Magnetism in asimplified approach

7/31/2019 Magnetism in asimplified approach

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Principles of Electric Circuits - Floyd Copyright 2006 Prentice-Hall

Chapter 10

Chapter 10


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Chapter 10

Magnetic fields are described by drawing flux lines

that represent the magnetic field.

Summary

Where lines are close

together, the flux

density is higher.

Where lines are furtherapart, the flux density

is lower.

Magnetic Quantities


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Chapter 10

Magnetic flux lines are invisible, but the effects can

be visualized with iron filings sprinkled in a magnetic

field.

Summary

Magnetic Quantities


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Chapter 10

Ferromagnetic materials such as iron, nickel and cobalthave randomly oriented magnetic domains, which becomealigned when placed in a magnetic field, thus they

effectively become magnets.

Magnetic Materials


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Chapter 10

The unit of flux is the weber. The unit of flux density is

the weber/square meter, which defines the unit tesla, (T),

which is a very large unit.

Summary

Flux density is given by the equationwhere

B = flux density (T)

j = flux (Wb)

A = area (m2

)

B= j

A

Flux lines (j

Area (m)2

Magnetic Quantities


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Chapter 10

Example: What is the flux density in a rectangular core

that is 8 mm by 10 mm if the flux is 4 mWb?

Summary

B=j

A

32

-3 -3

4 10 Wb50 Wb/m = 50 T

8 10 m 10 10 m

B

Magnetic Quantities


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Chapter 10

Magnetic flux lines surround a current carrying wire.

Summary

The field lines are concentric circles as shown in

Figure 10-10 of the text.

Magnetic Quantities

As in the case of bar magnets, the effects

of electrical current can be visualized with

iron filings around the wirethe current

must be large to see this effect.

Current-carrying wire

Iron filings


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Chapter 10Summary

Permeability (m) defines the ease with which a

magnetic field can be established in a given material. It is

measured in units of the weber per ampere-turn meter.

Magnetic Quantities

Relative Permeability (mr) is the ratio of the absolute

permeability to the permeability of a vacuum.

The permeability of a vacuum (m0) is 4p x 10-7 weber

per ampere-turn meter, which is used as a reference.

0m

mm

r


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Chapter 10Summary

Reluctance ( ) is the opposition to the establishment

of a magnetic field in a material.

= reluctance in A-t/Wb

l = length of the path

m= permeability (Wb/A-t m).A = area in m2

Magnetic Quantities

A

l

mR


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Chapter 10

Fm

=NI

Recall that magnetic flux lines surround a current-carrying

wire. A coil reinforces and intensifies these flux lines.

Summary

The cause of magnetic flux is called magnetomotive

force (mmf), which is related to the current and number of

turns of the coil.

Fm = magnetomotive force (A-t)N= number of turns of wire in a coil

I= current (A)

Magnetic Quantities


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Chapter 10Summary

Ohms law for magnetic circuits is

Magnetic Quantities

flux (j) is analogous to current

magnetomotive force (Fm) is analogous to voltage reluctance ( ) is analogous to resistance.

What flux is in a core that is wrapped with a300 turn coil with a current of 100 mA if the

reluctance of the core is 1.5 x 107 A-t/Wb? 2.0 mWb

R

mFj


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Chapter 10Summary

The magnetomotive force (mmf) is not a true force in

the physics sense, but can be thought of as a cause of

flux in a core or other material.

Current in the coil causes flux

in the iron core.

What is the mmf if a 250

turn coil has 3 A of current?

750 A-t

Magnetic Quantities

Iron core


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Chapter 10Summary

A solenoid produces mechanical motion

from an electrical signal.

Solenoids

One application is valves that can

remotely control a fluid in a pipe,

such as in sprinkler systems.

Stationary core Sliding cor

(plunger)

Spring Coil


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Chapter 10Summary

A relay is an electrically controlled switch; a small

control voltage on the coil can control a large current

through the contacts.

Relays

ArmatureContact points

TerminalsSpring

Electromagneticcoil

Terminals

Structure Schematic

symbol

CR1-1

CR1-2

NC

contacts

NO

contacts

CR1 Movableconta

Fixedcontact

Fixedcontact

Alternate schematic symbol


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Chapter 10Summary

Magnetic field intensity is the magnetomotive forceper unit length of a magnetic path.

H= Magnetic field intensity (Wb/A-t m)Fm = magnetomotive force (A-t)

l= average length of the path (m)

N= number of turns

I= current (A)

H=F

m

l

H=NI

lor

Magnetic field intensity represents the effort that a

given current must put into establishing a certain flux

density in a material.


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Chapter 10Summary

This relation betweenB andHis valid up to saturation,

when further increase inHhas no affect onB.

If a material is permeable, then a greater flux density

will occur for a given magnetic field intensity. The

relation betweenB (flux density) andH(the effort to

establish the field) is

B = mH

m= permeability (Wb/A-t m).

H=Magnetic field intensity (Wb/A-t m)

Magnetic Quantities


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Chapter 10Summary

As the graph shows, the flux density depends on boththe material and the magnetic field intensity.

Magnetic Field Intensity, , (At/m)H

Flux

density,,

(Wb//m

)

B

2

Saturation begins

Magnetic material

Non-magnetic material


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Chapter 10Summary

As H is varied, the magnetic hysteresis curve is developed.

(d)(c)

B

H

(b)

B

H

(a)

B

H

(f )

B

H

(g)

B

H

(e)

0 Hsat

Saturation

0

BsatBR

H = 0 H

Hsat

Bsat

Saturation B

HC

0

H0 0

H = 0

BR

B

Hsat

Bsat

HC

H

B

HC


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Chapter 10Summary

AB-Hcurve is referred to as a magnetization curve for

the case where the material is initially unmagnetized.

Magnetization Curve

Magnetic Field Intensity, H,(A-t/m)200 400 600 800 1000 1200 16001400 1800 2000

0

0.5

1.0

1.5

2.0

0

FluxDensity,

B,

(T) Annealed iron


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Chapter 10Summary

AB-Hcurve can be read to determine the flux density in

a given core. The next slide shows how to read the graph

to determine the flux density in an annealed iron core.

Magnetization Curve


0

0.5

1.0

1.5

2.0

0

FluxDensity,

B,

(T)

Annealed iron


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Chapter 10Summary

What isB for the core?

Magnetization Curve

NIH

l


0

0.5

1.0

1.5

2.0

0

FluxDen

sity,

B,

(T)

Annealed iron

380 t 0.9 A1487 A-t/m

0.23 m

Reading

the graph,

B = 1.63 T

I=0.9 A

Annealed iron core

380 turns


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Chapter 10

Relative motion

When a wire is moved across a magnetic field,

there is a relative motion between the wire and

the magnetic field.

When a magnetic field is moved past a

stationary wire, there is also relative motion.

N

S

N

S

In either case, the relative motion results in

an induced voltage in the wire.


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Chapter 10

The induced voltage due to the relative motion

between the conductor and the magnetic field when the

motion is perpendicular to the field is given by

Summary

Induced voltage

B = flux density in T

l = length of the conductor in the magnetic field in m

v = relative velocity in m/s

(motion is perpendicular)

vind =Blv


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Chapter 10

Faraday experimented with generating current by

relative motion between a magnet and a coil of wire.

The amount of voltage induced across a coil is

determined by two factors:

Summary

Faradays law

1. The rate of change of the

magnetic flux with respect

to the coil.S

V- +

Voltage is indicated only

when magnet is moving.


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Chapter 10

Faraday also experimented generating current by

relative motion between a magnet and a coil of wire.

The amount of voltage induced across a coil is

determined by two factors:

Summary

1. The rate of change of the

magnetic flux with respect

to the coil.

2. The number of turns of

wire in the coil.

S

V- +

Faradays law

Voltage is indicated only

when magnet is moving.


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Chapter 10

Just as a moving magnetic field induces a voltage,

current in a coil causes a magnetic field. The coil acts as

an electromagnet, with a north and south pole as in the

case of a permanent magnet.

Summary

Magnetic field around a coil

NorthSouth


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Chapter 10Summary

A dc motor includes a rotating coil, which receives

current through a split ring, called the commutator. The

commutator is connected to fixed brushes, which are

connected to an external circuit. The magnetic core is notshown for simplicity.

DC Motor

N S

commutator

armaturebrushes

Small motors may

use a fixed magnet,

as shown.


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Chapter 10

Magnetic field

Magnetic flux

Weber (Wb)

Permeability

Reluctance

The lines of force between the north pole and

south pole of a permanent magnet or an

electromagnet.

The SI unit of magnetic flux, which represents

108 lines.

A force field radiating from the north pole tothe south pole of a magnet.

Selected Key Terms

The measure of ease with which a magnetic

field can be established in a material.

The opposition to the establishment of a

magnetic field in a material.


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Chapter 10

Magnetic flux density

Flux

Magnetizing force

Magnetomotive force

Permeability

Tesla

Weber

Weber/ampere-turn-meter

Ampere-turn/WeberAmpere-turn

Ampere-turn/meter

B

f

m

RFm

H

Reluctance

It is useful to review the key magnetic units from this

chapter:

Quantity SI Unit Symbol

Magnetic units


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Chapter 10

Magnetomotiveforce (mmf)

Solenoid

Hysteresis

Retentivity

An electromagnetically controlled device in

which the mechanical movement of a shaft or

plunger is activated by a magnetizing current.

A characteristic of a magnetic material

whereby a change in magnetism lags the

application of the magnetic field intensity.

The cause of a magnetic field, measured inampere-turns.

Selected Key Terms

The ability of a material, once magnetized, to

maintain a magnetized state without the

presence of a magnetizing current.


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Chapter 10

Induced voltage(vind)

Faradays law

Lenzs law

A law stating that the voltage induced across a

coil of wire equals the number of turns in the

coil times the rate of change of the magneticflux.

Voltage produced as a result of a changingmagnetic field.

Selected Key Terms

A law stating that when the current through a

coil changes, the polarity of the induced

voltage created by the changing magneticfield is such that it always opposes the change

in the current that caused it. The current

cannot change instantaneously.


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Chapter 10Quiz

1. A unit of flux density that is the same as a Wb/m2 is the

a. ampere-turn

b. ampere-turn/weber

c. ampere-turn/meter

d. tesla


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Chapter 10Quiz

2. If one magnetic circuit has a larger flux than a second

magnetic circuit, then the first circuit has

a. a higher flux density

b. the same flux density

c. a lower flux density

d. answer depends on the particular circuit.


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Chapter 10Quiz

3. The cause of magnetic flux is

a. magnetomotive force

b. induced voltage

c. induced current

d. hysteresis


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Chapter 10Quiz

4. The measurement unit for permeability is

a. weber/ampere-turn


c. weber/ampere-turn-meter

d. dimensionless


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Chapter 10Quiz

5. The measurement unit for relative permeability is

a. weber/ampere-turn


c. weber/ampere-turn meter

d. dimensionless


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Chapter 10Quiz

6. Theproperty of a magnetic material to behave as if it

had a memory is called

a. remembranceb. hysteresis

c. reluctance

d. permittivity


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Chapter 10Quiz

7. Ohms law for a magnetic circuit is

a.

b.

c.

d.

Fm

=NI

B = mH

A

l

mR

RmF

j


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Chapter 10Quiz

8. The control voltage for a relay is applied to the

a. normally-open contacts

b. normally-closed contacts

c. coil

d. armature


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h


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Chapter 10Quiz

10. When the current through a coil changes, the induced

voltage across the coil will

a. oppose the change in the current that caused it

b. add to the change in the current that caused it

c. be zero

d. be equal to the source voltage

Ch 10


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Chapter 10Quiz

Answers:

1. d

2. d

3. a

4. c

5. d

6. b

7. c

8. c

9. b

10. a

Magnetism in asimplified approach

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