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1 The Magnetic Field Chapter 30

The Magnetic Field

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The Magnetic Field. Chapter 30. Magnetic Forces. Magnetic Force - A force present when an electric charge is in motion. A moving charge is said to produce a magnetic field . Magnetic fields exert forces on moving charges. Magnetic Fields. Represented by field lines . By definition: - PowerPoint PPT Presentation

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Page 1: The Magnetic Field

1

The Magnetic Field

Chapter 30

Page 2: The Magnetic Field

2

Magnetic Forces

• Magnetic Force - A force present when an electric charge is in motion.

• A moving charge is said to produce a magnetic field .

• Magnetic fields exert forces on moving charges.

Page 3: The Magnetic Field

3

Magnetic Fields

• Represented by field lines .• By definition:

• or more commonly:

• Where q is the angle between v and B.

B =F

Qvsinq

F = qvBsinq

F = qv B

Page 4: The Magnetic Field

4

Magnetic Field Units

• Standard Unit = Tesla (T)

• 1 T = 1 N/A•m

• 1 T = 104 gauss

Page 5: The Magnetic Field

5

Force on Moving Charges• The diagram below shows a uniform

magnetic field with several charges in motion.

+ +

+ – x

vv

vv

Page 6: The Magnetic Field

6

Force on Moving Charges

• The magnitude of the force on each charge can be found by qv X B or qvBsinq.

• The direction of the force is found by a right hand rule.

Page 7: The Magnetic Field

7

Right Hand Rule

• 1) Place your fingers in the direction of the velocity.

• 2) Curl your fingers toward the direction of the field. You might need to turn your hand.

• 3) Your thumb points in the direction of the force.

Page 8: The Magnetic Field

8

Direction of Force

+ +

+ – x

vv

vv

F = 0

F

F

F

Page 9: The Magnetic Field

9

Magnetic Field Lines

• NOT lines of force.• Force on charges is not in the direction of

the magnetic field.• Force is always perpendicular to the

velocity of the charge.• Force is always perpendicular to the

magnetic field.• RHR & LHR

Page 10: The Magnetic Field

10

Permanent Magnets• Magnetic field lines point away from north

poles• and toward south poles.

Page 11: The Magnetic Field

11

Magnetic Flux

• The amount of a magnetic field passing through a given area.

• Proportional to the number of magnetic field lines which pass through an area.

B = BA cosq = B • AB =

B d A

Page 12: The Magnetic Field

12

Magnetic Flux

Maximum Flux

No Flux

A

A

A

Page 13: The Magnetic Field

13

Flux Units

• Weber• 1 Wb = 1 T/m2

Page 14: The Magnetic Field

14

Gauss's Law for Magnetism

• The magnetic flux through any closed surface must be zero.

N S BdA 0

Page 15: The Magnetic Field

15

Example

• Exercise 4

Page 16: The Magnetic Field

16

homework

• E 1, 2, 7

Page 17: The Magnetic Field

17

Motion of Charges in a Magnetic Field

• Two possible paths can result for the motion of the charge:

• 1) If vo is perpendicular to B, a circular path will result.

• 2) If vo is not perpendicular to B, the charge will travel in a spiral path.

Page 18: The Magnetic Field

18

vo perpendicular to B

Page 19: The Magnetic Field

19

vo at an angle to B

Page 20: The Magnetic Field

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Magnetic Bottle

Page 21: The Magnetic Field

21

Van Allen Belts

Page 22: The Magnetic Field

22

Motion of Charges• As a charge circles or spirals in a magnetic

field, the radius of its path is dependent on the perpendicular component of its velocity.

FB = Fc

QvB =mv2

r

r =mv

QB

T =2rv

=2mqB

vr

qBm

Page 23: The Magnetic Field

23

Mass Spectrometer

r =mv

QB

Page 24: The Magnetic Field

24

Velocity Selector

• Only allows charges with a specific velocity to pass through undeflected.

• FB is opposite of FE

• E is perpendicular to B

Page 25: The Magnetic Field

25

Velocity Selector

+ v

–  –  –  –  –  –  –  –  –  –

+ + + + + + + + + +

••

•FE

FB

Page 26: The Magnetic Field

26

Velocity Selector

• For a specific value of v, the electric force and the magnetic force will be equal to each other and opposite in direction.

• FB = FE

• qvB = qE• vB = E

Page 27: The Magnetic Field

27

Current-Carrying Wire• Since a current is moving charges, a

current-carrying wire experiences a force in a magnetic field. (B into screen)

X X X X X X X X

X X X X X X X X

F

Page 28: The Magnetic Field

28

Magnitude of Force

F QvBsinq Q Itv Lt

Qv ItLt

IL

F ILBsinq F IL B

Page 29: The Magnetic Field

29

Example

• Exercise 14

Page 30: The Magnetic Field

30

homework

• E 19, 20

Page 31: The Magnetic Field

31

Sources of Magnetic Fields

Chapter 31

Page 32: The Magnetic Field

32

Long, straight wire

B =oI2r

o is equal to 4 x 10–7 T•m/A.

Page 33: The Magnetic Field

33

Current Carrying Wire

• Shape of the field is circular.• Concentric circles• The direction is given a Right Hand Rule:

– Thumb in the direction of the current.– Curl your fingers and they give the direction of

the field.

Page 34: The Magnetic Field

34

Moving Charge

+ • v

Page 35: The Magnetic Field

35

Wire

I

• • • • • • • • •

x x x x x x x x x

B

I

Page 36: The Magnetic Field

36

Parallel conductors

• Each creates a magnetic field that produces a force on the other

• Can calculate force per unit length

• To find direction, use both right hand rules

rII

lF

2

0

Page 37: The Magnetic Field

37

Definition of Ampere

• Comes from force exerted by two parallel conductors

• 1 A is the current necessary in each conductor (if 1 m apart) to produce a force of 2 x 10-7 N.

Page 38: The Magnetic Field

38

Field of a circular loop or coil

• At center of loop

• Direction found with right hand rule – like current in straight wire

RNIB

20

Page 39: The Magnetic Field

39

Field of a Solenoid• Long Spring-like Coil• Uniform field in the interior:

B = onI

B oNL

I

Page 40: The Magnetic Field

40

Examples

• Exercises 1 and 7

Page 41: The Magnetic Field

41

homework

• E 2, 6, 10, 12

Page 42: The Magnetic Field

42

Ampere’s Law

• Like Gauss’s law

encId 0sB

Iencparallel IsB 0

Page 43: The Magnetic Field

43

Long straight wire

I

rIB

IrB

2

2

0

0

encparallel IsB 0

Page 44: The Magnetic Field

44

Example• A wire has a radius of R and carries a current I that

is uniformly distributed across its area.• Determine how to calculate the magnitude of the

magnetic field inside and outside the conductor.

Page 45: The Magnetic Field

45

Inside• The current inside a circle of radius r would

be a fraction of the total current.• Same ratio as areas.• With total current, I:

Rr

B2r oI r2

R2

B oIr

2R2

Page 46: The Magnetic Field

46

Outside• A circle of radius r, where r > R, encloses

all the current.

B oI2rR

r

Page 47: The Magnetic Field

47

Example

• Determine the field inside a solenoid

lengthturns

n

Page 48: The Magnetic Field

48

Solenoid• Vertical sides – zero

because B is perpendicular to sides

• Side outside solenoid – if it is far away from the solenoid, B is zero

nLIBL 0

nIB 0

Page 49: The Magnetic Field

49

Paramagnetic materials

• Can become magnetized• An external magnetic field causes atoms to

line up so their currents add to the external field

Page 50: The Magnetic Field

50

Ferromagnetic materials

• Atomic currents line up even when no external field is present

• Permanent magnets

Page 51: The Magnetic Field

51

Electromagnets

Page 52: The Magnetic Field

52

homework

• E 24-26