Chapter 33. Electromagnetic Induction

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Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.

Chapter 33. Electromagnetic Induction

Electromagnetic induction

is the scientific principle

that underlies many

modern technologies, from

the generation of

electricity to

communications and data

storage.

Chapter Goal: To

understand and apply

electromagnetic induction.


Last Homework

• Reading: Chap. 33 and Chap. 33

• Suggested exercises: 33.1, 33.3, 33.5, 33.7,

33.9, 33.11, 33.13, 33.15, 33.17.

• Problems: 33.36, 33.37, 33.45, 33.49, 33.50,

33.52, 33.54, 33.55, 33.62, 33.63 (Due Dec. 7)

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Chapter 33. Electromagnetic Induction

Topics:

• Induced Currents

• Motional emf

• Magnetic Flux

• Lenz’s Law

• Faraday’s Law

• Induced Fields

• Induced Currents: Three Applications

• Inductors

• LC Circuits

• LR Circuits


Chapter 33. Basic Content and Examples

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Electric Field versus Magnetic Field

A current carrying wire generates magnetic field

E

Electric field magnetic field

Question: Can a magnetic field generate the

electric field or current?


Faraday's Law

Change of magnetic flux in a wire loop generates current!

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Faraday's Law

Change of magnetic flux in a wire loop generates emf:

N: total number of loops


Faraday's Law

Fix area A

Changing field B

Magnitude & Direction

Fix field B

Changing area A

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Changing Magnetic Field

S N S N

Change magnitude Change direction


Changing Area

Change magnitude Change direction

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Lenz’s Law

The direction of the induced emf:

The induced emf tends to generate a current that to create a magnetic

flux to oppose the change of the magnetic flux through the area of

the loop.


Example 12.1

L

d

b

x

v

B

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Example 12.2

A rectangular loop of dimensions l

and w, moved with a constant

velocity v away from a long wire that

carried a current I in the plane of the

loop. The total resistance of the loop

is R. Derive an expression that gives

the current in the loop at the instant

the near side is a distance r from the

wire.


Activity #1

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Activity #2


Activity #3

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Activity #4


Activity #5

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Applications

Generators Transformers

𝑉𝑠 =𝑁𝑠𝑁𝑝

𝑉𝑝


Applications

Metal detectors

Credit card readers

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Induced Electric Field

Changing B at the center of a loop of wire produces E in the wire.

The electric field is still there even if the wire is removed.

EE


Faraday’s Law Restated

The changing magnetic field B induces an electric field E, and

Thus,

One of the Maxwell’s equations

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Induced Electric Field

Symmetry shows that electric field lines make circular loops,

whether or not there is a wire:

E

How do you determine the direction of E?


Maxwell’s Equations

Gauss’ Law

Gauss’ Law

Faraday’s Law

Ampere’s Law

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Induced Electric & Magnetic Fields

The generation of electromagnetic waves:

Ampere’s Law & Faraday’s Law


Inductor & Inductance

Capacitor induces electric field

Inductor generates magnetic field

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Unit: Henry (H) 1 H = 1 Tm2/A

Symbol:

Inductance of a solenoid: 𝐿 =𝜇0𝑁

2𝐴

𝑙N: number of turns A: cross-section area

l: length



If the current is alternating as a function of time t, due to

Faraday’s law, the conductor will induce an emf which is against

the change of the current.

When a steady current passes through an inductor, if the

inductor is ideal with R = 0 , the potential difference across

the inductor is zero.

𝜀𝐿 = 𝑁𝑑Φ𝐵

𝑑𝑡

According to the definition, 𝑁Φ𝐵 = 𝐿𝑖

𝜀𝐿 = 𝐿𝑑𝑖

𝑑𝑡Thus,

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According to Lenz’s law, we have

Δ𝑉 = −𝐿𝑑𝑖

𝑑𝑡

Or the potential drop from a to b point is


Energy Stored in an Inductor

The power consumption:

The power consumed by an inductor is

𝑃 = 𝑖Δ𝑉

𝑃 = −𝑖𝐿𝑑𝑖

𝑑𝑡

The stored magnetic energy 𝑈𝐵 by an inductor is

𝑑𝑈𝐵𝑑𝑡

= 𝑖𝐿𝑑𝑖

𝑑𝑡

When i = 0, 𝑈𝐵 = 0, then

𝑈𝐵 =1

2𝐿𝑖2 𝑈𝐸 =

1

2𝐶𝑉2

Capacitor

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The current in an LC circuit

The current in an LC circuit where the initial

charge on the capacitor is Q0 is

The oscillation frequency is given by

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EXAMPLE 33.15 An AM radio oscillator

QUESTION:


EXAMPLE 33.15 An AM radio oscillator

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Chapter 33. Summary Slides


General Principles

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General Principles


General Principles

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Important Concepts


Important Concepts

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Applications


Applications

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Chapter 33. Clicker Questions


A square conductor moves through a

uniform magnetic field. Which of the

figures shows the correct charge

distribution on the conductor?

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A square conductor moves through a

uniform magnetic field. Which of the

figures shows the correct charge

distribution on the conductor?


Is there an induced current in this circuit? If

so, what is its direction?

A. No

B. Yes, clockwise

C. Yes, counterclockwise

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A. No

B. Yes, clockwise

C. Yes, counterclockwise

Is there an induced current in this circuit? If

so, what is its direction?


A. Fb = Fd > Fa = Fc

B. Fc > Fb = Fd > Fa

C. Fc > Fd > Fb > Fa

D. Fd > Fb > Fa = Fc

E. Fd > Fc > Fb > Fa

A square loop of copper

wire is pulled through a

region of magnetic field.

Rank in order, from

strongest to weakest, the

pulling forces Fa, Fb, Fc

and Fd that must be

applied to keep the loop

moving at constant speed.

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A. Fb = Fd > Fa = Fc

B. Fc > Fb = Fd > Fa

C. Fc > Fd > Fb > Fa

D. Fd > Fb > Fa = Fc

E. Fd > Fc > Fb > Fa

A square loop of copper

wire is pulled through a

region of magnetic field.

Rank in order, from

strongest to weakest, the

pulling forces Fa, Fb, Fc

and Fd that must be

applied to keep the loop

moving at constant speed.


A current-carrying wire is pulled away from a

conducting loop in the direction shown. As the

wire is moving, is there a cw current around the

loop, a ccw current or no current?

A. There is no current around the loop.

B. There is a clockwise current around the loop.

C. There is a counterclockwise current around the loop.

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A. There is no current around the loop.

B. There is a clockwise current around the loop.

C. There is a counterclockwise current around the loop.

A current-carrying wire is pulled away from a

conducting loop in the direction shown. As the

wire is moving, is there a cw current around the

loop, a ccw current or no current?


A conducting loop is

halfway into a magnetic

field. Suppose the

magnetic field begins to

increase rapidly in

strength. What happens

to the loop?

A. The loop is pulled to the left, into the magnetic field.

B. The loop is pushed to the right, out of the magnetic field.

C. The loop is pushed upward, toward the top of the page.

D. The loop is pushed downward, toward the bottom of the

page.

E. The tension is the wires increases but the loop does not

move.

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A. The loop is pulled to the left, into the magnetic field.

B. The loop is pushed to the right, out of the magnetic field.

C. The loop is pushed upward, toward the top of the page.

D. The loop is pushed downward, toward the bottom of the

page.

E. The tension is the wires increases but the loop does not

move.

A conducting loop is

halfway into a magnetic

field. Suppose the

magnetic field begins to

increase rapidly in

strength. What happens

to the loop?


The potential at a is higher than the

potential at b. Which of the following

statements about the inductor current I

could be true?

A. I is from b to a and is steady.

B. I is from b to a and is increasing.

C. I is from a to b and is steady.

D. I is from a to b and is increasing.

E. I is from a to b and is decreasing.

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A. I is from b to a and is steady.

B. I is from b to a and is increasing.

C. I is from a to b and is steady.

D. I is from a to b and is increasing.

E. I is from a to b and is decreasing.

The potential at a is higher than the

potential at b. Which of the following

statements about the inductor current I

could be true?


Rank in order, from largest to smallest, the

time constants τa, τb, and τc of these three

circuits.

A. τa > τb > τc

B. τb > τa > τc

C. τb > τc > τa

D. τc > τa > τb

E. τc > τb > τa

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A. τa > τb > τc

B. τb > τa > τc

C. τb > τc > τa

D. τc > τa > τb

E. τc > τb > τa

Rank in order, from largest to smallest, the

time constants τa, τb, and τc of these three

circuits.


Chapter 33. Reading Quizzes

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Currents circulate in a piece of metal that

is pulled through a magnetic field. What

are these currents called?

A. Induced currents

B. Displacement currents

C. Faraday’s currents

D. Eddy currents

E. This topic is not covered in Chapter 33.


Currents circulate in a piece of metal that

is pulled through a magnetic field. What

are these currents called?

A. Induced currents

B. Displacement currents

C. Faraday’s currents

D. Eddy currents

E. This topic is not covered in Chapter 33.

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Electromagnetic induction was

discovered by

A. Faraday.

B. Henry.

C. Maxwell.

D. Both Faraday and Henry.

E. All three.


Electromagnetic induction was

discovered by

A. Faraday.

B. Henry.

C. Maxwell.

D. Both Faraday and Henry.

E. All three.

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The direction that an induced

current flows in a circuit is

given by

A. Faraday’s law.

B. Lenz’s law.

C. Henry’s law.

D. Hertz’s law.

E. Maxwell’s law.


The direction that an induced

current flows in a circuit is

given by

A. Faraday’s law.

B. Lenz’s law.

C. Henry’s law.

D. Hertz’s law.

E. Maxwell’s law.

Chapter 33. Electromagnetic Induction

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Transcript of Chapter 33. Electromagnetic Induction