copyright © 2009 pearson education, inc. chapter 29 electromagnetic induction and faraday’s law

Copyright © 2009 Pearson Education, Inc.

Chapter 29Electromagnetic Induction

and Faraday’s Law


29-3 EMF Induced in a Moving Conductor

Example 29-7: Electromagnetic blood-flow measurement.

The rate of blood flow in our body’s vessels can be measured using the apparatus shown, since blood contains charged ions. Suppose that the blood vessel is 2.0 mm in diameter, the magnetic field is 0.080 T, and the measured emf is 0.10 mV. What is the flow velocity of the blood?

Remind you of the Hall effect?


29-3 EMF Induced in a Moving Conductor

Example 29-8: Force on the rod.

To make the rod move to the right at speed v, you need to apply an external force on the rod to the right. (a) Explain and determine the magnitude of the required force. (b) What external power is needed to move the rod?

If a coil is rotated as shown, If a coil is rotated as shown,

in a magnetic field pointing in a magnetic field pointing

to the left, in what direction to the left, in what direction

is the induced current? is the induced current?

1) clockwise1) clockwise

2) counterclockwise2) counterclockwise

3) no induced current3) no induced current

ConcepTest 29.5 ConcepTest 29.5 Rotating Wire LoopRotating Wire Loop

As the coil is rotated into the B field,

the magnetic flux through it increasesincreases.

According to Lenz’s law, the induced B

field has to oppose this increaseoppose this increase, thus

the new B field points to the rightto the right. An

induced counterclockwisecounterclockwise current

produces just such a B field.

If a coil is rotated as shown, If a coil is rotated as shown,

in a magnetic field pointing in a magnetic field pointing

to the left, in what direction to the left, in what direction

is the induced current? is the induced current?

1) clockwise1) clockwise

2) counterclockwise2) counterclockwise

3) no induced current3) no induced current

ConcepTest 29.5 ConcepTest 29.5 Rotating Wire LoopRotating Wire Loop


A generator is the opposite of a motor – it transforms mechanical energy into electrical energy. This is an ac generator:

The axle is rotated by an external force such as falling water or steam. The brushes are in constant electrical contact with the slip rings.

29-4 Electric Generators


29-4 Electric GeneratorsIf the loop is rotating with constant angular velocity ω, the induced emf is sinusoidal:

For a coil of N loops,


29-4 Electric Generators

Example 29-9: An ac generator.

The armature of a 60-Hz ac generator rotates in a 0.15-T magnetic field. If the area of the coil is 2.0 x 10-2 m2, how many loops must the coil contain if the peak output is to be V0 = 170 V?

A generator has a coil of wire A generator has a coil of wire

rotating in a magnetic field. rotating in a magnetic field.

If the If the rotation rate increasesrotation rate increases, ,

how is the how is the maximum output maximum output

voltagevoltage of the generator of the generator

affected?affected?

1) increases1) increases

2) decreases2) decreases

3) stays the same3) stays the same

4) varies sinusoidally4) varies sinusoidally

ConcepTest 29.10 ConcepTest 29.10 GeneratorsGenerators

The maximum voltage is the leading

term that multiplies sin sin tt and is

given by = = NBANBA. Therefore, if

increases increases, then must increase must increase

as well.

)sin( tNBA

A generator has a coil of wire A generator has a coil of wire

rotating in a magnetic field. rotating in a magnetic field.

If the If the rotation rate increasesrotation rate increases, ,

how is the how is the maximum output maximum output

voltagevoltage of the generator of the generator

affected?affected?

1) increases1) increases

2) decreases2) decreases

3) stays the same3) stays the same

4) varies sinusoidally4) varies sinusoidally

ConcepTest 29.10 ConcepTest 29.10 GeneratorsGenerators


29-5 Back EMF and Counter Torque; Eddy Currents

Bd d0 V I t R V I t R ABsin

dt dt

Back EMF


Induced currents can flow in bulk material as well as through wires. These are called eddy currents, and can dramatically slow a conductor moving into or out of a magnetic field.

29-5 Back EMF and Counter Torque; Eddy Currents


A transformer consists of two coils, either interwoven or linked by an iron core. A changing emf in one induces an emf in the other.

The ratio of the emfs is equal to the ratio of the number of turns in each coil:

29-6 Transformers and Transmission of Power


This is a step-up transformer – the emf in the secondary coil is larger than the emf in the primary:



Energy must be conserved; therefore, in the absence of losses, the ratio of the currents must be the inverse of the ratio of turns:


1) 1/4 A1) 1/4 A

2) 1/2 A2) 1/2 A

3) 1 A3) 1 A

4) 2 A4) 2 A

5) 5 A5) 5 A

Given that the intermediate Given that the intermediate

current is 1 A, what is the current is 1 A, what is the

current through the current through the

lightbulb? lightbulb?

ConcepTest 29.12b ConcepTest 29.12b TransformersTransformers

1 A1 A

120 V120 V 240 V240 V 120 V120 V

Power in = Power outPower in = Power out

240 V 1 A = 120 V ???

The unknown current is 2 AThe unknown current is 2 A.

1) 1/4 A1) 1/4 A

2) 1/2 A2) 1/2 A

3) 1 A3) 1 A

4) 2 A4) 2 A

5) 5 A5) 5 A

Given that the intermediate Given that the intermediate

current is 1 A, what is the current is 1 A, what is the

current through the current through the

lightbulb? lightbulb?

ConcepTest 29.12b ConcepTest 29.12b TransformersTransformers

1 A1 A

120 V120 V 240 V240 V 120 V120 V



Example 29-12: Cell phone charger.

The charger for a cell phone contains a transformer that reduces 120-V ac to 5.0-V ac to charge the 3.7-V battery. (It also contains diodes to change the 5.0-V ac to 5.0-V dc.) Suppose the secondary coil contains 30 turns and the charger supplies 700 mA. Calculate (a) the number of turns in the primary coil, (b) the current in the primary, and (c) the power transformed.


Transformers work only if the current is changing; this is one reason why electricity is transmitted as ac.




Example 29-13: Transmission lines.

An average of 120 kW of electric power is sent to a small town from a power plant 10 km away. The transmission lines have a total resistance of 0.40 Ω. Calculate the power loss if the power is transmitted at (a) 240 V and (b) 24,000 V.


A changing magnetic flux induces an electric field; this is a generalization of Faraday’s law. The electric field will exist regardless of whether there are any conductors around:

29-7 A Changing Magnetic Flux Produces an Electric Field

.


29-7 A Changing Magnetic Flux Produces an Electric Field

Example 29-14: E produced by changing B.

A magnetic field B between the pole faces of an electromagnet is nearly uniform at any instant over a circular area of radius r0. The current in the windings of the electromagnet is increasing in time so that B changes in time at a constant rate dB/dt at each point. Beyond the circular region (r > r0), we assume B = 0 at all times. Determine the electric field E at any point P a distance r from the center of the circular area due to the changing B.

B E

B

B

B

B

E

B


• Magnetic flux:

• Changing magnetic flux induces emf:

• Induced emf produces current that opposes original flux change.

Summary of Chapter 29


• Changing magnetic field produces an electric field.

• General form of Faraday’s law:

• Electric generator changes mechanical energy to electrical energy; electric motor does the opposite.

Summary of Chapter 29

.


Summary of Chapter 29• Transformer changes magnitude of voltage in ac circuit; ratio of currents is inverse of ratio of voltages:

and


Chapter 30Inductance, Electromagnetic Oscillations, and AC Circuits


• Mutual Inductance

• Self-Inductance

• Energy Stored in a Magnetic Field

• LR Circuits

• LC Circuits and Electromagnetic Oscillations

• LC Circuits with Resistance (LRC Circuits)

• AC Circuits with AC Source

Units of Chapter 30


• LRC Series AC Circuit

• Resonance in AC Circuits

• Impedance Matching

• Three-Phase AC

Units of Chapter 30


Mutual inductance: a changing current in one coil will induce a current in a second coil:

And vice versa; note that the constant M, known as the mutual inductance, is the same:

30-1 Mutual Inductance


Unit of inductance: the henry, H:

1 H = 1 V·s/A = 1 Ω·s.

A transformer is an example of mutual inductance.

30-1 Mutual Inductance


30-1 Mutual InductanceExample 30-1: Solenoid and coil.

A long thin solenoid of length l and cross-sectional area A contains N1 closely packed turns of wire. Wrapped around it is an insulated coil of N2 turns. Assume all the flux from coil 1 (the solenoid) passes through coil 2, and calculate the mutual inductance.


A changing current in a coil will also induce an emf in itself:

Here, L is called the self-inductance:

30-2 Self-Inductance


30-2 Self-Inductance

Example 30-3: Solenoid inductance.

(a) Determine a formula for the self-inductance L of a tightly wrapped and long solenoid containing N turns of wire in its length l and whose cross-sectional area is A.

(b) Calculate the value of L if N = 100, l = 5.0 cm, A = 0.30 cm2, and the solenoid is air filled.


30-2 Self-InductanceConceptual Example 30-4: Direction of emf in inductor.

Current passes through a coil from left to right as shown. (a) If the current is increasing with time, in which direction is the induced emf? (b) If the current is decreasing in time, what then is the direction of the induced emf?


Just as we saw that energy can be stored in an electric field, energy can be stored in a magnetic field as well, in an inductor, for example.

30-3 Energy Stored in a Magnetic Field

2 2

0 0

20B

s 0 s 0

2 2 2 2 22 20 0 s

20

dI L d 1P IV E I L dt I dt LI

dt 2 dt 2

Consider a solenoid: length , N turns, area A:

N ANN N NB I L I A

I I

N A N I B1 1 1 A 1E LI I

2 2 2 2

0

2s

0

Vol

BE

Vol 2

copyright © 2009 pearson education, inc. chapter 29 electromagnetic induction and faraday’s law

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