Magnetism and Electromagnetism

Magnetism and ElectromagnetismMagnetism and Electromagnetism

Chapter 7

Thomas L. Floyd

David M. Buchla

DC/AC Fundamentals: A Systems DC/AC Fundamentals: A Systems ApproachApproach

DC/AC Fundamentals: A Systems ApproachThomas L. Floyd

© 2013 by Pearson Higher Education, IncUpper Saddle River, New Jersey 07458 • All Rights Reserved

Magnetic fields are described by drawing flux lines that represent the magnetic field.

Where lines are close together, the flux density is higher.

Where lines are further apart, the flux density is lower.

Ch.7 Summary

Magnetic Quantities

N S



Magnetic fields are composed of invisible lines of force that radiate from the north pole to the south pole of a magnetic material.

Field lines can be visualized with the aid of iron filings sprinkled in a magnetic field.

Ch.7 Summary

The Magnetic Field



The magnetic field lines surrounding a magnet actually radiate in three dimensions. These magnetic field lines are always associated with moving charge.

In permanent magnets, the moving charge is due to the orbital motion of electrons. Ferromagnetic materials have minute magnetic domains in their structure.

Ch.7 Summary

The Magnetic Field



Ch.7 Summary

Magnetic Materials

In ferromagnetic materials such as iron, nickel, and cobalt, the magnetic domains are randomly oriented when not magnetized. When placed in a magnetic field, the domains become aligned, thus they effectively become magnets.



The unit of flux is the weber. The unit of flux density is the weber/square meter, which defines the unit tesla, (T), a very large unit.

Flux density is given by the equation

where B = flux density (T) = flux (Wb)A = area (m2)

Ch.7 Summary

Magnetic Quantities

Flux lines ()

Area (m2)AB



To measure magnetic fields, an instrument called a gaussmeter is used. A typical gaussmeter is shown.

The gauss is a unit of flux density and is a much smaller unit than the tesla (1 G = 104 T).

Gaussmeters are commonly used for testing motors, classifying magnets, mapping magnetic fields, and quality control by manufacturers of motors, relays, solenoids, and other magnetic devices.

Ch.7 Summary

Magnetic Quantities

Integrity Model IDR-329 distributedby Less EMF, Inc.



What is the flux density in a rectangular core that is 8.0 mm by 5.0 mm if the flux is 20 mWb?

Expressing this result in gauss:

Ch.7 Summary

Magnetic Quantities

T 0.5 Wb/m0.5m)10m)(5.010 (8.0

Wb1020 233

6

AB

G 5000T

G10T 0.5

4



Magnetic flux lines surround a current carrying wire.

The field lines form concentric circles.

As in the case of bar magnets, the effects of electrical current can be visualized with iron filings around the wire – the current must be large to see this effect.

Current-carrying wire

Iron filings

Ch.7 Summary

Magnetic Quantities



Permeability (m) is the ease with which a magnetic field can be established in a given material. It is measured in webers per ampere-turn meter.

Relative Permeability (mr) is the ratio of the absolute permeability to the permeability of a vacuum.

The permeability of a vacuum (0) is 4 x 10-7 webers per ampere-turn meter, which is used as a reference.

0 r

Ch.7 Summary

Magnetic Quantities



Reluctance () is the opposition to the establishment of a magnetic field in a material.

where: = reluctance in A-t/Wb l = length of the path = permeability (Wb/A-t m).A = area in m2

Ch.7 Summary

Magnetic Quantities

A

l



Recall that magnetic flux lines surround a current-carrying wire. A coil reinforces and intensifies these flux lines.

The cause of magnetic flux is called magnetomotive force (mmf), which is related to the current and number of turns of the coil. That is,

whereFm = magnetomotive force (A-t)

N = number of turns of wire in a coil I = current (A)

Ch.7 Summary

Magnetic Quantities

NIFm



Ohm’s law for magnetic circuits is

Flux () is analogous to current, magnetomotive force (Fm) is

analogous to voltage, and reluctance () is analogous to resistance.

What flux is in a core that is wrapped with a 300 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

Ch.7 Summary

Magnetic Quantities

mF



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.

What is the mmf if a 250 turn coil has 3 A of current?

750 A-t

Current in the coil generates flux in the iron core.Iron core

Ch.7 Summary

Magnetic Quantities



The Hall effect is occurrence of a very small voltage that is generated on opposite sides of a thin current-carrying conductor or semiconductor (the Hall element) that is in a magnetic field.

The Hall effect is widely employed by various sensors for directly measuring position or motion and can be used indirectly for other measurements.

Ch.7 Summary

The Hall Effect

N

+_ Magnetic field

Hall element(semiconductor)

Current

Hall voltage



A solenoid is a magnetic device that produces mechanical motion from an electrical signal.

One solenoid application is as a valve that can remotely control a fluid in a pipe, such as in sprinkler systems.

Ch.7 Summary

Solenoids

Spring

Stationary core Sliding core(plunger)



A relay is an electrically controlled switch; a small control voltage on the coil can control a large current through the contacts.

Ch.7 Summary

Relays

Armature

Contact points

TerminalsSpring

Electromagneticcoil

Terminals

Structure

Symbol

Alternate schematic symbol

CR1-1

CR1-2

NCcontacts

NOcontacts

Movable contact

Fixed contact

Fixed contact

Alternate schematic symbol

CR1-1

CR1-2

NCcontacts

NOcontacts

CR1 Movable contact

Fixed contact

Fixed contact



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

Magnetic field intensity represents the effort that a given current must put into establishing a certain flux density in a material.

Ch.7 Summary

Magnetic Field Intensity

mF

H

NIH or

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

= average length of the path (m)N = number of turns I = current (A)



This relation between B and H is valid up to saturation, where further increases in H have no affect on B.

If a material is permeable, then a greater flux density will occur for a given magnetic field intensity. The relationship between B (flux density) and H (the effort to establish the field) is:

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

Ch.7 Summary

Magnetic Quantities

HB μ



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

Ch.7 Summary

Flux Density

Saturation begins

Magnetic material

Non-magnetic material

Magnetic Field Intensity, H (At/m)

Flu

x D

ensi

ty, B

(W

b/m

2 )



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

Ch.7 Summary

Hysteresis Curves

(d)(c)

B

H

(b)

B

H

(a)

B

H

(f )

B

H

(g)

B

H

(e)

0 Hsat

Saturation

0

Bsat BR

H = 0 H

Hsat

Bsat

Saturation B

HC

0

H0 0

H = 0

BR

B

Hsat

Bsat

HC

H

B

HC



A B-H curve is referred to as a magnetization curve for the case where the material is initially unmagnetized. The B-H curve differs for different materials; magnetic materials have in common much larger flux density for a given magnetic field intensity, such as the annealed iron shown here.

Ch.7 Summary

Magnetization Curve

200 400 600 800 1000 1200 16001400 1800 20000

0.5

1.0

1.5

2.0

0

Magnetic Field Intensity, H (At/m)

Flu

x D

ensi

ty, B

(T

)



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.

NS

NS

In either case, the relative motion results in an induced voltage in the wire.

Ch.7 Summary

Relative Motion



When the motion is perpendicular, the induced voltage produced by the relative motion between the conductor and the magnetic field is dependent on three factors:

• the flux density

• the length of the conductor in the magnetic field

• the relative velocity (motion is perpendicular)

Ch.7 Summary

Induced Voltage



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:

1. The rate of change of the magnetic flux with respect to the coil.

NS

V- + Voltage is indicated only when magnet is moving.

Ch.7 Summary

Faraday’s Law



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:

1. The rate of change of the magnetic flux with respect to the coil.

2. The number of turns of wire in the coil.

NS

V- + Voltage is indicated only when magnet is moving.

Ch.7 Summary

Faraday’s Law



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.

Ch.7 Summary

Magnetic Field Around a Coil

NorthSouth



Mechanical drive turns the shaft

A DC generator includes a rotating coil that is driven by an external mechanical force (the coil is shown as a loop in this simplified view). As the coil rotates in a magnetic field, a pulsating voltage is generated.

Ch.7 Summary

DC Generator

S N

Rotating coil

CommutatorBrushes

To external circuit



A dc motor converts electrical energy to mechanical motion by action of a magnetic field set up by the rotor. The rotor

Mechanical output

field interacts with the stator field, producing torque that causesthe output shaft to rotate.

The commutator serves as a mechanical switch to reverse the current to the rotor at just the right time to continue the rotation.

Ch.7 Summary

DC Motor

–+I

NS

S

N



A brushless dc motor has rotating field and a permanent magnet rotor. An electronic controller periodically reverses the current in the field coils. This causes the stator field to rotate, and the permanent magnet rotor moves to keep up with the rotating field.

Permanent magnet rotor

Hall sensor

(Courtesy of Bodine Electric Company)

Ch.7 Summary

Brushless DC Motor



A series wound dc motor has the field coil(s) in series with the armature.

The series wound motor has very high starting torque.

It can run too fast if a load is not connected; therefore it is run only with a load connected.

Ch.7 Summary

Series Wound DC Motor

Field coil

DC Voltage Armature

Interpole windingsSpeed control

Internal resistance

Torque

Speed

Starting torque



A shunt wound dc motor has the field coil(s) in parallel with the armature.

The magnetic flux is constant because of the parallel arrangement.

Unlike the series wound motor, torque tends to be nearly constant for different loads.

Ch.7 Summary

Shunt Wound DC Motor

Field coil

DC VoltageArmature

Torque

Speed

Full load torque

RF RA



Magnetic flux density

Flux

Magnetizing force

Magnetomotive force

Permeability

Tesla

Weber

Weber/ampere-turn-meter

Ampere-turn/Weber

Ampere-turn

Ampere-turn/meter

B

RFmH

Reluctance

It is useful to review the key magnetic units from this chapter:

Quantity SI Unit Symbol

Ch.7 Summary

Magnetic Units



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 to the south pole of a magnet.

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.

Ch.7 SummaryKey Terms

Magnetic field

Magnetic flux

Weber (Wb)

Permeability

Reluctance



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 in ampere-turns.

The ability of a material, once magnetized, to maintain a magnetized state without the presence of a magnetizing current.

Ch.7 Summary

Magnetomotive force (mmf)

Solenoid

Hysteresis

Retentivity



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 magnetic flux.

Voltage produced as a result of a changing magnetic field.

A law stating that the polarity of the voltage induced by a changing magnetic field is such that it always opposes the change in the current that caused it. The current cannot change instantaneously.

Ch.7 Summary

Induced voltage (Vind)

Faraday’s law

Lenz’s law



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

Ch.7 Summary

Quiz



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.

Ch.7 Summary

Quiz



3. The cause of magnetic flux is

a. magnetomotive force

b. induced voltage

c. induced current

d. hysteresis

Ch.7 Summary

Quiz



4. The measurement unit for permeability is

a. weber/ampere-turn


c. weber/ampere-turn-meter

d. dimensionless

Ch.7 Summary

Quiz



5. The measurement unit for relative permeability is

a. weber/ampere-turn


c. weber/ampere-turn meter

d. dimensionless

Ch.7 Summary

Quiz



6. The property of a magnetic material to behave as if it had a memory is called

a. remembrance

b. hysteresis

c. reluctance

d. permittivity

Ch.7 Summary

Quiz



7. Ohm’s law for a magnetic circuit is

a.

b.

c.

d.

Fm = NI

B = mH

A

l

R

RmF

Ch.7 Summary

Quiz



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

a. normally-open contacts

b. normally-closed contacts

c. coil

d. armature

Ch.7 Summary

Quiz



9. A partial hysteresis curve is shown. At the point labeled BR, magnetic flux

a. is zero

b. exists with no magnetizing force

c. is maximum

d. is proportional to the current

Ch.7 Summary

Quiz

B

H

BR



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.7 Summary

Quiz



1. d

2. d

3. a

4. c

5. d

6. b

7. c

8. c

9. b

10. a

Ch.7 Summary

Answers

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Magnetism and Electromagnetism