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Electromagnetic Define and explain Faraday Law, Flemming Law, magnetic field, magnetik material, Magnetisation curve Define and explain magnetic equivalent circuit, electromagnetic induction, Sinusoidal excitation, Lenz’s law. Analyze and explain magnetic losses, eddy current, hysterisis

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Page 1: Electromagnetic Define and explain Faraday Law, Flemming Law, magnetic field, magnetik material, Magnetisation curve Define and explain magnetic equivalent

ElectromagneticDefine and explain Faraday Law, Flemming Law, magnetic field, magnetik material, Magnetisation curve

Define and explain magnetic equivalent circuit, electromagnetic induction, Sinusoidal excitation, Lenz’s law.

Analyze and explain magnetic losses, eddy current, hysterisis

Page 2: Electromagnetic Define and explain Faraday Law, Flemming Law, magnetic field, magnetik material, Magnetisation curve Define and explain magnetic equivalent

CHAPTER 11

MAGNETIC FIELDS

Page 3: Electromagnetic Define and explain Faraday Law, Flemming Law, magnetic field, magnetik material, Magnetisation curve Define and explain magnetic equivalent

11.2 Magnetic Fields

In the region surrounding a permanent magnet there exists a magnetic field, which can be represented by magnetic flux lines similar to electric flux lines.

Magnetic flux lines differ from electric flux lines in that they don’t have an origin or termination point.

Magnetic flux lines radiate from the north pole to the south pole through the magnetic bar.

Page 4: Electromagnetic Define and explain Faraday Law, Flemming Law, magnetic field, magnetik material, Magnetisation curve Define and explain magnetic equivalent

11.2 Magnetic Fields

Flux distribution for a permanent magnet

Page 5: Electromagnetic Define and explain Faraday Law, Flemming Law, magnetic field, magnetik material, Magnetisation curve Define and explain magnetic equivalent

11.2 Magnetic Fields

Continuous magnetic flux lines will strive to occupy as small an area as possible.

The strength of a magnetic field in a given region is directly related to the density of flux lines in that region.

If unlike poles of two permanent magnets are brought together the magnets will attract, and the flux distribution will be as shown below.

Page 6: Electromagnetic Define and explain Faraday Law, Flemming Law, magnetic field, magnetik material, Magnetisation curve Define and explain magnetic equivalent

11.2 Magnetic Fields

Flux distribution for two adjacent, opposite poles

Page 7: Electromagnetic Define and explain Faraday Law, Flemming Law, magnetic field, magnetik material, Magnetisation curve Define and explain magnetic equivalent

11.2 Magnetic Fields If like poles are brought together, the magnets

will repel, and the flux distribution will be as shown.

Page 8: Electromagnetic Define and explain Faraday Law, Flemming Law, magnetic field, magnetik material, Magnetisation curve Define and explain magnetic equivalent

11.2 Magnetic Fields

If a nonmagnetic material, such as glass per, is placed in the flux paths surrounding a permanent magnet, there will be an almost unnoticeable change in the flux distribution.

If a nonmagnetic material, such as copper, is placed in the flux paths surrounding a permanent magnet, there will be an almost noticeable change in the flux distribution.

Page 9: Electromagnetic Define and explain Faraday Law, Flemming Law, magnetic field, magnetik material, Magnetisation curve Define and explain magnetic equivalent

11.2 Magnetic Fields

Page 10: Electromagnetic Define and explain Faraday Law, Flemming Law, magnetic field, magnetik material, Magnetisation curve Define and explain magnetic equivalent

11.2 Magnetic Fields

This principle is put to use in the shielding of sensitive electrical elements and instruments that can be affected by stray magnetic fields.

Page 11: Electromagnetic Define and explain Faraday Law, Flemming Law, magnetic field, magnetik material, Magnetisation curve Define and explain magnetic equivalent

11.2 Magnetic Fields

A current-carrying conductor develops magnetic fields in the form of concentric circle around it.

Page 12: Electromagnetic Define and explain Faraday Law, Flemming Law, magnetic field, magnetik material, Magnetisation curve Define and explain magnetic equivalent

11.2 Magnetic Fields

If the coil is wound in a single-turn coil, the resulting flux flows in a common direction through the centre of the coil.

Page 13: Electromagnetic Define and explain Faraday Law, Flemming Law, magnetic field, magnetik material, Magnetisation curve Define and explain magnetic equivalent

11.2 Magnetic Fields

A coil of more than one turn produces a magnetic field that exists in a continuous path through and around the coil.

Page 14: Electromagnetic Define and explain Faraday Law, Flemming Law, magnetic field, magnetik material, Magnetisation curve Define and explain magnetic equivalent

11.2 Magnetic Fields

The flux distribution around the coil is quite similar to the permanent magnet.

The flux lines leaving the coil from the left and entering to the right simulate a north and a south pole.

The concentration of flux lines in a coil is less than that of a permanent magnet.

Page 15: Electromagnetic Define and explain Faraday Law, Flemming Law, magnetic field, magnetik material, Magnetisation curve Define and explain magnetic equivalent

11.2 Magnetic Fields

The field concentration (or field strength) may be increased effectively by placing a core made of magnetic materials (e.g. iron, steel, cobalt) within the coil – electromagnet.

Page 16: Electromagnetic Define and explain Faraday Law, Flemming Law, magnetic field, magnetik material, Magnetisation curve Define and explain magnetic equivalent

11.2 Magnetic Fields

The field strength of an electromagnet can be varied by varying one of the component values (i.e. currents, turns, material of the core etc.)

Page 17: Electromagnetic Define and explain Faraday Law, Flemming Law, magnetic field, magnetik material, Magnetisation curve Define and explain magnetic equivalent

11.2 Magnetic FieldsThe direction of the magnetic flux lines can be

found by placing the thumb of the right hand in the direction of conventional current flow and noting the direction of the fingers (commonly called the right hand rule).

Page 18: Electromagnetic Define and explain Faraday Law, Flemming Law, magnetic field, magnetik material, Magnetisation curve Define and explain magnetic equivalent

11.2 Magnetic Fields

Page 19: Electromagnetic Define and explain Faraday Law, Flemming Law, magnetic field, magnetik material, Magnetisation curve Define and explain magnetic equivalent

11.2 Magnetic Fields

Flux and Flux Density

In the SI system of units, magnetic flux is measured in webers (Wb) and is represented using the symbol

Page 20: Electromagnetic Define and explain Faraday Law, Flemming Law, magnetic field, magnetik material, Magnetisation curve Define and explain magnetic equivalent

Wilhelm Eduard Weber (1804 – 1891)Prof. of Physics, University of Göttingen

Page 21: Electromagnetic Define and explain Faraday Law, Flemming Law, magnetic field, magnetik material, Magnetisation curve Define and explain magnetic equivalent

11.2 Magnetic FieldsThe number of flux lines per unit area is

called flux density (B). Flux density is measured in teslas (T).

Its magnitude is determined by the following equation:

1 tesla = 1 T = 1 Wb/m2

Page 22: Electromagnetic Define and explain Faraday Law, Flemming Law, magnetic field, magnetik material, Magnetisation curve Define and explain magnetic equivalent

Nikola Tesla (1856 – 1943)Electrical Engineer and Inventor Recipient of the Edison Medal in 1917.

Page 23: Electromagnetic Define and explain Faraday Law, Flemming Law, magnetic field, magnetik material, Magnetisation curve Define and explain magnetic equivalent

11.2 Magnetic Fields

• The flux density of an electromagnet is directly related to:

• the number of turns of

• the current through

the coil

The product is the magnetomotive force:

At turns,-ampereNI

Page 24: Electromagnetic Define and explain Faraday Law, Flemming Law, magnetic field, magnetik material, Magnetisation curve Define and explain magnetic equivalent

11.2 Magnetic Fields

PermeabilityAnother factor affecting the field strength is

the type of core used.

If cores of different materials with the same physical dimensions are used in the electromagnet, the strength of the magnet will vary in accordance with the core used.

The variation in strength is due to the number of flux lines passing through the core.

Page 25: Electromagnetic Define and explain Faraday Law, Flemming Law, magnetic field, magnetik material, Magnetisation curve Define and explain magnetic equivalent

11.2 Magnetic Fields

Magnetic material is material in which flux lines can readily be created and is said to have high permeability.

Permeability () is a measure of the ease with which magnetic flux lines can be established in the material.

Page 26: Electromagnetic Define and explain Faraday Law, Flemming Law, magnetic field, magnetik material, Magnetisation curve Define and explain magnetic equivalent

11.2 Magnetic Fields

Permeability of free space 0 (vacuum) is

Materials that have permeability slightly less than that of free space are said to be diamagnetic and those with permeability slightly greater than that of free space are said to be paramagnetic.

Wb/A.m104 7 o

Page 27: Electromagnetic Define and explain Faraday Law, Flemming Law, magnetic field, magnetik material, Magnetisation curve Define and explain magnetic equivalent

11.2 Magnetic Fields

Magnetic materials, such as iron, nickel, steel and alloys of these materials, have permeability hundreds and even thousands of times that of free space and are referred to as ferromagnetic.

The ratio of the permeability of a material to that of free space is called relative permeability:

or

Page 28: Electromagnetic Define and explain Faraday Law, Flemming Law, magnetic field, magnetik material, Magnetisation curve Define and explain magnetic equivalent

11.2 Magnetic Fields

In general for ferromagnetic materials,

For nonmagnetic materials,

Relative permeability is a function of operating conditions.

100r

1r

Page 29: Electromagnetic Define and explain Faraday Law, Flemming Law, magnetic field, magnetik material, Magnetisation curve Define and explain magnetic equivalent

11.4 Induced Voltage If a conductor is moved through a magnetic

field so that it cuts magnetic lines of flux, a voltage will be induced across the conductor.

Page 30: Electromagnetic Define and explain Faraday Law, Flemming Law, magnetic field, magnetik material, Magnetisation curve Define and explain magnetic equivalent

11.4 Induced Voltage

The magnitude of the induced voltage is directly related to the speed of movement (i.e. at which the flux is cut).

Moving the conductor in parallel with the flux lines will result in zero volt of induced voltage.

dt

de

Page 31: Electromagnetic Define and explain Faraday Law, Flemming Law, magnetic field, magnetik material, Magnetisation curve Define and explain magnetic equivalent

11.4 Induced Voltage If a coil of conductor instead of a straight

conductor is used, the resultant induced voltage will be greater

Faraday’s law of electromagnetic induction

If a coil of N turns is placed in the region of the changing flux, as in the figure below, a voltage will be induced across the coil as determined by Faraday’s Law.

Page 32: Electromagnetic Define and explain Faraday Law, Flemming Law, magnetic field, magnetik material, Magnetisation curve Define and explain magnetic equivalent

11.4 Induced Voltage

Page 33: Electromagnetic Define and explain Faraday Law, Flemming Law, magnetic field, magnetik material, Magnetisation curve Define and explain magnetic equivalent

11.4 Induced Voltage

Changing flux also occurs in a coil carrying a variable current.

Similar voltage will be induced, the direction of which can be determined by Lenz’s Law.

Page 34: Electromagnetic Define and explain Faraday Law, Flemming Law, magnetic field, magnetik material, Magnetisation curve Define and explain magnetic equivalent

11.4 Induced Voltage

Lenz’s law

An induced effect is always such as to oppose the cause that produced it.

The magnitude of the induced voltage is given by:

L is known as inductance of the coil and is measure in henries (H)

dt

diLevL ind

di

dNL

Page 35: Electromagnetic Define and explain Faraday Law, Flemming Law, magnetic field, magnetik material, Magnetisation curve Define and explain magnetic equivalent

CHAPTER 12

MAGNETIC CIRCUITS

Page 36: Electromagnetic Define and explain Faraday Law, Flemming Law, magnetic field, magnetik material, Magnetisation curve Define and explain magnetic equivalent

12.1 Introduction

Magnetism is an integral part of almost every electrical device used today in industry, research, or the home.

Generators, motors, transformers, circuit breakers, televisions, computers, tape recorders and telephones all employ magnetic effects to perform a variety of important tasks.

Page 37: Electromagnetic Define and explain Faraday Law, Flemming Law, magnetic field, magnetik material, Magnetisation curve Define and explain magnetic equivalent

12.3 ReluctanceThe resistance of a material to the flow of

charge (current) is determined for electric circuits by the equation

The reluctance of a material to the setting up of magnetic flux lines in a material is determined by the following equation

A

l

A

lR

At/Wbor rels,A

l

tyconductivi

1

Page 38: Electromagnetic Define and explain Faraday Law, Flemming Law, magnetic field, magnetik material, Magnetisation curve Define and explain magnetic equivalent

12.4 Ohm’s Law for Magnetic Circuits

opposition

causeeffect

For magnetic circuits, the effect is the flux

The cause is the magnetomotive force (mmf) F, which is the external force (or “pressure”) required to set up the magnetic flux lines within the magnetic material.

The opposition to the setting up of the flux is the reluctance .

Page 39: Electromagnetic Define and explain Faraday Law, Flemming Law, magnetic field, magnetik material, Magnetisation curve Define and explain magnetic equivalent

12.4 Ohm’s Law for Magnetic Circuits

Substituting:

The magnetomotive force is proportional to the product of the number of turns around the core (in which the flux is to be established) and the current through the turns of wire

AtNI

Page 40: Electromagnetic Define and explain Faraday Law, Flemming Law, magnetic field, magnetik material, Magnetisation curve Define and explain magnetic equivalent

An increase in the number of turns of the current through the wire, results in an increased “pressure” on the system to establish the flux lines through the core.

12.4 Ohm’s Law for Magnetic Circuits

Page 41: Electromagnetic Define and explain Faraday Law, Flemming Law, magnetic field, magnetik material, Magnetisation curve Define and explain magnetic equivalent

12.5 Magnetizing ForceThe magnetomotive force per unit length is

called the magnetizing force (H).

Magnetizing force is independent of the type of core material.

Magnetizing force is determined solely by the number of turns, the current and the length of the core.

At/ml

H

Page 42: Electromagnetic Define and explain Faraday Law, Flemming Law, magnetic field, magnetik material, Magnetisation curve Define and explain magnetic equivalent

12.5 Magnetizing ForceSubstituting:

At/ml

NIH

Page 43: Electromagnetic Define and explain Faraday Law, Flemming Law, magnetic field, magnetik material, Magnetisation curve Define and explain magnetic equivalent

12.5 Magnetizing ForceThe flux density and the magnetizing force are

related by the equation:

HB

Page 44: Electromagnetic Define and explain Faraday Law, Flemming Law, magnetic field, magnetik material, Magnetisation curve Define and explain magnetic equivalent

12.6 Hysteresis

Hysteresis – The lagging effect between the flux density of a material and the magnetizing force applied.

The curve of the flux density (B) versus the magnetic force (H) is of particular interest to engineers.

Page 45: Electromagnetic Define and explain Faraday Law, Flemming Law, magnetic field, magnetik material, Magnetisation curve Define and explain magnetic equivalent

12.6 Hysteresis

Series magnetic circuit used to define the hysteresis curve.

Page 46: Electromagnetic Define and explain Faraday Law, Flemming Law, magnetic field, magnetik material, Magnetisation curve Define and explain magnetic equivalent

12.6 Hysteresis

The entire curve (shaded) is called the hysteresis curve.

The flux density B lagged behind the magnetizing force H during the entire plotting of the curve. When H was zero at c, B was not zero but had only begun to decline. Long after H had passed through zero and had equaled to –Hd did the flux density B finally become equal to zero

Page 47: Electromagnetic Define and explain Faraday Law, Flemming Law, magnetic field, magnetik material, Magnetisation curve Define and explain magnetic equivalent

12.6 Hysteresis

Hysteresis curve.

Page 48: Electromagnetic Define and explain Faraday Law, Flemming Law, magnetic field, magnetik material, Magnetisation curve Define and explain magnetic equivalent

12.6 Hysteresis If the entire cycle is repeated, the curve obtained for

the same core will be determined by the maximum H applied.

Page 49: Electromagnetic Define and explain Faraday Law, Flemming Law, magnetic field, magnetik material, Magnetisation curve Define and explain magnetic equivalent

12.6 Hysteresis

Normal magnetization curve for three ferromagnetic materials.

Page 50: Electromagnetic Define and explain Faraday Law, Flemming Law, magnetic field, magnetik material, Magnetisation curve Define and explain magnetic equivalent

12.6 Hysteresis

Expanded view for the low magnetizing force region.

Page 51: Electromagnetic Define and explain Faraday Law, Flemming Law, magnetic field, magnetik material, Magnetisation curve Define and explain magnetic equivalent

12.7 Ampere’s Circuital Law

Ampère’s circuital law: The algebraic sum of the rises and drops of the mmf around a closed loop of a magnetic circuit is equal to zero; that is, the sum of the rises in mmf equals the sum drops in mmf around a closed loop.

0 IRV or Hl

Page 52: Electromagnetic Define and explain Faraday Law, Flemming Law, magnetic field, magnetik material, Magnetisation curve Define and explain magnetic equivalent

12.7 Ampere’s Circuital LawAs an example:

0 cacabcbcabab lHlHlHNI

0

cacabcbcabab lHlHlHNI

Page 53: Electromagnetic Define and explain Faraday Law, Flemming Law, magnetic field, magnetik material, Magnetisation curve Define and explain magnetic equivalent

12.8 Flux The sum of the fluxes entering a junction is

equal to the sum of the fluxes leaving a junction

Page 54: Electromagnetic Define and explain Faraday Law, Flemming Law, magnetic field, magnetik material, Magnetisation curve Define and explain magnetic equivalent

12.8 Flux acba juction at

bacb junction at or

Page 55: Electromagnetic Define and explain Faraday Law, Flemming Law, magnetic field, magnetik material, Magnetisation curve Define and explain magnetic equivalent

12.9 Series Magnetic Circuits : Determining NI

Two types of problems is given, and the impressed mmf NI

must be computed – design of motors, generators and transformers

NI is given, and the flux of the magnetic circuit must be found – design of magnetic amplifiers

Page 56: Electromagnetic Define and explain Faraday Law, Flemming Law, magnetic field, magnetik material, Magnetisation curve Define and explain magnetic equivalent

12.9 Series Magnetic Circuits : Determining NI

Table method A table is prepared listing in the extreme

left-hand column the various sections of the magnetic circuit. The columns on the right are reserved for the quantities to be found for each section

Page 57: Electromagnetic Define and explain Faraday Law, Flemming Law, magnetic field, magnetik material, Magnetisation curve Define and explain magnetic equivalent

12.9 Series Magnetic Circuits : Determining NI

Example 12.3

Determine the secondary current I2 for the transformer if the resultant clockwise flux in the core is 1.5 x 10-5 Wb.

Page 58: Electromagnetic Define and explain Faraday Law, Flemming Law, magnetic field, magnetik material, Magnetisation curve Define and explain magnetic equivalent

12.9 Series Magnetic Circuits : Determining NI

Example 12.3 – solution

Tx

x

AB 1.0

1015.0

105.13

5

Page 59: Electromagnetic Define and explain Faraday Law, Flemming Law, magnetic field, magnetik material, Magnetisation curve Define and explain magnetic equivalent

12.9 Series Magnetic Circuits : Determining NI

Example 12.3 – solution (cont’d)

Based on B- H curve, is got mAtH abcd /30

Using ampere circuital law :

A

xx

N

lHINI

lHININ

lHININ

abcdabcd

abcdabcd

abcdabcd

84.330

)16.0(302602

112

1122

2211

Page 60: Electromagnetic Define and explain Faraday Law, Flemming Law, magnetic field, magnetik material, Magnetisation curve Define and explain magnetic equivalent
Page 61: Electromagnetic Define and explain Faraday Law, Flemming Law, magnetic field, magnetik material, Magnetisation curve Define and explain magnetic equivalent
Page 62: Electromagnetic Define and explain Faraday Law, Flemming Law, magnetic field, magnetik material, Magnetisation curve Define and explain magnetic equivalent

12.9 Series Magnetic Circuits : Determining NI

Example 12.2 – solution (cont’d)

3108.30470 efabefablH

Calculate Hl for each section;

At 34.21

3101271600 bcdebcdelH

At 2.203

Page 63: Electromagnetic Define and explain Faraday Law, Flemming Law, magnetic field, magnetik material, Magnetisation curve Define and explain magnetic equivalent

12.9 Series Magnetic Circuits : Determining NI

Example 12.2 – solution (cont’d)

The magnetic circuit equivalent

The electric circuit analogy

At 54.2242.20334.21 bcdebcdeefabefab lHlHNI

A 4.4950

54.224I

Page 64: Electromagnetic Define and explain Faraday Law, Flemming Law, magnetic field, magnetik material, Magnetisation curve Define and explain magnetic equivalent

12.10 Air GapsEffects of air gaps on a magnetic circuit

coreg coreg AA

The flux density of the air gap is given by;

where; and;

Page 65: Electromagnetic Define and explain Faraday Law, Flemming Law, magnetic field, magnetik material, Magnetisation curve Define and explain magnetic equivalent

12.10 Air GapsEffects of air gaps on a magnetic circuit

Assuming the permeability of air is equal to that of free space, the magnetizing force of the air gap is determined by;

And the mmf drop across the air gap is equal to Hg Lg;

Page 66: Electromagnetic Define and explain Faraday Law, Flemming Law, magnetic field, magnetik material, Magnetisation curve Define and explain magnetic equivalent

12.10 Air GapsExample

A flux 0f 0.2 x 10-4 Wb will establish sufficient attractive force for armature the armature of the relay.

a. Determine the required current to establishd this flux level.

b. The force exert on the armature is determined by the equation

Where Bg is the flux density within the ais gap and A is the common area of the air gap. Find the force in newton to establish the flux.

Page 67: Electromagnetic Define and explain Faraday Law, Flemming Law, magnetic field, magnetik material, Magnetisation curve Define and explain magnetic equivalent

12.10 Air GapsExample – solution