Concepts of Physics HC Verma Vol 2 PDF

Download RANKERSHALT app from Play Store: Click Here By - DhananjaY Edu CONCEPTS OF PHYSICS [VOLUME 2] H C VERMA, PhD...

Download RANKERSHALT app from Play Store: Click Here By - DhananjaY Edu CONCEPTS OF PHYSICS [VOLUME 2] H C VERMA, PhD Retired Professor Department of Physics IIT, Kanpur RANKERSHALT now have an APP, with tonnes of new and updated materials. Download it from Play Store. (Click Here) Also dont't forget to rate us and leave a review. Download RANKERSHALT app from Play Store: Click Here Dedicated to Indian Philosophy & Way of Life of which my parents were an integral part RANKERSHALT now have an APP, with tonnes of new and updated materials. Download it from Play Store. (Click Here) Also dont't forget to rate us and leave a review. Download RANKERSHALT app from Play Store: Click Here FOREWORD A few years ago I had an occasion to go through the book Calculus by L V Terasov. It unravels intricacies of the subject through a dialogue between Teacher and Student. I thoroughly enjoyed reading it. For me this seemed to be one of the few books which teach a difficult subject through inquisition, and using programmed concept for learning. After that book, Dr Harish Chandra Verma’s book on physics, CONCEPTS OF PHYSICS is another such attempt, even though it is not directly in the dialogue form. I have thoroughly appreciated it. It is clear that Dr Verma has spent considerable time in formulating the structure of the book, besides its contents. I think he has been successful in this attempt. Dr Verma’s book has been divided into two parts because of the size of the total manuscript. There have been several books on this subject, each one having its own flavour. However, the present book is a totally different attempt to teach physics, and I am sure it will be extremely useful to the undergraduate students. The exposition of each concept is extremely lucid. In carefully formatted chapters, besides problems and short questions, a number of objective questions have also been included. This book can certainly be extremely useful not only as a textbook, but also for preparation of various competitive examinations. Those who have followed Dr Verma’s scientific work always enjoyed the outstanding contributions he has made in various research areas. He was an outstanding student of Physics Department of IIT Kanpur during his academic career. An extremely methodical, sincere person as a student, he has devoted himself to the task of educating young minds and inculcating scientific temper amongst them. The present venture in the form of these two volumes is another attempt in that direction. I am sure that young minds who would like to learn physics in an appropriate manner will find these volumes extremely useful. I must heartily congratulate Dr Harish Chandra Verma for the magnificent job he has done. Y R Waghmare Professor of Physics IIT Kanpur. (v) RANKERSHALT now have an APP, with tonnes of new and updated materials. Download it from Play Store. (Click Here) Also dont't forget to rate us and leave a review. Download RANKERSHALT app from Play Store: Click Here PREFACE Why a new book ? Excellent books exist on physics at an introductory college level so why a new one ? Why so many books exist at the same level, in the first place, and why each of them is highly appreciated ? It is because each of these books has the privilege of having an author or authors who have experienced physics and have their own method of communicating with the students. During my years as a physics teacher, I have developed a somewhat different methodology of presenting physics to the students. Concepts of Physics is a translation of this methodology into a textbook. Prerequisites The book presents a calculus-based physics course which makes free use of algebra, trigonometry and co-ordinate geometry. The level of the latter three topics is quite simple and high school mathematics is sufficient. Calculus is generally done at the introductory college level and I have assumed that the student is enrolled in a concurrent first calculus course. The relevant portions of calculus have been discussed in Chapter 2 so that the student may start using it from the beginning. Almost no knowledge of physics is a prerequisite. I have attempted to start each topic from the zero level. A receptive mind is all that is needed to use this book. Basic philosophy of the book The motto underlying the book is physics is enjoyable. Being a description of the nature around us, physics is our best friend from the day of our existence. I have extensively used this aspect of physics to introduce the physical principles starting with common day occurrences and examples. The subject then appears to be friendly and enjoyable. I have taken care that numerical values of different quantities used in problems correspond to real situations to further strengthen this approach. Teaching and training The basic aim of physics teaching has been to let the student know and understand the principles and equations of physics and their applications in real life. However, to be able to use these principles and equations correctly in a given physical situation, one needs further training. A large number of questions and solved and unsolved problems are given for this purpose. Each question or problem has a specific purpose. It may be there to bring out a subtle point which might have passed unnoticed while doing the text portion. It may be a further elaboration of a concept developed in the text. It may be there to make the student react when several concepts introduced in different chapters combine and show up as a physical situation and so on. Such tools have been used to develop a culture: analyse the situation, make a strategy to invoke correct principles and work it out. Conventions I have tried to use symbols, names, etc., which are popular nowadays. SI units have been consistently used throughout the book. SI prefixes such as micro, milli, mega, etc., are used whenever they make the presentation −6 more readable. Thus, 20 µF is preferred over 20 × 10 F. Co-ordinate sign convention is used in geometrical optics. Special emphasis has been given to dimensions of physical quantities. Numerical values of physical quantities have been mentioned with the units even in equations to maintain dimensional consistency. I have tried my best to keep errors out of this book. I shall be grateful to the readers who point out any errors and/or make other constructive suggestions. H C Verma (vii) RANKERSHALT now have an APP, with tonnes of new and updated materials. Download it from Play Store. (Click Here) Also dont't forget to rate us and leave a review. Download RANKERSHALT app from Play Store: Click Here ACKNOWLEDGEMENTS The work on this book started in 1984. Since then, a large number of teachers, students and physics lovers have made valuable suggestions which I have incorporated in this work. It is not possible for me to acknowledge all of them individually. I take this opportunity to express my gratitude to them. However, to Dr S B Mathur, who took great pains in going through the entire manuscript and made valuable comments, I am specially indebted. I am also beholden to my colleagues Dr A Yadav, Dr Deb Mukherjee, Mr M M R Akhtar, Dr Arjun Prasad, Dr S K Sinha and others who gave me valuable advice and were good enough to find time for fruitful discussions. To Dr T K Dutta of B E College, Sibpur I am grateful for having taken time to go through portions of the book and making valuable comments. I thank my student Mr Shailendra Kumar who helped me in checking the answers. I am grateful to Dr B C Rai, Mr Sunil Khijwania & Mr Tejaswi Khijwania for helping me in the preparation of rough sketches for the book. Finally, I thank the members of my family for their support and encouragement. H C Verma (viii) RANKERSHALT now have an APP, with tonnes of new and updated materials. Download it from Play Store. (Click Here) Also dont't forget to rate us and leave a review. Download RANKERSHALT app from Play Store: Click Here TO THE STUDENTS Here is a brief discussion on the organisation of the book which will help you in using the book most effectively. The book contains 47 chapters divided in two volumes. Though I strongly believe in the underlying unity of physics, a broad division may be made in the book as follows: Chapters 1–14: Mechanics 15–17: Waves including wave optics 18–22: Optics 23–28: Heat and thermodynamics 29–40: Electric and magnetic phenomena 41–47: Modern physics Each chapter contains a description of the physical principles related to that chapter. It is well supported by mathematical derivations of equations, descriptions of laboratory experiments, historical background, etc. There are "in-text" solved examples. These examples explain the equation just derived or the concept just discussed. These will help you in fixing the ideas firmly in your mind. Your teachers may use these in-text examples in the classroom to encourage students to participate in discussions. After the theory section, there is a section on Worked Out Examples. These numerical examples correspond to various thinking levels and often use several concepts introduced in that chapter or even in previous chapters. You should read the statement of a problem and try to solve it yourself. In case of difficulty, look at the solution given in the book. Even if you solve the problem successfully, you should look into the solution to compare it with your method of solution. You might have thought of a better method, but knowing more than one method is always beneficial. Then comes the part which tests your understanding as well as develops it further. Questions for Short Answer generally touch very minute points of your understanding. It is not necessary that you answer these questions in a single sitting. They have great potential to initiate very fruitful dicussions. So, freely discuss these questions with your friends and see if they agree with your answer. Answers to these questions are not given for the simple reason that the answers could have cut down the span of such discussions and that would have sharply reduced the utility of these questions. There are two sections on multiple-choice questions, namely OBJECTIVE I and OBJECTIVE II. There are four options following each of these questions. Only one option is correct for OBJECTIVE I questions. Any number of options, zero to four, may be correct for OBJECTIVE II questions. Answers to all these questions are provided. Finally, a set of numerical problems are given for your practice. Answers to these problems are also provided. The problems are generally arranged according to the sequence of the concepts developed in the chapter but they are not grouped under section-headings. I don’t want to bias your ideas beforehand by telling you that this problem belongs to that section and hence use that particular equation. You should yourself look into the problem and decide which equations or which methods should be used to solve it. Many of the problems use several concepts developed in different sections of the chapter. Many of them even use the concepts from the previous chapters. Hence, you have to plan out the strategy after understanding the problem. Remember, no problem is difficult. Once you understand the theory, each problem will become easy. So, don’t jump to exercise problems before you have gone through the theory, the worked-out problems and the objectives. Once you feel confident in theory, do the exercise problems. The exercise problems are so arranged that they gradually require more thinking. I hope you will enjoy Concepts of Physics. H C Verma (ix) RANKERSHALT now have an APP, with tonnes of new and updated materials. Download it from Play Store. (Click Here) Also dont't forget to rate us and leave a review. Download RANKERSHALT app from Play Store: Click Here Table of Contents Chapters 1–22 Volume–1 Chapter 25 Calorimetry 39 Chapter 23 25.1 Heat as a Form of Energy 39 Heat and Temperature 1 25.2 Units of Heat 39 23.1 Hot and Cold Bodies 1 25.3 Principle of Calorimetry 39 23.2 Zeroth Law of Thermodynamics 1 25.4 Specific Heat Capacity and Molar Heat Capacity 39 25.5 Determination of Specific Heat Capacity 23.3 Defining Scale of Temperature : Mercury in Laboratory 40 and Resistance Thermometers 1 25.6 Specific Latent Heat of Fusion and Vaporization 41 23.4 Constant Volume Gas Thermometer 3 25.7 Measurement of Specific Latent Heat of 23.5 Ideal Gas Temperature Scale 5 Fusion of Ice 41 23.6 Celsius Temperature Scale 5 25.8 Measurement of Specific Latent Heat of 23.7 Ideal Gas Equation 5 Vaporization of Water 42 23.8 Callender’s Compensated Constant 25.9 Mechanical Equivalent of Heat 43 Pressure Thermometer 5 Worked Out Examples 44 23.9 Adiabatic and Diathermic Walls 6 Questions for Short Answer 46 23.10 Thermal Expansion 6 Objective I 46 Worked Out Examples 7 Objective II 46 Questions for Short Answer 11 Exercises 47 Objective I 11 Objective II 12 Chapter 26 Exercises 12 Laws of Thermodynamics 49 26.1 The First Law of Thermodynamics 49 Chapter 24 26.2 Work Done by a Gas 50 26.3 Heat Engines 51 Kinetic Theory of Gases 15 26.4 The Second Law of Thermodynamics 53 24.1 Introduction 15 26.5 Reversible and Irreversible Processes 54 24.2 Assumptions of Kinetic Theory of Gases 15 26.6 Entropy 55 24.3 Calculation of the Pressure of an Ideal Gas 16 26.7 Carnot Engine 55 24.4 rms Speed 16 Worked Out Examples 57 24.5 Kinetic Interpretation of Temperature 17 Questions for Short Answer 60 24.6 Deductions from Kinetic Theory 18 Objective I 61 24.7 Ideal Gas Equation 19 Objective II 61 24.8 Maxwell’s Speed Distribution Law 20 Exercises 62 24.9 Thermodynamic State 20 24.10 Brownian Motion 21 Chapter 27 24.11 Vapour 21 Specific Heat Capacities of Gases 65 24.12 Evaporation 22 27.1 Two Kinds of Specific Heat Capacities of Gases 65 24.13 Saturated and Unsaturated Vapour : 27.2 Relation Between Cp and Cv for an Ideal Gas 66 Vapour Pressure 22 27.3 Determination of Cp of a Gas 67 24.14 Boiling 23 27.4 Determination of Cv of a Gas 68 24.15 Dew Point 23 27.5 Isothermal and Adiabatic Processes 68 24.16 Humidity 24 27.6 Relations between p, V, T in 24.17 Determination of Relative Humidity 24 a Reversible Adiabatic Process 69 24.18 Phase Diagrams : Triple Point 25 27.7 Work Done in an Adiabatic Process 70 24.19 Dew and Fog 25 27.8 Equipartition of Energy 70 Worked Out Examples 26 Worked Out Examples 72 Questions for Short Answer 32 Questions for Short Answer 76 Objective I 33 Objective I 76 Objective II 33 Objective II 77 Exercises 34 Exercises 77 (xi) RANKERSHALT now have an APP, with tonnes of new and updated materials. 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(Click Here) Also dont't forget to rate us and leave a review. Download RANKERSHALT app from Play Store: Click Here Chapter 28 Chapter 31 Heat Transfer 81 Capacitors 144 28.1 Thermal Conduction 81 31.1 Capacitor and Capacitance 144 28.2 Series and Parallel Connection of Rods 82 31.2 Calculation of Capacitance 145 28.3 Measurement of Thermal Conductivity of a Solid 83 31.3 Combination of Capacitors 147 28.4 Convection 84 31.4 Force between the Plates of a Capacitor 150 28.5 Radiation 84 31.5 Energy Stored in a Capacitor and 28.6 Prevost Theory of Exchange 84 Energy Density in Electric Field 150 28.7 Blackbody Radiation 85 31.6 Dielectrics 151 28.8 Kirchhoff’s Law 85 31.7 Parallel-plate Capacitor with a Dielectric 152 28.9 Nature of Thermal Radiation 86 31.8 An Alternative Form of Gauss’s Law 153 28.10 Stefan–Boltzmann Law 87 31.9 Electric Field due to a Point Charge q 28.11 Newton’s Law of Cooling 87 Placed in an Infinite Dielectric 154 28.12 Detection and Measurement of Radiation 88 31.10 Energy in the Electric field in a Dielectric 154 Worked Out Examples 89 31.11 Corona Discharge 154 Questions for Short Answer 96 31.12 High-voltage Generator 155 Objective I 97 Worked Out Examples 156 Objective II 97 Questions for Short Answer 164 Exercises 98 Objective I 165 Objective II 165 Chapter 29 Exercises 166 Electric Field and Potential 104 Chapter 32 29.1 What Is Electric Charge ? 104 Electric Current In Conductors 172 29.2 Coulomb’s Law 105 29.3 Electric Field 106 32.1 Electric Current and Current Density 172 29.4 Lines of Electric Force 107 32.2 Drift Speed 173 29.5 Electric Potential Energy 107 32.3 Ohm’s Law 174 29.6 Electric Potential 108 32.4 Temperature Dependence of Resistivity 175 29.7 Electric Potential due to a Point Charge 109 32.5 Battery and emf 176 29.8 Relation between Electric Field and Potential 109 32.6 Energy Transfer in an Electric Circuit 177 29.9 Electric Dipole 110 32.7 Kirchhoff’s Laws 178 29.10 Torque on an Electric Dipole Placed 32.8 Combination of Resistors in Series and Parallel 179 in an Electric Field 112 32.9 Grouping of Batteries 180 29.11 Potential Energy of a Dipole Placed 32.10 Wheatstone Bridge 181 in a Uniform Electric Field 112 32.11 Ammeter and Voltmeter 182 29.12 Conductors, Insulators and Semiconductors 113 32.12 Stretched-wire Potentiometer 183 29.13 The Electric Field inside a Conductor 113 32.13 Charging and Discharging of Capacitors 185 Worked Out Examples 114 32.14 Atmospheric Electricity 186 Questions for Short Answer 119 Worked Out Examples 187 Objective I 119 Questions for Short Answer 196 Objective II 120 Objective I 196 Exercises 121 Objective II 197 Exercises 198 Chapter 30 Chapter 33 Gauss’s Law 127 30.1 Flux of an Electric Field through a Surface 127 Thermal and Chemical Effects of Electric 30.2 Solid Angle 128 Current 206 30.3 Gauss’s Law and Its Derivation 33.1 Joule’s Laws of Heating 206 from Coulomb’s Law 129 33.2 Verification of Joule’s Laws 207 30.4 Applications of Gauss’s Law 131 33.3 Seebeck Effect 207 30.5 Spherical Charge Distributions 134 33.4 Peltier Effect 209 30.6 Earthing a Conductor 135 33.5 Thomson Effect 210 Worked Out Examples 136 33.6 Explanation of Seebeck, Peltier Questions for Short Answer 139 and Thomson Effects 210 Objective I 139 33.7 Electrolysis 211 Objective II 140 33.8 Faraday’s Laws of Electrolysis 211 Exercises 141 33.9 Voltameter or Coulombmeter 213 (xii) RANKERSHALT now have an APP, with tonnes of new and updated materials. 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(Click Here) Also dont't forget to rate us and leave a review. Download RANKERSHALT app from Play Store: Click Here 33.10 Primary and Secondary Cells 214 36.14 Determination of M and BH 270 33.11 Primary Cells 214 36.15 Gauss’s Law for Magnetism 270 33.12 Secondary Cell : Lead Accumulator 215 Worked Out Examples 270 Worked Out Examples 215 Questions for Short Answer 275 Questions for Short Answer 217 Objective I 276 Objective I 217 Objective II 277 Objective II 218 Exercises 277 Exercises 218 Chapter 37 Chapter 34 Magnetic Properties of Matter 279 Magnetic Field 221 37.1 Magnetization of Materials : 34.1 Introduction 221 Intensity of Magnetization 279 → 34.2 Definition of Magnetic Field B 221 37.2 Paramagnetism, Ferromagnetism and 34.3 Relation between Electric and Magnetic Fields 222 Diamagnetism 280 34.4 Motion of a Charged Particle 37.3 Magnetic Intensity H 281 in a Uniform Magnetic Field 222 37.4 Magnetic Susceptibility 281 34.5 Magnetic Force on a Current-carrying Wire 223 37.5 Permeability 281 34.6 Torque on a Current Loop 224 37.6 Curie’s Law 282 Worked Out Examples 225 37.7 Properties of Dia-, Para- and Questions for Short Answer 228 Ferromagnetic Substances 282 Objective I 229 37.8 Hysteresis 283 Objective II 229 37.9 Soft Iron and Steel 283 Exercises 230 Worked Out Examples 284 Questions for Short Answer 285 Chapter 35 Objective I 285 Objective II 286 Magnetic Field due to a Current 237 Exercises 286 35.1 Biot–Savart Law 237 35.2 Magnetic Field due to Current in a Straight Wire 238 Chapter 38 35.3 Force between Parallel Currents 239 35.4 Field due to a Circular Current 239 Electromagnetic Induction 288 35.5 Ampere’s Law 241 38.1 Faraday’s Law of Electromagnetic Induction 288 35.6 Magnetic Field at a Point 38.2 Lenz’s Law 289 due to a Long, Straight Current 241 38.3 The Origin of Induced emf 289 35.7 Solenoid 242 38.4 Eddy Current 291 35.8 Toroid 243 38.5 Self-induction 291 Worked Out Examples 243 38.6 Growth and Decay of Current in an LR Circuit 292 Questions for Short Answer 248 38.7 Energy Stored in an Inductor 294 Objective I 248 38.8 Mutual Induction 295 Objective II 249 38.9 Induction Coil 295 Exercises 249 Worked Out Examples 296 Questions for Short Answer 303 Chapter 36 Objective I 304 Objective II 305 Permanent Magnets 255 Exercises 306 36.1 Magnetic Poles and Bar Magnets 255 36.2 Torque on a Bar Magnet Chapter 39 Placed in a Magnetic Field 257 36.3 Magnetic Field due to a Bar Magnet 258 Alternating Current 316 36.4 Magnetic Scalar Potential 258 39.1 Alternating Current 316 36.5 Terrestrial Magnetism 260 39.2 AC Generator or AC Dynamo 316 36.6 Determination of Dip at a Place 261 39.3 Instantaneous and rms Current 317 36.7 Neutral Point 263 39.4 Simple AC Circuits 318 36.8 Tangent Galvanometer 263 39.6 Vector Method to Find the Current 36.9 Moving-coil Galvanometer 264 in an AC Circuit 320 36.10 Shunt 265 39.6 More AC Circuits 320 36.11 Tangent Law of Perpendicular Fields 265 39.7 Power in AC Circuits 322 36.12 Deflection Magnetometer 266 39.8 Choke Coil 323 36.13 Oscillation Magnetometer 268 39.9 Hot-wire Instruments 323 (xiii) RANKERSHALT now have an APP, with tonnes of new and updated materials. 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(Click Here) Also dont't forget to rate us and leave a review. Download RANKERSHALT app from Play Store: Click Here 38.10 DC Dynamo 324 43.2 Hydrogen Spectra 369 39.11 DC Motor 325 43.3 Difficulties with Rutherford’s Model 370 39.12 Transformer 325 43.4 Bohr’s Model 370 Worked Out Examples 327 43.5 Limitations of Bohr’s Model 373 Questions for Short Answer 328 43.6 The Wave Function of an Electron 374 Objective I 329 43.7 Quantum Mechanics of the Hydrogen Atom 374 Objective II 329 43.8 Nomenclature in Atomic Physics 375 Exercises 330 43.9 Laser 375 Worked Out Examples 378 Chapter 40 Questions for Short Answer 382 Objective I 383 Electromagnetic Waves 332 Objective II 383 40.1 Introduction 332 Exercises 384 40.2 Maxwell’s Displacement Current 332 40.3 Continuity of Electric Current 333 Chapter 44 40.4 Maxwell’s Equations and Plane Electromagnetic Waves 334 X-rays 388 40.5 Energy Density and Intensity 335 44.1 Production of X-rays 388 40.6 Momentum 336 44.2 Continuous and Characteristic X-rays 388 40.7 Electromagnetic Spectrum and 44.3 Soft and Hard X-rays 390 Radiation in Atmosphere 336 44.4 Moseley’s Law 390 Worked Out Examples 337 44.5 Bragg’s Law 391 Questions for Short Answer 338 44.6 Properties and Uses of X-rays 391 Objective I 338 Worked Out Examples 392 Objective II 339 Questions for Short Answer 393 Exercises 339 Objective I 393 Objective II 394 Chapter 41 Exercises 395 Electric Current through Gases 341 Chapter 45 41.1 Discharge through Gases at Low Pressure 341 41.2 Cathode Rays 343 Semiconductors and Semiconductor Devices 397 41.3 Canal Rays or Positive Rays 343 45.1 Introduction 397 41.4 Discovery and Properties of Electron 344 45.2 Energy Bands in Solids 397 41.5 Thermionic Emission 345 45.3 The Semiconductor 400 41.6 Diode Valve 346 45.4 p-type and n-type Semiconductors 400 41.7 Triode Valve 347 45.5 Density of Charge Carriers and Conductivity 401 41.8 Triode as an Amplifier 349 45.6 p-n Junction 402 Worked Out Examples 349 45.7 p-n Junction Diode 403 Questions for Short Answer 351 45.8 p-n Junction as a Rectifier 405 Objective I 351 45.9 Junction Transistors 406 Objective II 352 45.10 Logic Gates 409 Exercises 352 Worked Out Examples 414 Questions for Short Answer 416 Chapter 42 Objective I 417 Objective II 418 Photoelectric Effect and Wave–Particle Duality 355 Exercises 419 42.1 Photon Theory of Light 355 42.2 Photoelectric Effect 356 Chapter 46 42.3 Matter Waves 359 Worked Out Examples 359 The Nucleus 422 Questions for Short Answer 363 46.1 Properties of a Nucleus 422 Objective I 363 46.2 Nuclear Forces 424 Objective II 364 46.3 Binding Energy 425 Exercises 365 46.4 Radioactive Decay 427 46.5 Law of Radioactive Decay 429 Chapter 43 46.6 Properties and Uses of Nuclear Radiation 431 46.7 Energy from the Nucleus 431 Bohr’s Model and Physics of the Atom 368 46.8 Nuclear Fission 432 43.1 Early Atomic Models 368 46.9 Uranium Fission Reactor 433 (xiv) RANKERSHALT now have an APP, with tonnes of new and updated materials. Download it from Play Store. (Click Here) Also dont't forget to rate us and leave a review. Download RANKERSHALT app from Play Store: Click Here 46.10 Nuclear Fusion 435 46.11 Fusion in Laboratory 436 Worked Out Examples 437 Questions for Short Answer 440 Objective I 440 Objective II 441 Exercises 442 Chapter 47 The Special Theory of Relativity 446 47.1 The Principle of Relativity 446 47.2 Are Maxwell’s Laws Independent of Frame ? 446 47.3 Kinematical Consequences 447 47.4 Dynamics at Large Velocity 451 47.5 Energy and Momentum 452 47.6 The Ultimate Speed 453 47.7 Twin Paradox 453 Worked Out Examples 455 Questions for Short Answer 456 Objective I 457 Objective II 457 Exercises 458 APPENDIX A 461 APPENDIX B 462 INDEX 463 (xv) RANKERSHALT now have an APP, with tonnes of new and updated materials. Download it from Play Store. (Click Here) Also dont't forget to rate us and leave a review. Download RANKERSHALT app from Play Store: Click Here  &+$37(5  +($7 $1' 7(03(5$785(  +27 $1' &2/' %2',(6  =(527+ /$: 2) 7+(502' Q2, t1 > t2 (b) Q1 > Q2, t1 < t2 (B) The equivalent internal resistance is smaller than (c) Q1 < Q2, t1 > t2 (d) Q1 < Q2, t1 < t2 either of the two internal resistances. OBJECTIVE II 1. Electrons are emitted by a hot filament and are (b) the average speed of a free electron over a large accelerated by an electric field as shown in figure period of time is zero (32-Q1). The two stops at the left ensure that the (c) the average velocity of a free electron over a large electron beam has a uniform cross-section. period of time is zero (a) The speed of the electron is more at B than at A. (d) the average of the velocities of all the free electrons (b) The electric current is from left to right. at an instant is zero. (c) The magnitude of the current is larger at B than 4. Which of the following quantities do not change when a at A. resistor connected to a battery is heated due to the (d) The current density is more at B than at A. current ? E (a) Drift speed (b) Resistivity (c) Resistance (d) Number of free electrons A B 5. As the temperature of a conductor increases, its resistivity and conductivity change. The ratio of resistivity to conductivity Figure 32-Q1 (a) increases (b) decreases (c) remains constant (d) may increase or decrease depending on the actual 2. A capacitor with no dielectric is connected to a battery temperature. at t = 0. Consider a point A in the connecting wires and 6. A current passes through a wire of nonuniform a point B in between the plates. cross-section. Which of the following quantities are (a) There is no current through A. independent of the cross section ? (b) There is no current through B. (a) The charge crossing in a given time interval (c) There is a current through A as long as the charging (b) Drift speed is not complete. (c) Current density (d) There is a current through B as long as the charging (d) Free-electron density is not complete. 7. Mark out the correct options. 3. When no current is passed through a conductor, (a) An ammeter should have small resistance. (a) the free electrons do not move (b) An ammeter should have large resistance. RANKERSHALT now have an APP, with tonnes of new and updated materials. Download it from Play Store. (Click Here) Also dont't forget to rate us and leave a review. Download RANKERSHALT app from Play Store: Click Here 198 Concepts of Physics (c) A voltmeter should have small resistance. separately discharged through equal resistors. Both the (d) A voltmeter should have large resistance. discharge circuits are connected at t  0. 8. A capacitor of capacitance 500F is connected to a (a) The current in each of the two discharging circuits battery through a 10 k resistor. The charge stored on is zero at t  0. the capacitor in the first 5 s is larger than the charge (b) The currents in the two discharging circuits at t  0 stored in the next are equal but not zero. (a) 5 s (b) 50 s (c) 500 s (d) 5000 s (c) The currents in the two discharging circuits at t  0 9. A capacitor C1 of capacitance 1F and a capacitor C2 of are unequal. capacitance 2F are separately charged by a common (d) C1 loses 50% of its initial charge sooner than C2 loses battery for a long time. The two capacitors are then 50% of its initial charge. EXERCISES 1. The amount of charge passed in time t through a 11. A copper wire of radius 0.1 mm and resistance 1 k is cross-section of a wire is connected across a power supply of 20 V. (a) How many Qt  At  Bt  C. 2 electrons are transferred per second between the supply (a) Write the dimensional formulae for A, B and C. and the wire at one end ? (b) Write down the current (b) If the numerical values of A, B and C are 5, 3 and density in the wire. 1 respectively in SI units, find the value of the current 12. Calculate the electric field in a copper wire of at t  5 s. cross-sectional area 2.0 mm carrying a current of 1 A. 2 8 2. An electron gun emits 2.0  10 electrons per second. 16 The resistivity of copper  1.7  10  m. What electric current does this correspond to? 13. A wire has a length of 2.0 m and a resistance of 5.0 . 3. The electric current existing in a discharge tube is Find the elecric field existing inside the wire if it carries 2.0 A. How much charge is transferred across a a current of 10 A. cross-section of the tube in 5 minutes ? 14. The resistances of an iron wire and a copper wire at 20C 4. The current through a wire depends on time as are 3.9  and 4.1  respectively. At what temperature will i  i0  t, the resistances be equal ? Temperature coefficient of 3 1 1 where i0  10 A and   4 A s. Find the charge crossed resistivity for iron is 5.0  10 K and for copper it is.   4 0  10 K. Neglect any thermal expansion. 3 1 through a section of the wire in 10 seconds. 5. A current of 1.0 A exists in a copper wire of cross-section 15. The current in a conductor and the potential difference 1.0 mm. Assuming one free electron per atom calculate 2 across its ends are measured by an ammeter and a the drift speed of the free electrons in the wire. The voltmeter. The meters draw negligible currents. The –3 density of copper is 9000 kg m. ammeter is accurate but the voltmeter has a zero error 6. A wire of length 1 m and radius 0.1 mm has a resistance (that is, it does not read zero when no potential of 100 . Find the resistivity of the material. difference is applied). Calculate the zero error if the readings for two different conditions are 1.75 A, 14.4 V 7. A uniform wire of resistance 100  is melted and recast and 2.75 A, 22.4 V. in a wire of length double that of the original. What would be the resistance of the wire ? 16. Figure (32-E2) shows an arrangement to measure the emf E and internal resistance r of a battery. The voltmeter has 8. Consider a wire of length 4 m and cross-sectional area 1 2 mm carrying a current of 2 A. If each cubic metre of the a very high resistance and the ammeter also has some 29 material contains 10 free electrons, find the average time resistance. The voltmeter reads 1.52 V when the switch S taken by an electron to cross the length of the wire. is open. When the switch is closed the voltmeter reading drops to 1.45 V and the ammeter reads 1.0 A. Find the 9. What length of a copper wire of cross-sectional area emf and the internal resistance of the battery. 0.01 mm will be needed to prepare a resistance of 2 8 1 k ? Resistivity of copper  1.7  10  m. V 10. Figure (32-E1) shows a conductor of length l having a r circular cross section. The radius of cross section varies linearly from a to b. The resistivity of the material is . S Assuming that b  a  2 . Coulomb force between the charges is switched off. (a)  eB0  Find the maximum value vm of the projection speed so that the two particles do not collide. (b) What would be d the minimum and maximum separation between the particles if v = vm/2 ? (c) At what instant will a collision B occur between the particles if v = 2vm ? (d) Suppose Figure 34-E20 v = 2vm and the collision between the particles is 53. A rectangular coil of 100 turns has length 5 cm and completely inelastic. Describe the motion after the width 4 cm. It is placed with its plane parallel to a collision. uniform magnetic field and a current of 2 A is sent through the coil. Find the magnitude of the magnetic field B, if the torque acting on the coil is 0.2 N m. −1 v v q –q. 54. A 50-turn circular coil of radius 2 0 cm carrying a d current of 5.0 A is rotated in a magnetic field of strength B 0.20 T. (a) What is the maximum torque that acts on the coil ? (b) In a particular position of the coil, the Figure 34-E19 torque acting on it is half of this maximum. What is the 46. A uniform magnetic field of magnitude 0.20 T exists in angle between the magnetic field and the plane of the space from east to west. With what speed should a coil ? particle of mass 0.010 g and having a charge 55. A rectangular loop of sides 20 cm and 10 cm carries a 1.0 × 10 – 5 C be projected from south to north so that current of 5.0 A. A uniform magnetic field of magnitude it moves with a uniform velocity ? 0.20 T exists parallel to the longer side of the loop. 47. A particle moves in a circle of diameter 1.0 cm under (a) What is the force acting on the loop ? (b) What is the the action of a magnetic field of 0.40 T. An electric field torque acting on the loop ? 56. A circular coil of radius 2.0 cm has 500 turns in it and −1 of 200 V m makes the path straight. Find the charge/mass ratio of the particle. carries a current of 1.0 A. Its axis makes an angle of 48. A proton goes undeflected in a crossed electric and 30° with the uniform magnetic field of magnitude 0.40 T magnetic field (the fields are perpendicular to each that exists in the space. Find the torque acting on the other) at a speed of 2.0 × 10 m s. The velocity is 5 −1 coil. perpendicular to both the fields. When the electric field 57. A circular loop carrying a current i has wire of total is switched off, the proton moves along a circle of radius length L. A uniform magnetic field B exists parallel to 4.0 cm. Find the magnitudes of the electric and the the plane of the loop. (a) Find the torque on the loop. magnetic fields. Take the mass of the proton (b) If the same length of the wire is used to form a = 1.6 × 10 square loop, what would be the torque ? Which is larger? – 27 kg. 49. A particle having a charge of 5.0 µC and a mass of 58. A square coil of edge l having n turns carries a current 5.0 × 10 kg is projected with a speed of 1.0 km s – 12 −1. i. It is kept on a smooth horizontal plate. A uniform in a magnetic field of magnitude 5 0 mT. The angle magnetic field B exists in a direction parallel to an edge. between the magnetic field and the velocity is The total mass of the coil is M. What should be the sin (0.90). Show that the path of the particle will be −1 minimum value of B for which the coil will start tipping a helix. Find the diameter of the helix and its pitch. over ? 50. A proton projected in a magnetic field of 0.020 T travels 59. Consider a nonconducting ring of radius r and mass m along a helical path of radius 5.0 cm and pitch 20 cm. which has a total charge q distributed uniformly on it. Find the components of the velocity of the proton along The ring is rotated about its axis with an angular speed and perpendicular to the magnetic field. Take the mass ω. (a) Find the equivalent electric current in the ring. of the proton = 1.6 × 10 – 27 kg. (b) Find the magnetic moment µ of the ring. (c) Show RANKERSHALT now have an APP, with tonnes of new and updated materials. Download it from Play Store. (Click Here) Also dont't forget to rate us and leave a review. Download RANKERSHALT app from Play Store: Click Here Magnetic Field 235 q 61. Consider a solid sphere of radius r and mass m which that µ = l where l is the angular momentum of the 2m has a charge q distributed uniformly over its volume. ring about its axis of rotation. The sphere is rotated about a diameter with an angular 60. Consider a nonconducting plate of radius r and mass m speed ω. Show that the magnetic moment µ and the which has a charge q distributed uniformly over it. The angular momentum l of the sphere are related as plate is rotated about its axis with an angular speed ω. q µ= l. Show that the magnetic moment µ and the angular 2m q momentum l of the plate are related as µ = l. 2m ANSWERS OBJECTIVE I ilbB 22. µmg 1. (d) 2. (d) 3. (d) 4. (a) 5. (d) 6. (a) 23. 0.12 7. (c) 8. (c) 9. (d) 10. (d) µmg 24. il OBJECTIVE II 25. (a) idlB towards the centre (b) iaB 2 1. (a), (d) 2. (a), (d) 3. (c), (d) ia B 26. 2 4. (a), (b), (d) 5. (b) 6. (a), (b) πr Y 7. (a), (b) 8. (b), (d) 9. (a), (b) 27. iB0 l 10. (b), (c) 28. (a) evB (b) vB (c) lBv i iB EXERCISES 29. (a) (b) upwards in the figure Ane An iB iBd 1. 9.6 × 10 (c) (d) − 12 N towards west Ane Ane 2. (a) left (b) ≈ 1.5 cm 30. 20 cm, 6.3 × 10 s −4 → → −1 3. (− 75 i + 100 j) m s 31. 2 cm 4. 3.0 32. 3.4 × 10 T, 9.4 × 10 −4 6 5. 3.7 × 10 m −6 2mp K  √ ma0 2ma0 33. where mp = mass of a proton el 6. towards west, downward e ev0 34. 12 cm 7. 0.08 N perpendicular to both the wire and the field 35. (a) 3.2 × 10 N (b) 2.1 × 10 m (c) 1.31 × 10 s − 15 −4 −7 8. 0.02 N on each wire, on da and cb towards left and on 36. 1.72 × 10 m s 14 −2 dc and ab downward 37. (a) 8.8 × 10 m s (b) 4.8 × 10 m s 10 −1 7 −1 9. 0.16 N mv 10. √2 B0 il 38. (a) (b) π − 2θ qB 11. 0.50 N towards the inside of the circuit m mv , m (c) (π − 2θ) (d) π + 2θ, (π + 2θ) 12. 2πaiB, perpendicular to the plane of the figure going qB qB qB into it 39. (a) π/2 (b) π/6 (c) π 2 2πa iB0 12 40. C and C 14 13.  √ 2 2 a +d 41. 119 cm and 120 cm 42. 0.75 mm 14. 2iBa 43. 8 cm 17. 0.25 N qBd d 3d πm 18. iλB 45. (a) (b) , (c) (d) the particles stick together 2m 2 2 6 qB 19. 2iRB, upward in the figure and the combined mass moves with constant speed vm along 20. 4.9 × 10 T −5 the straight line drawn upward in the plane of figure through 21. (a) 1 13 N (b) 1.25 N. the point of collision RANKERSHALT now have an APP, with tonnes of new and updated materials. Download it from Play Store. (Click Here) Also dont't forget to rate us and leave a review. Download RANKERSHALT app from Play Store: Click Here 236 Concepts of Physics 54. (a) 6.3 × 10 N m (b) 60° −1 46. 49 m s –2 47. 2.5 × 10 C kg 55. (a) zero (b) 0.02 N m parallel to the shorter side. 5 −1 48. 1.0 × 10 N C , 0.05 T 56. 0.13 N m 4 −1 49. 36 cm, 55 cm iL B 2 iL B 2 57. (a) (b) 50. 6.4 × 10 m s , 1.0 × 10 4π 16 4 −1 5 Mg 51.  √2qE0 z m 58. 2nil qω qωr 2 53. 0.5 T 59. (a) (b) 2π 2 RANKERSHALT now have an APP, with tonnes of new and updated materials. Download it from Play Store. 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Download it from Play Store. (Click Here) Also dont't forget to rate us and leave a review. Download RANKERSHALT app from Play Store: Click Here 238 Concepts of Physics 2 7 1 10 m sin 45 Field on a Perpendicular Bisector  10 T mA  10 A 2 m 2 Suppose, the length MN  a and the point P is on  1.8  10 T. 9 its perpendicular bisector. So, OM  ON  a/2 and The direction of B is the same as that of dl  r. From a/2 a the figure, it is vertically downward. cos1       2 2 a 2 a 4d d 2 35.2 MAGNETIC FIELD DUE TO CURRENT 4 IN A STRAIGHT WIRE a and cos2    Let MN (figure 35.3) be a portion of a straight wire carrying a current i. Let P be a point at a distance   2 a 4d 2 OP  d from it. The point O is the foot of the Equation (35.4) then becomes perpendicular from P to the wire. 0 i 2a B 4d   2 a 4d 2 0 ia    (35.5) 2d  a 4 2 2 d Field due to a Long, Straight Wire In this case 1  0 and 2  . From equation (35.4), the magnetic field is 0 i B   (35.6) 2d Figure 35.3 The direction of the magnetic field at a point P due Let us consider an element dl of the wire at a to a long, straight wire can be found by a slight variation distance l from the point O. The vector joining the in the right-hand thumb rule. If we stretch the thumb of the right hand along the long current and curl our fingers element dl with the point P is r. Let  be the angle to pass through the point P, the direction of the fingers between dl and r. The magnetic field at P due to the at P gives the direction of the magnetic field there. element is i i 0 dl sin dB  i 2   (i) 4 r The direction of the field is determined by the vector dl  r. It is perpendicular to the plane of the P Q diagram and going into it. The direction of the field is the same for all elements of the wire and hence the net field due to the wire MN is obtained by integrating equation (i) under proper limits. Figure 35.4 From the figure, l   d cot Example 35.2 2 or, dl  d cosec  d. Figure (35.5) shows two long, straight wires carrying Also, r  d cosec. electric currents in opposite directions. The separation Putting in (i), between the wires is 5.0 cm. Find the magnetic field at a point P midway between the wires. 0 i dB  sin d 4d 0 i  or, B [ cos]21 4d 0 i  cos1  cos2.  (35.4) 4d Figure 35.5 Here 1 and 2 are the values of  corresponding Solution : The right-hand thumb rule shows that the to the lower end and the upper end respectively. magnetic field at P due to each of the wires is RANKERSHALT now have an APP, with tonnes of new and updated materials. Download it from Play Store. (Click Here) Also dont't forget to rate us and leave a review. Download RANKERSHALT app from Play Store: Click Here Magnetic Field due to a Current 239 perpendicular to the plane of the diagram and is going towards the wire W1. The force per unit length of the into it. The magnitude of the field due to each wire is wire W2 due to the wire W1 is 0 i B dF 0 i1i2 2d    (35.7) dl 2d 7 1 2  10 T mA  10 A  If we take an element dl in the wire W1 and. 2 2 5  10 m calculate the magnetic force per unit length of wire  80 T. W1 due to W2, it is again given by (35.7). The net field due to both the wires is 2  80 T If the parallel wires carry currents in opposite  160 T. directions, the wires repel each other. Example 35.3 We can draw magnetic field lines on the pattern Two long, straight wires, each carrying an electric of electric field lines. A tangent to a magnetic field line current of 5.0 A, are kept parallel to each other at a gives the direction of the magnetic field existing at separation of 2.5 cm. Find the magnitude of the magnetic that point. For a long straight wire, the field lines are force experienced by 10 cm of a wire. circles with their centres on the wire (figure 35.6). Solution : The field at the site of one wire due to the other is 0 i 2  10 T mA  5.0 A 7 1  4.0  10 T. 5 B  2.5  10 m 2 2d The force experienced by 10 cm of this wire due to the other is F  i lB Figure 35.6  5.0 A 10  10 m 4.0  10 T 2 5 35.3 FORCE BETWEEN PARALLEL CURRENTS  2.0  10 N. 5 Definition of Ampere Consider two parallel wires separated by 1 m and carrying a current of 1 A each. Then i1  i2  1 A and d  1 m, so that from equation (35.7), dF 7 1  2  10 N m. Figure 35.7 dl Consider two long wires W1 and W2 kept parallel This is used to formally define the unit ‘ampere’ to each other and carrying currents i1 and i2 of electric current. If two parallel, long wires, kept 1 m respectively in the same direction (figure 35.7). The apart in vacuum, carry equal currents in the same separation between the wires is d. Consider a small direction and there is a force of attraction of 7 element dl of the wire W2. The magnetic field at dl 2  10 newton per metre of each wire, the current due to the wire W1 is in each wire is said to be 1 ampere. 0 i1 B   (i) 35.4 FIELD DUE TO A CIRCULAR CURRENT 2d The field due to the portions of the wire W2, above Field at the Centre and below dl, is zero. Thus, (i) gives the net field at dl. The direction of this field is perpendicular to the plane of the diagram and going into it. The magnetic force at the element dl is dF  i2 dl  B 0 i1 or, dF  i2 dl  2d Figure 35.8 The vector product dl  B has a direction towards Consider a circular loop of radius a carrying a the wire W1. Thus, the length dl of wire W2 is attracted current i. We have to find the magnetic field due to RANKERSHALT now have an APP, with tonnes of new and updated materials. Download it from Play Store. (Click Here)