Ch 20 1

Chapter 20

Magnetism

© 2006, B.J. LiebSome figures electronically reproduced by permission of Pearson

Education, Inc., Upper Saddle River, New Jersey Giancoli, PHYSICS,6/E © 2004.

Ch 20 2

Magnets•Occur naturally in some parts of the world.•Each magnet has two faces called “poles”•A magnet suspended freely becomes a compass•The end of the compass that points toward the earth’s geographic north pole is called the north pole of the magnet.•The other pole points to the south and is called the south pole.•For magnets, unlike poles attract but don’t confuse with electric charge:

S N

N S

N S N S

N S

S N Repulsive

Repulsive

Attractive

Ch 20 3

Magnetic Fields•Magnetic field symbolized by letter B

•B is measured in tesla (T) or gauss (G)

•1G = 10-4 T

•Direction determined by direction the north end of a magnet points.

•Points out of north pole and into south pole.

Ch 20 4

Magnetic Field of Earth

•Earth’s magnetic field is not due to a permanent magnet– appears due to molten iron core and earth’s rotation.

•North geographic pole is a south magnetic pole

•Magnetic field lines are not parallel to surface

•Angle of dip θ: angle the field makes with horizontal.

North

Ch 20 5

Electric Currents Produce Magnetic Fields

•A wire carrying a current produces a magnetic field which circles wire as shown

•Right hand rule: grasp wire such that thumb points in direction of current, fingers give magnetic field direction.

Ch 20 6

Magnetic Field of Long Straight Wire

r

IB

2

0

•I is current in wire

• r is distance from wire

0 is permeability of free space

0 = 4 x 10-7 T m / A

Ch 20 7

Example 20-1. A long horizontal wire carries 22.0 A of current due north. What is the net magnetic field 20.0 cm due west of the wire if the Earth’s field there points north but downward, 37° below the horizontal, and has magnitude 5.0x10-5 T.

r

IBwire

2

0

The magnetic field due to the long horizontal wire points straight up at the point in question. The wire would be parallel to the red line shown and outside the page. The two fields are oriented as shown in the diagram. The net field is the vector sum of the two fields.

T

m

AAmT 57

102.2)200.0(2

)0.22(/104

T5100.5 earth

BwireB

earthB netB

NorthSouth

Ch 20 8

Example 20-1. Continued A long horizontal wire carries 22.0 A of current due north. What is the net magnetic field 20.0 cm due west of the wire if the Earth’s field there points north but downward, 37° below the horizontal, and has magnitude 5.0x10-5 T.

37cosearthxnet

BB T51000.4

37sinearthwireynet

BBB T51081.0

22

ynetxnetnetBBB TTT 52525 101.4)1081.0()1000.4(

xnet

ynet

B

B1tan

T

T5

5

1

1000.4

1081.0tan

11

below the horizontal

wireB

earthB netB

South North

Ch 20 9

Magnetic Field of Long Straight Wire

X

X

X

X

X

X

X

X

X

X

X

X

This drawing represents the magnetic field of a wire carrying a current directed upward. The wire is in the plane of the screen and the magnetic field is shown in the plane of the screen The dots to the left of the wire represent a magnetic field directed out of the screen and the X’s to the right of the wire represent a magnetic field into the screen.

Ch 20 10

Magnetic Field of Current Loop•A loop of wire carrying a current has a magnetic field similar to a bar magnet.

•Many loops produce a strong uniform field in the center and this is referred to as a solenoid.

Ch 20 11

Magnetic Force on Moving Charge

•If electric current exerts a force on a compass, we expect magnetic field exerts a force on current-carrying wire (Newton’s Third Law)

•Second Right Hand Rule: orient outstretched fingers in current direction and bend them to field direction, thumb points in F direction.

Ch 20 12

Magnetic Force on Current-Carrying Wire

WireI

l

sinBlIF

• l is the length of the wire inside of field

•F is into screen in above drawing

Ch 20 13

)90)(sin106.0)(10)(15( 4 TmA F

Example 20-2A. At a certain place the Earth’s magnetic field is 0.60 x 10-4 T, pointing 75o below the horizontal in a north-south plane. A 10.0 m wire carries a 15-A current. If the current is directed horizontally toward the east, what is the magnitude and direction of the magnetic force on the wire?

sinBlIF

N3109 F

•The wire points out of the page.

•Force is perpendicular to current and B.

•Direction of force is shown. It is in the plane formed by the north-south with the vertical.

Ch 20 14

Example 20-2B. At a certain place the Earth’s magnetic field is 0.60 x 10-4 T, pointing 75o below the horizontal in a north-south plane. A 10.0 m wire carries a 15-A current. What would be the magnitude and direction of the force if the current is directed upward?

)165)(sin106.0)(10)(15( 4 TmA F

sinBlIF

N3103.2 F

165

Direction of Force: into paper or West

Ch 20 15

Magnetic Force on Moving Charge

•Just as there is a force on a wire carrying a current, there is also a force on a moving charge in a magnetic field.•Can again use right hand rule for a positive particle moving with velocity v in magnetic field B

sinBvqF

Ch 20 16

Circular Path

r

vmBvq

2

•A charged particle moving perpendicular to a magnetic field experiences a force perpendicular to velocity (centripetal force) resulting in circular motion

magnetic force = centripetal force

•In figure, “x” indicates B is into paper (like feathers of an arrow) and “•” indicates field out of paper (like point of arrow).

Bq

vmr

Ch 20 17

20-3. (61) In a mass spectrometer, germanium atoms have radii of curvature equal to 21.0, 21.6, 21.9, 22.2, and 22.8 cm. The largest radius corresponds to an atomic mass of 76 u. What are the atomic masses of the other isotopes?

All ions have the same velocity when they enter magnetic field.

For circular motion:r

vmBvq

2

constantv

Bq

r

m

cmr

m

cm

m

8.22

764

0.210.21

ucmcm

m 70)0.21(8.22

7640.21

ucmcm

m 72)6.21(8.22

7646.21

ucmcm

m 73)9.21(8.22

7649.21

ucmcm

m 74)2.22(8.22

7642.22

For r21 = 21.0 cm

Ch 20 18

Force Between Parallel Wires

•In the drawing below, the left wire produces a magnetic field. Because of this field, the right wire experiences a force to the left.

•For the same reason, the left wire experiences force to right.

•If current I2 is reversed, the result is the wires repel each other.

Ch 20 19

Torque on Current Loop

•A loop of wire carrying a current experiences a torque.

•This torque can cause it to rotate up to 1800

•If the current is then reversed, then it will rotate another 1800

•This is the basis for the electric motor.

•It is easy to reverse current mechanically and thus achieve continuous rotation

Ch 20 20

Magnetic Field of Earth

•There is evidence that the earth’s magnetic field has reversed 5 or 6 times with a separation of about 200,000 years

•The next reversal is “overdue”

•The picture is the result of a computer model of the earths magnetic field.

Ch 20 21

Magnetic Field of Earth is Radiation Shield

protons

•The sun emits a stream of high speed protons

•The magnetic force on the protons bends them into the screen and thus they don’t strike the earth

•This protects the earth from what would be a high radiation environment.

•At times when the earths magnetic field is weak, evolutional changes are accelerated.

Ch 20 22

Magnetic Field of Atoms

•An electron in an atomic orbit is similar to a loop of wire carrying a current and thus produces a magnetic field.

•There is also a magnetic field from the “spin” of the electron.

•The nucleus also has a magnetic field due to the motion of the protons and neutrons and their spin.

•The above picture is simplistic because it does not consider Quantum Mechanics

Ch 20 23

FerromagnetismIron atoms have a strong magnetic field and all of the atoms in a “domain” of size ~ 1mm are oriented in the same direction. Thus each domain acts like a strong magnet but the random orientation of the domains (see Fig A) produces no net field. When placed in an external magnetic field, the domains are preferentially aligned in one direction. In Fig. B the alignment is downward. This results in a net field that is much stronger than the original external field.