Hafez a radi, john o rasmussen auth principles of physics for scientists and engineers 2 01

Undergraduate Lecture Notes in Physics

Hafez A. Radi
John O. Rasmussen

Principles of
Physics
For Scientists and Engineers


Undergraduate Lecture Notes in Physics
Series Editors
Neil Ashby
William Brantley
Michael Fowler
Elena Sassi
Helmy S. Sherif

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The purpose of ULNP is to provide intriguing, absorbing books that will continue
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Hafez A. Radi
John O. Rasmussen
•

Principles of Physics
For Scientists and Engineers

123


Hafez A. Radi
October University for Modern Sciences and Arts (MSA)
6th of October City
Egypt
John O. Rasmussen
University of California at Berkeley and Lawrence Berkeley Lab
Berkeley, CA
USA

Solutions to the exercises are accessible to qualified instructors at springer.com on this book’s product
page. Instructors may click on the link additional information and register to obtain their restricted
access.

ISSN 2192-4791

ISBN 978-3-642-23025-7
DOI 10.1007/978-3-642-23026-4

ISSN 2192-4805 (electronic)
ISBN 978-3-642-23026-4 (eBook)

Springer Heidelberg New York Dordrecht London
Library of Congress Control Number: 2012947066
Ó Springer-Verlag Berlin Heidelberg 2013
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Preface

This book on Principles of Physics is intended to serve fundamental college
courses in scientific curricula.
Physics is one of the most important tools to aid undergraduates, graduates, and
researchers in their technical fields of study. Without it many phenomena cannot
be described, studied, or understood. The topics covered here will help students
interpret such phenomena, ultimately allowing them to advance in the applied
aspects of their fields.
The goal of this text is to present many key concepts in a clear and concise, yet
interesting way, making use of practical examples and attractively colored illustrations
whenever appropriate to satisfy the needs of today’s science and engineering students.
Some of the examples, proofs, and subsections in this textbook have been identified
as optional and are preceded with an asterisk *. For less intensive courses these optional
portions may be omitted without significantly impacting the objectives of the chapter.
Additional material may also be omitted depending on the course’s requirements.
The first author taught the material of this book in many universities in the
Middle East for almost four decades. Depending on the university, he leveraged
different international textbooks, resources, and references. These used different
approaches, but were mainly written in an expansive manner delivering a plethora
of topics while targeting students who wanted to dive deeply into the subject
matter. In this textbook, however, the authors introduce a large subset of these
topics but in a more simplified manner, with the intent of delivering these topics
and their key facts to students all over the world and in particular to students in the
Middle East and neighboring regions where English may not be the native language. The second author went over the entire text with the background of study
and/or teaching at Caltech, UC Berkeley, and Yale.
Instructors teaching from this textbook will be able to gain online access from
the publisher to the solutions manual, which provides step-by-step solutions to all
exercises contained in the book. The solutions manual also contains many tips,

colored illustrations, and explanations on how the solutions were derived.

v


vi

Preface

Acknowledgments from Prof. Hafez A. Radi
I owe special thanks to my wife and two sons Tarek and Rami for their ongoing
support and encouragement. I also owe special thanks to my colleague and friend
Prof. Rasmussen for his invaluable contributions to this book, and for everything
that I learned from him over the years while carrying out scientific research at
Lawrence Berkeley Lab. Additionally, I would like to express my gratitude to
Prof. Ali Helmy Moussa, Prof. of Physics at Ain Shams University in Egypt, for
his assistance, support, and guidance over the years. I also thank all my fellow
professors and colleagues who provided me with valuable feedback pertaining to
many aspects of this book, especially Dr. Sana’a Ismail, from Dar El Tarbiah
School, IGCSE section and Dr. Hesham Othman from the Faculty of Engineering
at Cairo University. I would also like to thank Professor Mike Guidry, Professor of
Physics and Astronomy at the University of Tennessee Knoxville, for his valuable
recommendations. I am also grateful to the CD Odessa LLC for their ConceptDraw software suite which was used to create almost all the figures in this book.
I finally extend my thanks and appreciation to Professor Nawal El-Degwi,
Professor Khayri Abdel-Hamid, Professor Said Ashour, and the staff members and
teaching assistants at the faculty of Engineering at MSA University, Egypt, for all
their support and input.
Hafez A. Radi

Acknowledgments from Prof. John O. Rasmussen

I would like to thank Prof. Radi for the opportunity to join him as coauthor. I am
grateful to the many teachers, students, and colleagues from whom I learned
various aspects of the fascinating world of the physical sciences, notably the late
Drs. Linus Pauling, Isadore Perlman, Stanley Thompson, Glenn Seaborg, Earl
Hyde, Hilding Slätis, Aage Bohr, Gaja Alaga, and Hans-Järg Mang. There are
many others, still living, too numerous to list here. I would also like to extend my
special thanks to my wife for her support and encouragement.
John O. Rasmussen



Contents

Part I

Fundamental Basics

1

Dimensions and Units . . . . . . . . . . . . . . . . .
1.1
The International System of Units . . .
1.2
Standards of Length, Time, and Mass .
1.3
Dimensional Analysis . . . . . . . . . . . .
1.4
Exercises . . . . . . . . . . . . . . . . . . . . .

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3
3
5
9
12

2

Vectors . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.1
Vectors and Scalars . . . . . . . . . . . . .
2.2
Properties of Vectors. . . . . . . . . . . . .
2.3
Vector Components and Unit Vectors .
2.4
Multiplying Vectors . . . . . . . . . . . . .
2.5
Exercises . . . . . . . . . . . . . . . . . . . . .

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17
17
19
22
27
33

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41
41
42
44
48
52
57
62

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and Acceleration
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71

Part II

Mechanics

3

Motion in One Dimension . . . . . . . . . . . . . .
3.1
Position and Displacement . . . . . . . . .
3.2
Average Velocity and Average Speed .
3.3
Instantaneous Velocity and Speed . . . .
3.4
Acceleration . . . . . . . . . . . . . . . . . . .
3.5
Constant Acceleration . . . . . . . . . . . .
3.6
Free Fall . . . . . . . . . . . . . . . . . . . . .
3.7
Exercises . . . . . . . . . . . . . . . . . . . . .

4

Motion in Two Dimensions . . . . . . . . .
4.1

Position, Displacement, Velocity,
Vectors . . . . . . . . . . . . . . . . . .
4.2
Projectile Motion . . . . . . . . . . .

71
79

vii


viii

Contents

4.3
4.4
4.5
4.6

Uniform Circular Motion . . . . . . . .
Tangential and Radial Acceleration.
Non-uniform Circular Motion. . . . .
Exercises . . . . . . . . . . . . . . . . . . .

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87
90
91
93

5

Force
5.1
5.2
5.3
5.4

and Motion. . . . . . . . . . . . . . . . . . . . . . . . . .
The Cause of Acceleration and Newton’s Laws
Some Particular Forces . . . . . . . . . . . . . . . . .
Applications to Newton’s Laws . . . . . . . . . . .
Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . .

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103
103
106
113
124

6

Work,
6.1
6.2
6.3
6.4
6.5
6.6
6.7

6.8
6.9

Energy, and Power . . . . . . . . . . . . . . . .
Work Done by a Constant Force . . . . . . .
Work Done by a Variable Force. . . . . . . .
Work-Energy Theorem . . . . . . . . . . . . . .
Conservative Forces and Potential Energy .
Conservation of Mechanical Energy . . . . .
Work Done by Non-conservative Forces . .
Conservation of Energy . . . . . . . . . . . . . .
Power . . . . . . . . . . . . . . . . . . . . . . . . . .
Exercises . . . . . . . . . . . . . . . . . . . . . . . .

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137
137
142
148
151
157
159
162
166
170

7

Linear
7.1
7.2
7.3

Momentum, Collisions, and Center of Mass . . . . . . . .
Linear Momentum and Impulse . . . . . . . . . . . . . . . . . .
Conservation of Linear Momentum. . . . . . . . . . . . . . . .
Conservation of Momentum and Energy in Collisions . . .
7.3.1
Elastic Collisions in One and Two Dimensions .
7.3.2
Inelastic Collisions . . . . . . . . . . . . . . . . . . . . .

Center of Mass (CM) . . . . . . . . . . . . . . . . . . . . . . . . .
Dynamics of the Center of Mass . . . . . . . . . . . . . . . . .
Systems of Variable Mass . . . . . . . . . . . . . . . . . . . . . .
7.6.1
Systems of Increasing Mass . . . . . . . . . . . . . . .
7.6.2
Systems of Decreasing Mass; Rocket Propulsion
Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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181
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184
187
187
194
195
199
203
204
205
209

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227
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232
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238
240
248

7.4
7.5
7.6

7.7
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Rotational Motion . . . . . . . . . . . . . . . . . . . . . . . .
8.1
Radian Measures . . . . . . . . . . . . . . . . . . . .
8.2
Rotational Kinematics; Angular Quantities. . .
8.3
Constant Angular Acceleration . . . . . . . . . . .
8.4
Angular Vectors . . . . . . . . . . . . . . . . . . . . .
8.5
Relating Angular and Linear Quantities. . . . .
8.6
Rotational Dynamics; Torque . . . . . . . . . . . .
8.7
Newton’s Second Law for Rotation . . . . . . .
8.8
Kinetic Energy, Work, and Power in Rotation

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Contents

8.9
8.10
9

ix

Rolling Motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Angular Momentum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
9.1
Angular Momentum of Rotating Systems . . . . . . . . . .
9.1.1
Angular Momentum of a Particle . . . . . . . . . .
9.1.2
Angular Momentum of a System of Particles . .
9.1.3
Angular Momentum of a Rotating Rigid Body .
9.2
Conservation of Angular Momentum. . . . . . . . . . . . . .
9.3
The Spinning Top and Gyroscope. . . . . . . . . . . . . . . .
9.4
Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

10 Mechanical Properties of Matter. . . . . . . . . . . . . . . .
10.1
Density and Relative Density . . . . . . . . . . . . . .

10.2
Elastic Properties of Solids . . . . . . . . . . . . . . .
10.2.1 Young’s Modulus: Elasticity in Length .
10.2.2 Shear Modulus: Elasticity of Shape . . .
10.2.3 Bulk Modulus: Volume Elasticity . . . . .
10.3
Fluids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
10.4
Fluid Statics . . . . . . . . . . . . . . . . . . . . . . . . . .
10.5
Fluid Dynamics . . . . . . . . . . . . . . . . . . . . . . .
10.6
Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Part III

252
259

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269
269
269
271
271
277

285
289

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303
304
306
307
310
312
314
316
328
345

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357
357
360
361
362
365
371

........
........

379
379

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379
380

384
390
395
396
406
416

Introductory Thermodynamics

11 Thermal Properties of Matter . . . . . . . . . . . . .
11.1
Temperature . . . . . . . . . . . . . . . . . . . . .
11.2
Thermal Expansion of Solids and Liquids
11.2.1 Linear Expansion . . . . . . . . . . .
11.2.2 Volume Expansion . . . . . . . . . .
11.3
The Ideal Gas . . . . . . . . . . . . . . . . . . .
11.4
Exercises . . . . . . . . . . . . . . . . . . . . . . .

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12 Heat and the First Law of Thermodynamics . . . . . . . .
12.1
Heat and Thermal Energy . . . . . . . . . . . . . . . . .
12.1.1 Units of Heat, The Mechanical
Equivalent of Heat . . . . . . . . . . . . . . . .
12.1.2 Heat Capacity and Specific Heat . . . . . .
12.1.3 Latent Heat . . . . . . . . . . . . . . . . . . . . .
12.2
Heat and Work . . . . . . . . . . . . . . . . . . . . . . . . .
12.3
The First Law of Thermodynamics . . . . . . . . . . .
12.4
Applications of the First Law of Thermodynamics
12.5
Heat Transfer . . . . . . . . . . . . . . . . . . . . . . . . . .
12.6
Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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x

Contents

13 Kinetic Theory of Gases . . . . . . . . . . . . . . . . . . . . . . . .
13.1
Microscopic Model of an Ideal Gas . . . . . . . . . . .

13.2
Molar Specific Heat Capacity of an Ideal Gas . . . .
13.2.1 Molar Specific Heat at Constant Volume .
13.2.2 Molar Specific Heat at Constant Pressure .
13.3
Distribution of Molecular Speeds . . . . . . . . . . . . .
13.4
Non-ideal Gases and Phases of Matter . . . . . . . . .
13.5
Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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427
427
434
435
436
441
442
444

14 Oscillations and Wave Motion . . . . . . . . . . . . . . . . . . . .
14.1
Simple Harmonic Motion . . . . . . . . . . . . . . . . . . .
14.1.1 Velocity and Acceleration of SHM . . . . . . .
14.1.2 The Force Law for SHM . . . . . . . . . . . . . .
14.1.3 Energy of the Simple Harmonic Oscillator. .
Ã

14.2
Damped Simple Harmonic Motion . . . . . . . . . . . .
14.3
Sinusoidal Waves . . . . . . . . . . . . . . . . . . . . . . . . .
14.3.1 Transverse and Longitudinal Waves . . . . . .
14.3.2 Wavelength and Frequency . . . . . . . . . . . .
14.3.3 Harmonic Waves: Simple Harmonic Motion
14.4
The Speed of Waves on Strings . . . . . . . . . . . . . . .
14.5
Energy Transfer by Sinusoidal Waves on Strings . . .
14.6
The Linear Wave Equation . . . . . . . . . . . . . . . . . .
14.7
Standing Waves . . . . . . . . . . . . . . . . . . . . . . . . . .
14.7.1 Reflection at a Boundary . . . . . . . . . . . . . .
14.7.2 Standing Waves and Resonance . . . . . . . . .
14.8
Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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451
451
452
455
459
462
463
463
465
466
470
472
476
477
481
482
486

Part IV

Sound and Light Waves

15 Sound
15.1
15.2
15.3
15.4
15.5
15.6
15.7
15.8

Waves . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Speed of Sound Waves . . . . . . . . . . . . . . . . .
Periodic Sound Waves. . . . . . . . . . . . . . . . . .
Energy, Power, and Intensity of Sound Waves .
The Decibel Scale . . . . . . . . . . . . . . . . . . . .
Hearing Response to Intensity and Frequency .
The Doppler Effect . . . . . . . . . . . . . . . . . . . .
Supersonic Speeds and Shock Waves . . . . . . .
Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . .

16 Superposition of Sound Waves . . . . . . . . . . .
16.1
Superposition and Interference . . . . . . .
16.2
Spatial Interference of Sound Waves . .
16.3
Standing Sound Waves . . . . . . . . . . . .
16.4
Standing Sound Waves in Air Columns.

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499
499
502
505
510
514
514
521
523

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531
531
533
537
541


Contents

16.5

16.6

xi

Temporal Interference of Sound Waves: Beats . . . . . . . . . . .
Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Waves and Optics . . . . . . . . . . . . . . . . . . .
Light Rays . . . . . . . . . . . . . . . . . . . . . . . .
Reflection and Refraction of Light . . . . . . .
Total Internal Reflection and Optical Fibers.
Chromatic Dispersion and Prisms . . . . . . . .
Formation of Images by Reflection . . . . . . .
17.5.1 Plane Mirrors . . . . . . . . . . . . . . . .
17.5.2 Spherical Mirrors . . . . . . . . . . . . .
17.6
Formation of Images by Refraction. . . . . . .
17.6.1 Spherical Refracting Surfaces . . . .
17.6.2 Flat Refracting Surfaces . . . . . . . .
17.6.3 Thin Lenses . . . . . . . . . . . . . . . . .
17.7
Exercises . . . . . . . . . . . . . . . . . . . . . . . . .

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561
561
563
568
571
575
575
576
583
583
584
586
595

18 Interference, Diffraction and Polarization of Light . .
18.1
Interference of Light Waves . . . . . . . . . . . . . .

18.2
Young’s Double Slit Experiment . . . . . . . . . . .
18.3
Thin Films—Change of Phase Due to Reflection
18.4
Diffraction of Light Waves . . . . . . . . . . . . . . .
18.5
Diffraction Gratings . . . . . . . . . . . . . . . . . . . .
18.6
Polarization of Light Waves . . . . . . . . . . . . . .
18.7
Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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603
603
604
611
615
620
624
627

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637
637
639
642
651

20 Electric Fields . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
20.1
The Electric Field . . . . . . . . . . . . . . . . . . . . . . . . . . . .
20.2
The Electric Field of a Point Charge . . . . . . . . . . . . . .
20.3
The Electric Field of an Electric Dipole . . . . . . . . . . . .
20.4
Electric Field of a Continuous Charge Distribution . . . . .
20.4.1 The Electric Field Due to a Charged Rod . . . . .
20.4.2 The Electric Field of a Uniformly Charged Arc .
20.4.3 The Electric Field of a Uniformly Charged Ring
20.4.4 The Electric Field of a Uniformly Charged Disk
20.5
Electric Field Lines. . . . . . . . . . . . . . . . . . . . . . . . . . .

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659
659
660
666
670
672
679
681
682
684

17 Light
17.1
17.2
17.3
17.4
17.5

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549
554

Part V Electricity
19 Electric Force . . . . . . . . . . . . . . . . . . . .
19.1
Electric Charge. . . . . . . . . . . . . . .
19.2
Charging Conductors and Insulators
19.3
Coulomb’s Law . . . . . . . . . . . . . .
19.4

Exercises . . . . . . . . . . . . . . . . . . .

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xii

Contents

20.6
20.7

Motion of Charged Particles in a Uniform Electric Field . . . .
Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

21 Gauss’s Law. . . . . . . . . . . . . . . . . . . . . . . . .
21.1
Electric Flux . . . . . . . . . . . . . . . . . . .
21.2
Gauss’s Law . . . . . . . . . . . . . . . . . . .
21.3
Applications of Gauss’s Law . . . . . . . .
21.4
Conductors in Electrostatic Equilibrium.
21.5
Exercises . . . . . . . . . . . . . . . . . . . . . .

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701
701
705
707
717
720

22 Electric Potential . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
22.1
Electric Potential Energy . . . . . . . . . . . . . . . . . . . . .
22.2
Electric Potential . . . . . . . . . . . . . . . . . . . . . . . . . .
22.3
Electric Potential in a Uniform Electric Field. . . . . . .
22.4
Electric Potential Due to a Point Charge . . . . . . . . . .
22.5
Electric Potential Due to a Dipole . . . . . . . . . . . . . .
22.6
Electric Dipole in an External Electric Field . . . . . . .
22.7
Electric Potential Due to a Charged Rod . . . . . . . . . .
22.8
Electric Potential Due to a Uniformly Charged Arc . .
22.9
Electric Potential Due to a Uniformly Charged Ring. .
22.10 Electric Potential Due to a Uniformly Charged Disk . .
22.11 Electric Potential Due to a Uniformly Charged Sphere
22.12 Electric Potential Due to a Charged Conductor . . . . .

22.13 Potential Gradient . . . . . . . . . . . . . . . . . . . . . . . . . .
22.14 The Electrostatic Precipitator . . . . . . . . . . . . . . . . . .
22.15 The Van de Graaff Generator . . . . . . . . . . . . . . . . . .
22.16 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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731
731
733
735
741
745
747
749
752
753
754
756
757
758
761
762
763

23 Capacitors and Capacitance . . . . . . . . . . . .
23.1
Capacitor and Capacitance . . . . . . . . .
23.2
Calculating Capacitance. . . . . . . . . . .
23.3
Capacitors with Dielectrics . . . . . . . .

23.4
Capacitors in Parallel and Series. . . . .
23.5
Energy Stored in a Charged Capacitor.
23.6
Exercises . . . . . . . . . . . . . . . . . . . . .

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686
691

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773
773
775
781
790
795
797

24 Electric Circuits . . . . . . . . . . . . . . . . . . . . . . . . . .

24.1
Electric Current and Electric Current Density.
24.2
Ohm’s Law and Electric Resistance . . . . . . .
24.3
Electric Power . . . . . . . . . . . . . . . . . . . . . .
24.4
Electromotive Force . . . . . . . . . . . . . . . . . .
24.5
Resistors in Series and Parallel. . . . . . . . . . .
24.6
Kirchhoff’s Rules . . . . . . . . . . . . . . . . . . . .

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809
809
814
823
825
829
834


Contents

24.7
24.8
Part VI

xiii

The RC Circuit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

838
844

Magnetism

25 Magnetic Fields . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
25.1
Magnetic Force on a Moving Charge . . . . . . . . . . .
25.2
Motion of a Charged Particle in a Uniform Magnetic
25.3
Charged Particles in an Electric and Magnetic Fields
25.3.1 Velocity Selector . . . . . . . . . . . . . . . . . . .
25.3.2 The Mass Spectrometer . . . . . . . . . . . . . . .
25.3.3 The Hall Effect . . . . . . . . . . . . . . . . . . . .
25.4
Magnetic Force on a Current-Carrying Conductor. . .
25.5
Torque on a Current Loop . . . . . . . . . . . . . . . . . . .
25.5.1 Electric Motors. . . . . . . . . . . . . . . . . . . . .
25.5.2 Galvanometers . . . . . . . . . . . . . . . . . . . . .
25.6
Non-Uniform Magnetic Fields . . . . . . . . . . . . . . . .
25.7
Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

.....
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Field .

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859
859
863
865
866

866
867
869
874
876
877
878
879

26 Sources of Magnetic Field. . . . . . . . . . . . . . . . . . . . . . . .
26.1
The Biot-Savart Law . . . . . . . . . . . . . . . . . . . . . . .
26.2
The Magnetic Force Between Two Parallel Currents.
26.3
Ampere’s Law . . . . . . . . . . . . . . . . . . . . . . . . . . .
26.4
Displacement Current and the Ampere-Maxwell Law
26.5
Gauss’s Law for Magnetism. . . . . . . . . . . . . . . . . .
26.6
The Origin of Magnetism . . . . . . . . . . . . . . . . . . .
26.7
Magnetic Materials . . . . . . . . . . . . . . . . . . . . . . . .
26.8
Diamagnetism and Paramagnetism . . . . . . . . . . . . .
26.9
Ferromagnetism . . . . . . . . . . . . . . . . . . . . . . . . . .
26.10 Some Applications of Magnetism . . . . . . . . . . . . . .
26.11 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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889
889
895
897
901
903
904
908
910
914
919
921

27 Faraday’s Law, Alternating Current, and Maxwell’s Equations .
27.1
Faraday’s Law of Induction . . . . . . . . . . . . . . . . . . . . . . .
27.2
Motional emf . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
27.3
Electric Generators . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

27.4
Alternating Current . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
27.5
Transformers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
27.6
Induced Electric Fields . . . . . . . . . . . . . . . . . . . . . . . . . .
27.7
Maxwell’s Equations of Electromagnetism . . . . . . . . . . . .
27.8
Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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933
933
936
940
942
943
945
947
950

28 Inductance, Oscillating Circuits, and AC Circuits . . . . . . . . . . . .
28.1
Self-Inductance. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

961
961

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xiv

Contents

28.2
28.3
28.4
28.5
28.6
28.7
28.8
28.9

28.10

Mutual Inductance . . . . . . . . . . . .
Energy Stored in an Inductor . . . . .
The L–R Circuit . . . . . . . . . . . . . .
The Oscillating L–C Circuit . . . . . .
The L–R–C Circuit . . . . . . . . . . . .
Circuits with an ac Source . . . . . . .
L–R–C Series in an ac Circuit . . . .
Resonance in L–R–C Series Circuit
Exercises . . . . . . . . . . . . . . . . . . .

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964
966
967
971
974
977
984
988
988

Appendix A Conversion Factors . . . . . . . . . . . . . . . . . . . . . . . . . . . .

999

Appendix B Basic Rules and Formulas . . . . . . . . . . . . . . . . . . . .

1003

Appendix C The Periodic Table of Elements . . . . . . . . . . . . . . . . . .

1013

Answers to All Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1015

Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1057


Fundamental Physical Constants
Quantity

Symbol

Approximate value

Speed of light in vacuum

c

3:00 Â 108 m/s

Avogadro’s number

NA

6:02 Â 1023 molÀ1 ¼ 6:02 Â 1026 kmolÀ1

Gas constant

R

8:314 J/mol ÁK ¼ 8 314J/kmol Á K

Boltzmann’s constant

k

1:38 Â 10À23 J/K

Gravitational constant

G

6:67 Â 10À11 N Á m2 =kg2

Planck’s constant

h

6:63 Â 10À34 J Á s

Permittivity of free space

0

8:85 Â 10À12 C2 =N Á m2

Permeability of free space

l0 ¼ 1=ðc2 0 Þ

4p  10À7 T Á m/A

Atomic mass unit

1u

1:6605 Â 10À27 kg ¼ 931:49 MeV/c2

Electron charge

-e

À1:60 Â 10À19 C

Electron rest mass

me

9:11 Â 10À31 kg ¼ 0:000549 u
¼ 0:511 MeV/c2

Proton rest mass

mp

1:6726 Â 10À27 kg ¼ 1:00728 u
¼ 938:27 MeV/c2

Neutron rest mass

mn

1:6749 Â 10À27 kg ¼ 1:008665 u
¼ 939:57 MeV/c2

xv


Other useful constants
Acceleration due to gravity at the Earth’s surface (av.)

g ¼ 9:8 m/s2

Absolute zero (0 K)

À273:15  C

Joule equivalent (1 kcal)

4; 186 J


Speed of sound in air (20 C)

343 m/s

Density of air (dry)

1:29 kg/m3

Standard atmosphere

1:01 Â 105 Pa

Electric breakdown strength

3 Â 106 V/m

Earth: Mass
Radius (av.)

5:98 Â 1024 kg
6:38 Â 103 km

Moon: Mass
Radius (av.)

7:35 Â 1022 kg
1:74 Â 103 km

Sun: Mass
Radius (av.)

1:99 Â 1030 kg

6:96 Â 105 km

Earth–Moon distance (av.)

3:84 Â 105 km

Earth–Sun distance (av.)

1:5 Â 108 km

The greek alphabet
Alpha

A

a

Nu

M

m

Beta

B

b

Xi

N

n

Gamma

C

c

Omicron

O

o

Delta

D

d

Pi

P

p

Epsilon

E

e

Rho

Q

q

Zeta

F

f

Sigma

R

r

Eta

H

g

Tau

S

s

Theta

H

h

Upsilon

T

t

Iota

I

i

Phi

U

/

Kappa

J

j

Chi

V

v

Lambda

K

k

Psi

W

w

Mu

L

l

Omega

X

x

xvi


Some SI base units and derived units
Quantity

Unit name

Unit symbol

In terms of base units

Mass

kilogram

kg

Length

meter

m

Time

second

s

Electric current

ampere

A

{

Force

newton

N

kgÁm=s2

Energy and work

joule

J

kgÁm2 =s2

Power

watt

W

kgÁm2 =s3

Pressure

pascal

Pa

kg=ðmÁs2 Þ

Frequency

hertz

Hz

s-1

Electric charge

coulomb

C

AÁs

Electric potential

volt

V

kgÁm2 =ðAÁs3 Þ

Electric resistance

ohm

X

kgÁm2 =ðA2 Ás3 Þ

Capacitance

farad

F

A2 Ás4 =ðkgÁm2 Þ

Magnetic field

tesla

T

kg=ðAÁs2 Þ

Magnetic flux

weber

Wb

kgÁm2 =ðAÁs2 Þ

Inductance

henry

H

kgÁm2 =ðs2 ÁA2 Þ

Base
SI
units

xvii


SI multipliers
yotta

Y

1024

zeta

Z

1021

exa

E

1018

peta

P

1015

tera

T

1012

giga

G

109

mega

M

106

kilo

k

103

hecto

h

102

deka

da

101

deci

d

10-1

centi

c

10-2

milli

m

10-3

micro

l

10-6

nano

n

10-9

pico

p

10-12

femto

f

10-15

atto

a

10-18

zepto

z

10-21

yocto

y

10-24

xviii

Part I

Fundamental Basics


1

Dimensions and Units

The laws of physics are expressed in terms of basic quantities that require a clear
definition for the purpose of measurements. Among these measured quantities are
length, time, mass, temperature, etc.
In order to describe any physical quantity, we first have to define a unit of
measurement (which was among the earliest tools invented by humans), i.e. a measure that is defined to be exactly 1.0. After that, we define a standard for this quantity,
i.e. a reference to compare all other examples of the same physical quantity.

1.1

The International System of Units

Seven physical quantities have been selected as base quantities in the 14th General
Conference on Weights and Measurements, held in France in 1971. These quantities
form the basis of the International System of Units, abbreviated SI (from its French
name Système International) and popularly known as the metric system. Table 1.1
depicts these quantities, their unit names, and their unit symbols.
Many SI derived units are defined in terms of the first three quantities of Table 1.1.
For example, the SI unit for force, called the newton (abbreviated N), is defined in
terms of the base units of mass, length, and time. Thus, as we will see from the study
of Newton’s second law, the unit of force is given by:
1 N = 1 kg.m/s2

(1.1)

When dealing with very large or very small numbers in physics, we use the
so-called scientific notation which employs powers of 10, such as:

H. A. Radi and J. O. Rasmussen, Principles of Physics,
Undergraduate Lecture Notes in Physics, DOI: 10.1007/978-3-642-23026-4_1,
© Springer-Verlag Berlin Heidelberg 2013

3


4

1 Dimensions and Units

3 210 000 000 m = 3.21 × 109 m

(1.2)

0.000 000 789 s = 7.89 × 10−7 s

(1.3)

Table 1.1 The seven independent SI base units
Quantity

Unit name

Unit symbol

Length

Meter

m

Time

Second

s

Mass

Kilogram

kg

Temperature

Kelvin

K

Electric current

Ampere

A

Amount of substance

Mole

mol

Luminous intensity

Candela

cd

An additional convenient way to deal with very large or very small numbers in
physics is to use the prefixes listed in Table 1.2. Each one of these prefixes represents
a certain power of 10.
Table 1.2 Prefixes for SI unitsa
Factor
1024
1021

Prefix

Symbol

Factor

Prefix

Symbol

yotta-

Y

10−24

yocto-

y

zeta-

Z

10−21

zepto-

z

1018

exa-

E

10−18

atto-

a

1015

peta-

P

10−15

femto-

f

1012

tera-

T

10−12

pico-

p

109

giga-

G

10−9

nano-

n

106

mega-

M

10−6

micro-

µ

103

kilo-

k

10−3

milli-

m

h

10−2

centi-

c

da

10−1

deci-

d

102
101
a

hectadeca-

The most commonly used prefixes are shown in bold face type

Accordingly, we can express a particular magnitude of force as:
1.23 × 106 N = 1.23 mega newtons

= 1.23 MN

(1.4)


1.1 The International System of Units

5

or a particular time interval as:
1.23 × 10−9 s = 1.23 nano seconds

(1.5)

= 1.23 ns

We often need to change units in which a physical quantity is expressed. We
do that by using a method called chain-link conversion, in which we multiply by a
conversion factor that equals unity. For example, because 1 minute and 60 seconds
are identical time intervals, then we can write:
60 s
1 min
= 1 and
=1
60 s
1 min
This does not mean that
treated together.

1

60

(1.6)

= 1 or 60 = 1, because the number and its unit must be

Example 1.1

Convert the following: (a) 1 kilometer per hour to meter per second, (b) 1 mile
per hour to meter per second, and (c) 1 mile per hour to kilometer per hour [to a
good approximation 1mi = 1.609 km].
Solution: (a) To convert the speed from the kilometers per hour unit to meters
per second unit, we write:
1 km/h = 1

km
h

×

103 m
1 km

×

1h
60 × 60 s

= 0.2777...

m
= 0.278 m/s
s

(b) To convert from miles per hour to meters per second, we write:
1 mi/h = 1

1609 m
1h
mi
×
×
h
1 mi
60 × 60 s

= 0.447

m
= 0.447 m/s
s

(c) To convert from miles per hour to kilometers per hour, we write:
1mi/h = 1

1.2

mi
h

×

1.609 km
1 mi

= 1.609

km
= 1.609 km/h
h

Standards of Length, Time, and Mass

Definitions of the units of length, time, and mass are under constant review and are
changed from time to time. We only present in this section the latest definitions of
those quantities.


6

1 Dimensions and Units

Length (L)
In 1983, the precision of the meter was redefined as the distance traveled by a light
wave in vacuum in a specified time interval. The reason is that the measurement of
the speed of light has become extremely precise, so it made sense to adopt the speed
of light as a defined quantity and to use it to redefine the meter. In the words of the
17th General Conference on Weights and Measurements:
One Meter
One meter is the distance traveled by light in vacuum during the time interval

of 1/299 792 458 of a second.
This time interval number was chosen so that the speed of light in vacuum c will be
exactly given by:
c = 299 792 458 m/s

(1.7)

For educational purposes we usually consider the value c = 3 × 108 m/s.
Table 1.3 lists some approximate interesting lengths.
Table 1.3 Some approximate
lengths

Length

Meters

Distance to farthest known galaxy

4 × 1025

Distance to nearest star

4 × 1016

Distance from Earth to Sun

1.5 × 1011

Distance from Earth to Moon

4 × 108

Mean radius of Earth

6 × 106

Wave length of light

5 × 10−7

Radius of hydrogen atom

5 × 10−11

Radius of proton

1 × 10−15

Time (T)
Recently, the standard of time was redefined to take advantage of the high-precision
measurements that could be obtained by using a device known as an atomic clock.
Cesium is most common element that is typically used in the construction of atomic
clocks because it allows us to attain high accuracy.


1.2 Standards of Length, Time, and Mass

7

Since 1967, the International System of Measurements has been basing its unit

of time, the second, on the properties of the isotope cesium-133 (133
55 Cs). One of the
133
transitions between two energy levels of the ground state of 55 Cs has an oscillation frequency of 9 192 631 770 Hz, which is used to define the second in SI
units. Using this characteristic frequency, Fig. 1.1 shows the cesium clock at the
National Institute of Standards and Technology. The uncertainty is about 5 × 10−16
(as of 2005). Or about 1 part in 2 × 1015 . This means that it would neither gain nor
lose a second in 64 million years.
One Second
One second is the time taken for the cesium atom

133 Cs
55

to perform

9 192 631 770 oscillations to emit radiation of a specific wavelength

Fig. 1.1 The cesium atomic
clock at the National Institute
of Standards and Technology
(NIST) in Boulder, Colorado
(photo with permission)

Table 1.4 lists some approximate interesting time intervals.
Table 1.4 Some approximate
time intervals

Time intervals

Seconds

Lifetime of proton (predicted)

1 × 1039

Age of the universe

5 × 1017

Age of the Earth

1.3 × 1017

Period of one year

3.2 × 107

Time between human heartbeats

8 × 10−1

Period of audible sound waves

1 × 10−3

Period of visible light waves

2 × 10−15

Time for light to cross a proton

3.3 × 10−24