Dedication
This book is dedicated to my loving teacher, Prof. P.V. Krishnan (retired professor, IIT Delhi), and his wife, mother Krishangi Devi , whose teachings gave me life. Whatever I am today, I owe it to them.
Preface Having experienced teaching at various levels and with a varied group of students, I have experienced the shortcomings faced by most of the students. I can also remember my own experiences of failure and dejection when I used to study. Often, I did not find answers to my questions, or I could not find a book that could help me think, nor did I find a collection of problems that stimulate the mind. In this book, finally I have come to fulfill a vision of a book that has an international collection of problems, the theory to such depth as we cover at Bansal Classes, Kota, and American quality of printing . This book is not a substitute for a teacher. I strictly believe and this has been proven over the years: To learn, you need a teacher. But learning under a qualified teacher will help you understand this book better. Often students find Physics tough or at least challenging. Perhaps it is both because it tries to encourage you to think and it does not follow any stereotyped pattern. A thinking individual will do well in physics. In the modern learning atmosphere, perhaps we are never even encouraged to think. I have made an attempt to cross this barrier and challenge you to think at numerous places. For this purpose, I have scattered numerous checkpoints throughout the chapters. The problem section begins with a set of assertions and reason problems, and the student is required to find whether those statements are correct or not. And if they are, what are the reasons. Those of you who are accustomed to the original Halliday, Resnick, and Walker would be in for a surprise because although this is supposed to be an adaptation, I have freely made the changes as per the needs of the students who are appearing in competitive examinations like Physics Olympiads, IIT JEE, and so on. So the net result is that you have an altogether new book, my style. Three new chapters have been added and many have been deleted. All over the world, slowly objective type examinations are replacing subjective papers. So we have added extensive collection of objective problems on each and every concept covered in chapter. Each chapter has been started with a chapter opener which illustrates real world phenomena based on that chapter. Some of them are fun, and some of them are real phenomena which should set your mind thinking. The book follows a particular format. I introduce a concept and try to illustrate it by the means of an example. In the spirit of what we did in Volume I of this book, we have explained each illustration in four sections: Conceptualize, classify, compute, and conclude. Conceptualize explains the problem with a clue to the solution.
• •
Classify contains details of the principles of physics used to solve the problem.
•
Compute gives the detailed solution.
•
The real punch lies in the conclude section where many a times the student has to think on the lines of great physicists.
In the exercises that follow at the end of each chapter, I am trying to take the students through the same ideas. The spirit of the book will be marred if the student just focuses on the theory and does not try out the exercises that follow. I have tried to arrange the exercises in increasing order of difficulty. The answers are given at the end of the chapter. If one is not able to solve a particular question, then it will do him good to go back to the illustration and try it out himself.
iv
Preface
How to Approach the Question Bank To gain the most, I would suggest the following sequence: •
•
•
•
Step 1: First, go through the text of a section thoroughly with the help of a qualified teacher. Try solving the illustrations yourself and feel the joy of discovering physics. Step 2: Then go through the multiple choice questions and the subjective exercises pertaining to that section. Step 3: At the end of that, when you are confident of the basic concepts of the entire chapter, there are additional problems given at the end of problems section. Step 4: After doing all these, you should go to the Assertion and Reasons (Reasoning Type Questions) section and solve them to see if you do understand the principles completely.
These problems take you to the realm of IIT JEE, Physics Olympiad, and even beyond. Do not feel discouraged if you have not been able to solve the problems at the first go. Remember, even Einstein and Newton had faced failures in their lives. Failure is a stepping stone to success. I wish you all the best in your endeavors. My team and I have tried our level best to offer you an error-free book, even going through the whole manuscript three or four times. All the questions that have been set in the problem section has been solved twice, once by me personally and then by my colleague. Yet, it may be possible that errors may remain in the book. Comments or suggestions on the content and presentation of the book will be received with great interest and highly appreciated. Manish Kumar Singhal Email:
[email protected]
Acknowledgment I have dedicated this book to my loving teacher Prof. P.V. Krishnan and his wife, mother Krishangi Devi. Truly, if they did not give me a spiritual vision of life, I would never even have the boldness of taking up teaching as a profession, much less to venture writing this book. He taught me the real meaning of Science and opened my eyes to a Science which is much more profound and vast than what we are studying here. I encourage all my readers to study his books, “Science and Nescience” and “Wake up! Intellectuals.” They gave me an entirely new perspective to life, they will surely change yours. This book was made possible only by an extensive help rendered by a big group of friends. The leader among them was my friend and colleague Ajit Aggarwal who laboriously went through the entire book and solved each problem personally in detail. My friend Dr. G. Partheepan at IIT Delhi was extremely prompt with his valuable help with the research papers. I am indeed very grateful to Mr. Jearl Walker for allowing me to edit the book the way I wanted. Thanks! Thanks are also due to Amit Gupta, author of Vol. I, who introduced me to the idea. Prominent among those who helped me with the books are Kishore Rane of Paravyoma classes, Vishakhapatnam; Anurag Mishra, Bansal Classes, Kota; and Ambarish Srivastava, FIITJEE, Delhi. The kind of open heartedness which these three individuals showed in sharing their collection of books with me is a rare example in this age of hypocrisy and cynicism. I am also deeply indebted to Mr. V.K. Bansal of Bansal classes, Kota, who gave us such an open learning atmosphere at Kota. His dedication to teaching excellence is something which is unparalleled and would be hard to beat in years to come. My editor Meenakshi Sehrawat and her entire team deserve a gold medal for keeping up with my vision of giving the students gem of a book. My typist Prashant Gupta deserves a special applause for making figures that match the quality of the original book. Special thanks are due to my students of today and past whose thought-provoking questions helped me to explore Phys ics deeper and deeper. Last but not the least, I owe a special thanks to Paras Bansal and Vikas Gupta at Wiley India for putting so much faith in me and risking a big investment for bringing out their first ever textbook in India in color. And that too at Indian prices! This project would have never been successful without these people supporting me. Manish Kumar Singhal April 2010
Note to the Student The IIT-JEE is one of the hardest exams to crack for students. For a very simple reason – concepts cannot be learned by rote, they have to be absorbed, and IIT believes in strong concepts. Each question in the IIT-JEE entrance exam is meant to push the analytical ability of the student to its limit. That is why the questions are called brainteasers! This is where Halliday, Resnick and Walker’s Fundamentals of Physics comes in. This text has been the definitive text for learning Physics concepts and solving problems conceptually for the last 33 years. Its unparalleled approach to teaching physics has been appreciated globally by students and teachers alike. And that is why it is probably the best resource for an IIT aspirant like you today. In collaboration with experts from IIT-JEE coaching, the original Halliday, Resnick and Walker edition has been customized to give you the tools that will help you crack the toughest entrance exam in India. If you take full advantage of the unique features and elements of this textbook, we believe your experience will be fulfilling and enjoyable. Let's walk through some of the special book features that will help you in your efforts to crack IIT-JEE.
A. PEDAGOGY
OPENING TEASER The opening teaser and the related image at the beginning are meant to serve two purposes: First, they are real-life phenomena and thus make the concept something real and not just a bookish detail. And second, they make the student curious and incite him/her to get deeper into the chapter and its contents. Courtesy NASA/JSC
At 2:45 A.M. on March 13, 1989, the entire power-grid system for the Canadian province of Quebec failed, leaving milli ons of people without power on that cold night. In fact, many power-grid systems in the Northern Hemisphere malfunctioned that night, creating a nightmare situation for the engineers who maintained the systems. The cause was not a sudden overtaxing demand for power or a failure of aging equipment. Rather, the cause was an explosion that had occurred on the Sun’s surface three days earlier .
How can a solar explosion shut down a power-grid system? The answer is in this chapter.
CONCEPT EXPLANATION The concept explanation follows. This will lead you to the answer of the teaser in the beginning. The inimitable style of Halliday, Resnick and Walker is obvious in the simple language and real-life examples.
24-1 WHAT IS PHYSICS? One goal of physics is to identify basic forces in our world, such as the electric force we discussed in Chapter 22. A related goal is to determine whether a force is conservative—that is, whether a potential energy can be associated with it. The motivation for associating a potential energy with a force is that we can then apply the principle of the conservation of mechanical energy to closed systems involving the force. This extremely powerful principle allows us to calculate the results of experiments for which force calculations alone would be very difficult. Experimentally, physicists and engineers discovered that the electrostatic force is conservative and thus has an associated electric potential energy. In this chapter we first define this type of potential energy and then put it to use.
24-2 | Electric Potential Energy Any charge in an electric field experiences the action of a force. Consequently, a certain work is done when a charge moves in the field. This work depends on the field strength at different points and on the charge displacement. However, if a charge describes a closed curve, that is, returns to the original position, the work done by the field is equal to zero irrespective of the field configuration and the
shape of the path along which the charge has moved.
IMPORTANT POINTS
Electric potential is a scalar property associated with an electric field, regardless of whether a charged object has been placed in that field; it is measured in joules per coulomb, or volts.
Throughout the book, important tips will be given in a box marked with a pointed finger. This technique highlights the tips and also aids retention.
CHECKPOINTS These are important points after each section in the chapter that help check your understanding of what has been covered till then.
CHECKPOINT 4
The figure here shows three arrangements of two protons.
Rank the arrangements according to the net electric potential produced at point P by the protons, greatest first. D
D
d
d P
d
D P
(a )
PROBLEM-SOLVING TACTICS Tactic 1: The Symbol V and Potential Difference In previous chapters, the symbol V represents an electric potential at a point or along an equipotential surface. However, in matters concerning electrical devices, V often represents a potential difference between two points or two equipotential surfaces. Equation 26-1 is an example of this second use of the symbol. In Section 26-3, you will see a mixture of the two meanings of V . There and in later chapters, you need to be alert as to the intent of this symbol.
P
You will also be seeing, in this book and elsewhere, a variety of phrases regarding potential difference. A potential difference or a “potential” or a “voltage” may be applied to a device, or it may be across a device. A capacitor can be charged to a potential difference, as in “a capacitor is charged to 12 V.” Also, a battery can be characterized by the potential difference across it, as in “a 12 V battery.” Always keep in mind what is meant by such phrases: There is a potential difference between two points, such as two points in a circuit or at the terminals of a device such as a battery.
(b )
(c )
PROBLEM-SOLVING TACTICS These contain helpful instructions to guide the beginning physics student as to how to solve problems and avoid common errors.
B.
THE 4Cs CONCEPT It is normal to be nervous about solving tough IIT-JEE problems. But not if you know how to solve them using the 4Cs. The 4Cs is a unique and logical technique of solving problems conceptually. It is a step-based approach intended to simplify the process of applying formulas and concepts in the computation of the solution. See the Halliday way of 4Cs for solving the problem with explanations
CONCEPTUALIZE
provided for each step. The purpose of each C is explained below.
First, the concept used in the problem is identified and a brief explanation of the problem is given.
CLASSIFY
Based on what value needs to be obtained and what values are given in the question, the formulae used are listed.
COMPUTE The actual solution comes next, including the application of formulae and the resultant equations.
CONCLUDE The problem ends with the explanation of the values derived as the answer. Sample Problem
35-26
What is the relationship between A and n, so that no rays come out of second face (Fig. 35-58)?
Compute: Applying Snell’s law at the first surface: 1
FIG. 35-58 The prism has such a refractive index and an angle of prism combination that all the incident rays undergo total internal reflection.
× sin 90° = n sin r − 1 r = sin n − 1 r = A − sin . n 1
1
1
i
r 1
r 2
r 2 > q c
Conceptualize: Here, we want to choose the refractive index of the prism such that a ray will always undergo total internal reflection. Note that this total internal reflection can occur only when the light ray goes from denser to rarer medium. In other words, this will occur only when the ray is incident on the second surface. The situation implies that for the smallest angle r 2 also, the total internal reflection should occur. Classify: r 1 + r 2 = A. So when r 2 is minimum, r 1 is maximum. The angle of incidence i is also maximum by Snell’s law. But the maximum angle of incidence can be 90 ° . This problem implies that if a total internal reflection occurs when angle of incidence is 90°, then total internal reflection will occur at all the angles.
1
2
But for total internal reflection at the second surface: r 2
> θ
c
1 > 1 sinθ n − 1 − 1 A − sin > sin . n n sin r 2
c
1
1
Thus, the condition becomes n
A > cosec . 2
Conclude: Many optical instruments, such as binoculars, periscopes, and telescopes, use glass prisms and total internal reflection to turn a beam of light through 90° or 180°.
C.
ASSESSMENT – AS PER IIT-JEE PATTERN
Mere theory is not enough. It is also important to test what has been taught. For the test to be effective, the assessment technique should be comprehensive. In the context of this book, the assessment also needs to be in resonance with the IIT-JEE paper pattern because unless the student practices the IIT-JEE way, he/ she will not be sufficiently equipped to crack the exam. Keeping this in mind, the assessment has been divided into three main parts – Reasoning Type Questions, Multiple Choice Questions, and Problem s – plus a section of Additional Problems for students interested in testing their understanding of the whole chapter. Each part contributes to the preparation of IIT-JEE because each part is modeled on the actual IIT-JEE paper.
REASONING TYPE The first section of the assessment is reasoningtype questions, similar to the ones asked in the IIT-JEE paper. Practicing these would mean effective preparation for the exam.
REASONING TYPE QUESTIONS In the following set of questions, a statement 1 is given and a corresponding statement 2 is given just below it. Mark the correct answer as:
Statement 2: x component of electric field is given by E x =
∂ x
,
(a) If both Statement 1 and Statement 2 are true and Statement 2 is the correct explanation of Statement 1.
and on equipotential surface potential V is constant.
(b) If both Statement 1 and Statement 2 are true but Statement 2 is not the correct explanation of Statement 1.
4. Statement 1: If the distance between two point charges increases, their potential energy decreases.
(c) If Statement 1 is true but Statement 2 is false. (d) If Statement 1 is false but Statement 2 is true.
1. Statement 1: It is less dangerous to touch a faulty electrical appliance at 200 V than a Van de Graff generator at 20 000 V. Statement 2: If we have two similar bodies at the different potential, the body with a higher potential will have more charge on it.
Statement 2: The potential energy of two point charges is inversely proportional to the distance between the two charges.
5. Statement 1: If the electric potential at all the points in space is zero, the electric field at all the points in space must be zero. Statement 2: If the electric field at al l the points in space i s zero, the electric potential at all the points in space must be zero.
MULTIPLE CHOICE QUESTIONS sec. 24-2 Electric Potential Energy 1. A point charge Q is moved along a circular path around another fixed point charge. The work done by the electric field for one complete circle is zero (a) If fixed charge is at the center of the circular path (b) If the two charges have the same magnitude (c) If the two charges have the same magnitude and opposite signs (d) All above cases
2. Three charged particles are initially in a position 1. They are free to move and they come to another position 2 after some time. Let U 1 and U 2 be the electrostatic potential energies in position 1 and 2. Then (a) U 1 > U 2 (b) U 2 > U 1 (c) U 1 = U 2
∂ V
−
3. When a negative charge moves in a direction opposite to the direction of an electric field, (a) (b) (c) (d)
The field does work on the charge The charge does work on the field The charge gains potential energy The charge loses potential energy
4. A point charge q moves from point P to point S along the path P , Q, R, and E S in a uniform electric field P (a , b , 0 ) pointing parallel to the positive direction of the x (0, 0, 0)S Q (2a , 0, 0) axis. The coordinates of the R (a , − b , 0 ) points P , Q, R, and S are (a, b, 0), (2a, 0, 0), (a, − b, 0), and (0, 0, 0), respectively FIG. 24-37 Multiple (Fig. 24-37). The work done choice question 4. by the field in the above proc-
MULTIPLE CHOICE QUESTIONS This form of Assessment forms the basis of the IIT-JEE paper. If a student becomes adept at attempting these types of questions, he/she has a good chance of doing well in the exam.
PROBLEMS
PROBLEMS sec. 24-2 Electric Potential Energy 1. Electrostatic work w is done on a charged particle, going from point A to point B, without any other external force acting on it. You next apply a force to move the particle back to point A, increasing its kinetic energy by an amount equal to 2w. How much work did you do? 2. How much work is required to set up the arrangement of Fig. 24-48 if q = 2.0 m C, a = 9.0 cm, and the particles are initially infinitely far apart and at rest?
+q +
–q
a
a
a
3. A particle of charge + 7.5 m C is a + released from rest at the point x = –q +q 60 cm on an x axis. The particle beFIG. 24-48 Problem 2. gins to move due to the presence of a charge Q that remains fixed at the origin. What is the kinetic energy of the particle at the instant it has moved 40 cm if Q = + 20 m C?
undergoes a change in electric potential of 12 V, how much energy is involved?
7. A positron (charge + e, mass equal to the electron mass) is V (V) moving at 1.0 107 m/s in the posi- V s tive direction of an x axis when, at x = 0, it encounters an electric field directed along the x axis. The x (cm) 20 50 electric potential V associated 0 with the field is given in Fig. 24- FIG. 24-49 Problem 7. 49. The scale of the vertical axis is set by V 500.0 V. (a) Does the positron emerge from s = the field at x = 0 (which means its motion is reversed) or at x = 0.50 m (which means its motion is not reversed)? (b) What is its speed when it emerges? sec. 24-5 Calculating the Potential from the Field 8. When an electron moves from A to B along an electric field line in Fig. 24-50, the electric field does 3.84 10–19 J of
4. Two charged objects are held a distance r apart. The first object has a mass m and a charge + 2q, while the second object has a mass 2m and a charge + q. The objects are released from rest. Assume that the only force acting on either charge is the electrostatic force from the other charge. (a) When the objects are in motion what is the ratio of the first object’s kinetic energy to that of the second object? What is the speed of (b) the first object and (c) the second object when they are at a large disctance from each other?
Electric field line
Some bonus extra problems are given as part of Assessment at the end of each chapter. These problems are not ordered or sorted in any way so that a studentmust determine which parts of the chapter apply to any given problem.
A
B
C
Equipotentials
5. Two electrons are fixed 2.0 cm apart. Another electron is shot from infinity and stops midway between the two. What is its initial speed?
ADDITIONAL PROBLEMS
A number of numerical problems testing different concepts covered within the chapter are given here. All problems are of different levels of difficulty and meant to help students apply the concepts. Sections are mentioned for students to know which section to refer to in case of doubt.
FIG. 24-50 Problem 8.
ADDITIONAL PROBLEMS 41. A nonconducting sphere has radius R = 2.31 cm and uniformly distributed charge q = + 3.50 fC. Take the electric potential at the sphere’s center to be V 0. What is V at 0 radial distance (a) r = 1.45 cm and (b) r = R.
45. The smiling face of Fig. 24-66 consists of three items:
42. Two charged particles are shown in Fig. 24-64a. Particle 1, with charge q1, is fixed in place at distance d. Particle 2, with charge q2, can be moved along the x axis. Figure 24-64b gives the net electric potential V at the origin due to the two particles as a function of the x coordinate of particle 2. The scale of the x axis is set by x s = 16.0 cm. The plot has an asymptote of
(b) a second thin rod of charge 2.0 m C that forms a circular arc of radius 4.0 cm, subtending an angle of 90° about the center of the full circle;
=
4
y ) V 7 –
d x 1
2
0
x s
0 1 (
x (cm)
V
–10 (a )
(b )
FIG. 24-64 Problem 42. −7
V = 5.76 × 10 V as x →∞ . What is q2 in terms of e?
43. A nonuniform linear charge distribution given by λ = bx, where b is a constant, is located along an x axis from x = 0 to x = 0.20 m. If b = 20 nC/m2 and V = 0 at infinity, what is the electric potential at (a) the origin and (b) the point y = 0.15 m on the y axis? 44. Proton in a well. Figure 24-65 shows electric potential V along an x axis. The scale of the vertical axis is set by V s = 10.0 V. A proton is to be released at x = 3.5 cm with initial kinetic
(a) a thin rod of charge –3.0 m C that forms a full circle of radius 6.0 cm;
(c) an electric dipole with a dipole moment that is perpendicular to a radial line and has magnitude 1.28 × 10–21 C ⋅ m.
FIG. 24-66 Problem 45.
What is the net electric potential at the center?
46. In Fig. 24-67, we move a particle of charge + 2e from infinity to the x axis. How much work do we do? Distance D is 4.00 m.
∞
+ 2e
+ 2e
+e x
47. A particle of positive charge Q is D D fixed at point P . A second particle of FIG. 24-67 mass m and negative charge –q moves at constant speed in a circle of radius Problem 46. r 1, centered at P . Derive an expression for the work W that must be done by an external agent on the second particle to increase the radius of the circle of motion to r 2.
ANSWERS The Answer key at the end of each chapter contains answers to all questions including checkpoints, reasoning questions, multiple choice questions, problems and additional problems.
ANSWERS Checkpoints 1. a 2. (a) 11h/6 from fish itself; (b) 17 h/6 3. The straw is not a ray! Note that the straw has a lateral shift as well as a bend. Actually, the rays from the straw reach our eyes after refraction from the water and the apparent depth of different parts of the straw is different from its actual value. So the straw appears to be bent.
4.
da
3
θ
3
φ
d cos =
n cos
5. (a) e; (b) virtual, same 7. Virtual, same as object, diverging
Reasoning Type Questions 1. (a)
6. (a)
2. (a)
7. (b)
3. (d)
8. (c)
4. (d)
9. (b)
5. (a)
10. (b)
Multiple Choice Questions 1. (d)
12. (c)
2. (b)
13. (c)
3. (c)
14. (d)
4. (a)
15. (d)
5. (c)
16. (b)
6. (b)
17. (c)
7. (c), (d)
18. (b)
8. (a)
19. (c)
9. (b)
20. (a)
10. (a)
21. (b)
11. (b)
22. (d)
ABOUT VOLUME I The topics covered in the first volume are: •
General Physics
Mechanics
•
•
Thermal Physics
It has been adapted by an expert IIT-JEE teacher – Mr. Amit Gupta.
RELATED WILEY TITLES IN PHYSICS •
•
•
The Flying Circus of Physics with Answers Jearl Walker ISBN: 9788126517824 Understanding Physics Cummings et al. ISBN: 9788126508822 Physics, 5 ed. Cutnell & Johnson ISBN: 9788126514519
•
•
•
Modern Physics, 2 ed. Kenneth Krane ISBN: 9788126508266 Solutions to Irodov’s Problems in General Physics, Vol. I, Third ed. Abhay Kumar Singh ISBN: 9788126520763 Solutions to Irodov’s Problems in General Physics, Vol. II, Third ed. Abhay Kumar Singh ISBN: 9788126520770
We welcome your feedback about this book. Email us at:
[email protected]
Contents Preface
vii
Note to the Student 22
xi
Coulomb’s Law and Electric Field
1
Can you find the bacterial source? 22-1 What is Physics? 2 22-2 Electric Charge 2 22-3 Coulomb’s Law 6 22-4 Charge Is Quantized 12 22-5 Charge Is Conserved 13 22-6 The Electric Field 14 22-7 Electric Field Lines 15 22-8 The Electric Field Due to a Point Charge 16 22-9 The Electric Field Due to Continuous Charge Distribution 20 22-10 The Electric Field Due to a Charged Disk 25 22-11 A Point Charge in an Electric Field 27 22-12 A Dipole in an Electric Field 30 Reasoning Type Questions 34 Multiple Choice Questions 34 Problems 37 Additional Problems 41 Answers 42
23
Gauss’ Law
45
What is this additional danger of a lightning storm? 23-1 What Is Physics? 46 23-2 23-3
Flux 46 Electric Flux 47
23-4
Statement of Gauss’ Law 51
23-5
Gauss’ Law and Coulomb’s Law 53
23-6
Applying Gauss’ Law: Spherical Symmetry 58
23-7
Applying Gauss’ Law: Cylindrical Symmetry 61
Applying Gauss’ Law: Planar Symmetry 63 Reasoning Type Questions 65 Multiple Choice Questions 65 Problems 66 Additional Problems 69 Answers 70 23-8
24
Finding the Electric Potential
What is the danger in these situations? 24-1 What Is Physics? 72 24-2
Electric Potential Energy 72
71
24-3
Electric Potential 77
24-4
Equipotential Surfaces 79
24-5
Calculating the Potential from the Field 80
24-6
Potential Due to a Point Charge 82
24-7
Potential Due to a Group of Point Charges 84
24-8
Potential Due to a Continuous Charge Distribution 86
Calculating the Field from the Potential 90 24-10 Potential Due to an Electric Dipole 93 Reasoning Type Questions 97 Multiple Choice Questions 97 Problems 101 Additional Problems 104 Answers 105 24-9
25
Conductors
107
What causes the pollen to jump, first to the bee and then away from it? 25-1 What Is Physics? 108 25-2 Conductors and Insulators 108 25-3 Electric Field Inside a Conductor 109 25-4 A Charged Isolated Conductor 111 25-5 The Net Electric Field Near the Surface of a Conductor 112 25-6 Electrostatic Shielding 115 25-7 Potential of a Charged Isolated Conductor 117 25-8 Earthing 121 25-9 Electrostatic Self-Energy 124 Reasoning Type Questions 126 Multiple Choice Questions 127 Problems 129 Additional Problems 131 Answers 132
26
Capacitors and Capacitance
135
What determines whether sparking will cause an explosion of airborne dust? 26-1 What Is Physics? 136 26-2
Capacitance 136
26-3
Calculating the Capacitance 138
26-4
Combination of Capacitors 141
xx
Contents
Energy Stored in an Electric Field 146
26-5
Capacitor with a Dielectric 150 26-7 Dielectrics: An Atomic View 153 26-8 Dielectrics and Gauss’ Law 154 Reasoning Type Questions 158 Multiple Choice Questions 159 Problems 161 Additional Problems 164 Answers 165 26-6
27
Ohm’s Law
167
How can you reduce your risk from ground current? 27-1 What Is Physics? 168
29-3
The Definition of B 232
29-4
A Circulating Charged Particle 235
29-5
Cyclotrons 239
29-6
Crossed Fields: Discovery of the Electron 242
29-7
The Hall Effect and the Force on a Current–Carrying Wire 246
29-8
Torque on a Current Loop 250
The Magnetic Dipole Moment 252 Reasoning Type Questions 256 Multiple Choice Questions 257 Problems 261 Additional Problems 264 Answers 264 29-9
27-2
Electric Current 168
27-3
Current Density 170
30
27-4
Resistance and Resistivity 173
27-5
Ohm’s Law 178
27-6
A Microscopic View of Ohm’s Law 179
27-7
Power in Electric Circuits 182
So, how can brain activation produce amagnetic field? 30-1 What Is Physics? 268 30-2 Calculating the Magnetic Field Due to a Current 268 30-3 Magnetic Field of Moving Charged Particles 278 30-4 Force Between Two Parallel Currents 280 30-5 Ampere’s Law 282 30-6 Solenoids and Toroids 287 Reasoning Type Questions 293 Multiple Choice Questions 294 Problems 296 Additional Problems 298 Answers 299
27-8
Superconductors 183 Reasoning Type Questions 184 Multiple Choice Questions 184 Problems 186 Additional Problems 188 Answers 189
28
Circuit Theory
191
What precaution must be taken to prevent such a fire? 28-1 What Is Physics? 192 28-2
Work, Energy, and Emf 192
28-3 28-4
Calculating the Current in a Single-Loop Circuit 194 Multiloop Circuits 203
28-5
Electricity-Related Instruments 209
214 Reasoning Type Questions 218 Multiple Choice Questions 218 Problems 221 Additional Problems 224 Answers 225 28-6
RC Circuits
29 Magnetic Force 227 What produces this huge display, and what makes it so thin? 29-1 What is Physics? 228 29-2
What Produces a Magnetic Field? 228
Current-Produced Magnetic Fields
267
31 Electromagnetic Induction 301 How then does the metal become hot enough to melt? 31-1 What Is Physics? 302 31-2 Gauss’ Law for Magnetic Fields 302 31-3 Two Experiments 303 31-4 Faraday’s Law of Induction 304 31-5 Lenz’s Law 307 31-6 Motional EMF 310 31-7 Induction and Energy Transfers 312 31-8 Induced Electric Fields 317 31-9 Inductors and Inductance 321 31-10 Self-Induction 322 31-11 RL Circuits 324 31-12 Energy Stored in a Magnetic Field 328 31-13 Mutual Induction 332 Reasoning Type Questions 336 Multiple Choice Questions 337
Contens
Problems 341 Additional Problems 347 Answers 349
32
Laws of Reflection 416 34-4 Formation of Image by a Mirror 419 34-5 Formation of Image by a Spherical Mirror 425 Reasoning Type Questions 436 Multiple Choice Questions 436 Problems 438 Additional Problems 439 Answers 439 34-3
Alternating Fields and Current
351
How can a solar explosion shut down a power-grid system? 32-1 What Is Physics? 352 32-2 LC Oscillations, Qualitatively 352 32-3
The Electrical–Mechanical Analogy 355
32-4
LC Oscillations,
32-5
Alternating Current 359
32-6
Forced Oscillations 360
32-7
Three Simple Circuits 360
32-8
The Series RLC Circuit 367
32-9
Power in Alternating-Current Circuits 371
35
Quantitatively 356
Transformers 375 Reasoning Type Questions 379 Multiple Choice Questions 379 Problems 381 Additional Problems 383 Answers 383 32-10
33 Nature of Electromagnetic Waves What produces sun dogs? 33-1 What Is Physics? 386
385
Maxwell’s Rainbow
386
33-3
The Traveling Electromagnetic Wave, Qualitatively 387
33-4
The Traveling Electromagnetic Wave, Quantitatively 390
33-5
Energy Transport and the Poynting Vector 393
33-6
Radiation Pressure 396
33-7
Polarization 396
33-8
Reflection and Refraction 400
441
Optical Interference
493
How do color-shifting inks shift colors? 36-1 What Is Physics? 494
Polarization by Reflection 404 Reasoning Type Questions 405 Multiple Choice Questions 405 Problems 409 Additional Problems 410 Answers 411 33-9
Geometrical Optics: Reflection
Geometrical Optics: Refraction
How can its eyes function in both air and water? 35-1 What is Physics? 442 35-2 Snell’s Laws of Refraction 442 35-3 Apparent Depth and Normal Shift 444 35-4 Total Internal Reflection 450 35-5 Refraction at Spherical Surfaces 456 35-6 Thin Spherical Lens 461 35-7 Lens Mirror Combination 471 35-8 Prism 473 35-9 Chromatic Dispersion 477 Reasoning Type Questions 482 Multiple Choice Questions 482 Problems 487 Additional Problems 490 Answers 491
36
33-2
34
xxi
36-2
Light as a Wave 494
36-3
Diffraction 498
36-4
Young’s Interference Experiment 498
36-5
Coherence 506
36-6 36-7
Intensity in Double-Slit Interference 507 Modifications of Young’s Double-Slit Experiment 513
36-8
Interference from Thin Films 516
36-9
Diffraction and the Wave Theory of Light 522
36-10 Diffraction
by a Single Slit: Locating the Minima 523
36-11 Intensity in
Single-Slit Diffraction, Quantitatively 526
36-12 Diffraction
by a Circular Aperture 527
36-13 Diffraction
413
Can you find those subtle distortions of reality? 34-1 What Is Physics? 414 34-2 Principle of Rectilinear Propagation of Light 414
by a Double Slit 530 Reasoning Type Questions 532 Multiple Choice Questions 533 Problems 537 Additional Problems 542 Answers 544
xxii 37
Contents
Special Relativity
How can we tell what monster lies at the center of M87? 37-1 What Is Physics? 548 37-2
The Postulates 548
37-3
Measuring an Event 549
37-4
The Relativity of Simultaneity 551
37-5
The Relativity of Time 554
37-6
The Relativity of Length 558
37-7
The Lorentz Transformation 561
37-8
Some Consequences of the Lorentz Equations 563 Electricity and Magnetism 565
37-9
37-10 The
Relativity of Velocities 567
37-11 Doppler Effect for Light 568 37-12 A
40 The Nucleus 651 What, then, is so different about the light from a laser? 40-1 What Is Physics? 652 40-2 Some Properties of Atoms 652 40-3
Electron Spin 654
40-4
Angular Momenta and Magnetic Dipole Moments 655
40-5
The Pauli Exclusion Principle 657
40-6
Building the Periodic Table 658
40-7
X Rays and the Ordering of the Elements 659
40-8
Lasers and Laser Light 665
New Look at Momentum 572
37-13 A
New Look at Energy 572 Reasoning Type Questions 577 Multiple Choice Questions 578 Problems 579 Additional Problems 582 Answers 584
38
Quantum Numbers for the Hydrogen Atom (Optional) 638 Reasoning Type Questions 643 Multiple Choice Questions 643 Problems 647 Additional Problems 648 Answers 649 39-7
547
Light Quanta, Matter Waves
How Lasers Work 666 Reasoning Type Questions 669 Multiple Choice Questions 670 Problems 672 Additional Problems 675 Answers 675 40-9
587
Can a particle be a wave? 38-1 What Is Physics? 588 38-2
The Photon, the Quantum of Light 588
38-3
The Photoelectric Effect 591
38-4
Photons Have Momentum 596
38-5
Light as a Probability Wave 599
38-6
Electrons and Matter Waves 601
41-2
Discovering the Nucleus 678
38-7
Schrödinger’s Equation 604
41-3
Some Nuclear Properties 679
38-8
Heisenberg’s Uncertainty Principle 607
41-4 41-5
Radioactive Decay 686 Probability of Decay 688
41-6
Alpha Decay 690
41-7 41-8
Beta Decay 692 Gamma Decay 695
41-9
Radioactive Dating 696
Barrier Tunneling 608 Reasoning Type Questions 610 Multiple Choice Questions 610 Problems 613 Additional Problems 614 Answers 615 38-9
39
Hydrogen Atom
617
Why does the pickle glow only yellow in color? 39-1 What Is Physics? 618 39-2
String Waves and Matter Waves 618
39-3
Energies of a Trapped Electron 619
39-4 39-5
Wave Functions of a Trapped Electron 623 The Bohr Model of the Hydrogen Atom 626
39-6
Spectra of the Hydrogen Atom 631
41 Coulomb’s Law 677 What is the physics behind this image that has so horrified the world? 41-1 What Is Physics? 678
41-10 Nuclear
Models (Optional) 697
41-11
Nuclear Fission: The Basic Process 700
41-12
Thermonuclear Fusion: The Basic Process 702
Thermonuclear Fusion in the Sun and Other Stars 703 Reasoning Type Questions 705 Multiple Choice Questions 705 41-13
Problems 710 Additional Problems 713 Answers 713
Contens
Appendices A B C D E F G
The International System of Unit (SI) 717 Some Fundamental Constants of Physics 719 Some Astronomical Data 720 Conversion Factors 721 Mathematical Formulas 725 Properties of the Elements 728 Periodic Table of the Elements 731
IIT-JEE Physics Paper 2010
733
xxiii
