux and Fringing

Leakage flux

fringing

Leakage Flux

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

Leakage coefficient λ =Total flux produced

Useful flux available

Fringing

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

Forces on Charges Moving in Magnetic

Fields

Forces on Charges Moving in Magnetic

FieldsBuf q

sinquBf

Forces on Current-Carrying Wires

Blf idd

sinilBf

Force on a current-carrying conductor

It is found that whenever a current-carrying conductor is placed in a magnetic field, it experiences a force which acts in a direction perpendicular both to the direction of the current and the field.

N

S


It is found that whenever a current-carrying conductor is placed in a magnetic field, it experiences a force which acts in a direction perpendicular both to the direction of the current and the field.

N

S

On the left hand side, the two fields in the same direction

On the right hand side, the two fields in the opposition


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

N

S




Hence, the combined effect is to strengthen the magnetic field on the left hand side and weaken it on the right hand side, thus giving the distribution shown below.

N

S




This distorted flux acts like stretched elastic cords bend out of the straight , the line of the flux try to return to the shortest paths, thereby exerting a force F urging the conductor out of the way.

N

S


On the right hand side, the two fields in the oppositionF

Faraday’s Law

First Law.

Whenever the magnetic flux linked with a coil changes, an emf (voltage) is always induced in it.

Or

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

Faraday’s Law

Second Law.

The magnitude of the induced emf (voltage) is equal to the rate of change of flux-linkages.

dt

de

Nwhere

dt

Nd

dt

Nde

)(

Direction of Induced emf

The direction (polarity) of induced emf (voltage) can be determined by applying Lenz’s Law.

Lenz’s law is equivalent to Newton’s law.

Lenz’s law states that the polarity of the induced voltage is such that the voltagewould produce a current that opposes the change in flux linkages responsible for inducing that emf.

Lenz’s Law

N S

I

SELF INDUCTANCE, L

i

e

Φ

From Faraday’s Law:

dt

dNe

By substituting

Ф =μ NIA

l

v

SELF INDUCTANCE, L

i

e

Φ

Rearrange the equation, yield

dtl

NIAd

Ne

dt

di

l

ANe

2

v

SELF INDUCTANCE, L

i

e

Φdt

di

l

ANe

2

dt

diLe

or

where

l

ANL

2

v

MUTUAL INDUCTANCE, M

i

e1

ΦFrom Faraday’s Law:

v1 v2

e2

dt

dNe

22

Ф =μ N1i1A

l

substituting


i

e1

Φ

v1 v2

e2

rearrange

dt

l

AiNd

Ne

11

22

dt

di

l

ANNe 1

122


i

e1

Φ

v1 v2

e2

or

dt

di

l

ANNe 1

122

dt

diMe 1

2

where

l

ANNM 12


l

ANNM 12

For M 2,2

21

22

22

l

ANNM

l

ANM 2

12

l

AN 2

2 = L1 x L2


M 2 = L1 x L2

M = √(L1 x L2)

or

M = k√(L1 x L2)

k = coupling coeeficient (0 --- 1)

Dot ConventionAiding fluxes are produced by currents entering like marked terminals.

Hysteresis Loss

• Hysteresis loop

Uniform distribution

• From Faraday's law

Where A is the cross section area

Hysteresis Loss

• Field energy

Input power :

Input energy from t1 to t2

where Vcore is the volume of the core

Hysteresis Loss

• One cycle energy loss

where is the closed area of B-H hysteresis loop

• Hysteresis power loss

where f is the operating frequency and T is the period

Hysteresis Loss

• Empirical equation

Summary : Hysteresis loss is proportional to f and ABH

Eddy Current Loss• Eddy currentAlong the closed path, apply Faraday's law

where A is the closed areaChanges in B → = BA changes

→induce emf along the closed path→produce circulating circuit (eddy current) in the core

• Eddy current loss where R is the equivalent resistance along the closed path

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 closed

by closed path

Lamination thickness

0.5~5mm for machines, transformers at line frequency

0.01~0.5mm for high frequency devices

Eddy Current Loss

• Calculation of eddy current loss

– Finite element analysis

Use software: Ansys®, Maxwell®, Femlab®, etc

– Empirical equation

Core Loss

• Core Loss

losscurrenteddyP

losshysteresisPwhere

PPP

e

h

ehc

SEE 2053 Teknologi Elektrik Chapter 2 Electromagnetism.

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