4. electricity and magnetism

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  • 1.Book 4 in the Light and Matter series of free introductory physics textbooks www.lightandmatter.com

2. The Light and Matter series of introductory physics textbooks: 1 Newtonian Physics 2 Conservation Laws 3 Vibrations and Waves 4 Electricity and Magnetism 5 Optics 6 The Modern Revolution in Physics 3. Benjamin Crowell www.lightandmatter.com 4. Fullerton, California www.lightandmatter.com copyright 1999-2006 Benjamin Crowell edition 2.3 rev. April 16, 2008 This book is licensed under the Creative Com- mons Attribution-ShareAlike license, version 1.0, http://creativecommons.org/licenses/by-sa/1.0/, except for those photographs and drawings of which I am not the author, as listed in the photo credits. If you agree to the license, it grants you certain privileges that you would not otherwise have, such as the right to copy the book, or download the digital version free of charge from www.lightandmatter.com. At your option, you may also copy this book under the GNU Free Documentation License version 1.2, http://www.gnu.org/licenses/fdl.txt, with no invariant sections, no front-cover texts, and no back-cover texts. ISBN 0-9704670-4-4 5. To Arnold Arons. 6. Brief Contents 1 Electricity and the Atom 13 2 The Nucleus 41 3 Circuits, Part 1 77 4 Circuits, Part 2 105 5 Fields of Force 123 6 Electromagnetism 143 A Capacitance and Inductance 169 7. Contents 1 Electricity and the Atom 1.1 The quest for the atomic force . . . 14 1.2 Charge, electricity and magnetism . 15 Charge, 15.Conservation of charge, 17.Electrical forces involving neutral objects, 18.The path ahead, 18. Magnetic forces, 18. 1.3 Atoms . . . . . . . . . . . . . 20 Atomism, 20.Atoms, light, and every- thing else, 22.The chemical elements, 23.Making sense of the elements, 24. Direct proof that atoms existed, 25. 1.4 Quantization of charge . . . . . . 26 1.5 The electron . . . . . . . . . . 30 Cathode rays, 30.Were cathode rays a form of light, or of matter?, 30. Thomsons experiments, 31.The cathode ray as a subatomic particle: the electron, 33. 1.6 The raisin cookie model of the atom 34 Summary . . . . . . . . . . . . . 37 Problems . . . . . . . . . . . . . 39 2 The Nucleus 2.1 Radioactivity . . . . . . . . . . 41 Becquerels discovery of radioactivity, 41.Three kinds of radiations, 43. Radium: a more intense source of radioactivity, 43.Tracking down the na- ture of alphas, betas, and gammas, 43. 2.2 The planetary model of the atom. . 45 Some phenomena explained with the plan- etary model, 48. 2.3 Atomic number . . . . . . . . . 48 2.4 The structure of nuclei . . . . . . 53 The proton, 53.The neutron, 54. Isotopes, 55.Sizes and shapes of nuclei, 56. 2.5 The strong nuclear force, alpha decay and ssion. . . . . . . . . . . . . 56 Randomness in physics, 59. 2.6 The weak nuclear force; beta decay 59 The solar neutrino problem, 61. 2.7 Fusion. . . . . . . . . . . . . 63 2.8 Nuclear energy and binding energies 64 2.9 Biological effects of ionizing radiation 67 2.10 The creation of the elements . . 70 Creation of hydrogen and helium in the Big Bang, 70.We are stardust, 70.Articial synthesis of heavy elements, 71. Summary . . . . . . . . . . . . . 72 Problems . . . . . . . . . . . . . 74 3 Circuits, Part 1 3.1 Current . . . . . . . . . . . . 78 Unity of all types of electricity, 78. Electric current, 79. 3.2 Circuits . . . . . . . . . . . . 81 3.3 Voltage . . . . . . . . . . . . 82 The volt unit, 82.The voltage concept in general, 83. 3.4 Resistance . . . . . . . . . . . 87 Resistance, 87.Superconductors, 89. Constant voltage throughout a conductor, 90.Short circuits, 91.Resistors, 91. Lightbulb, 92.Polygraph, 92.Fuse, 92.Voltmeter, 93. 3.5 Current-conducting properties of materials . . . . . . . . . . . . . 94 Solids, 94.Gases, 95.Liquids, 95. Speed of currents and electrical signals, 96. 3.6 Applications of Calculus . . . . 97 Summary . . . . . . . . . . . . . 99 Problems . . . . . . . . . . . . . 101 10 8. 4 Circuits, Part 2 4.1 Schematics . . . . . . . . . . 106 4.2 Parallel resistances and the junction rule. . . . . . . . . . . . . . . . 107 4.3 Series resistances. . . . . . . . 112 Summary . . . . . . . . . . . . . 118 Problems . . . . . . . . . . . . . 119 5 Fields of Force 5.1 Why elds? . . . . . . . . . . 123 Time delays in forces exerted at a distance, 123.More evidence that elds of force are real: they carry energy., 124. 5.2 The gravitational eld . . . . . . 125 Sources and sinks, 127.Superposition of elds, 127.Gravitational waves, 128. 5.3 The electric eld . . . . . . . . 129 Denition, 129.Dipoles, 130. Alternative denition of the electric eld, 132.Voltage related to electric eld, 132. 5.4 Voltage for Nonuniform Fields . . 134 5.5 Two or Three Dimensions. . . . . 136 5.6 Electric Field of a Continuous Charge Distribution . . . . . . . . . 138 Summary . . . . . . . . . . . . . 140 Problems . . . . . . . . . . . . . 141 6 Electromagnetism 6.1 The magnetic eld. . . . . . . . 144 No magnetic monopoles, 144.Denition of the magnetic eld, 145. 6.2 Calculating magnetic elds and forces. . . . . . . . . . . . . . . 146 Magnetostatics, 146.Force on a charge moving through a magnetic eld, 148. 6.3 Induction. . . . . . . . . . . . 149 Electromagnetism and relative motion, 149.The principle of induction, 151. 6.4 Electromagnetic waves. . . . . . 154 Polarization, 154.Light is an electro- magnetic wave, 155.The electromagnetic spectrum, 155. 6.5 Calculating energy in elds . . . . 156 6.6 Symmetry and handedness . . . 160 Summary . . . . . . . . . . . . . 162 Problems . . . . . . . . . . . . . 163 A Capacitance and Inductance A.1 Capacitance and inductance . . . 169 Capacitors, 170.Inductors, 170. A.2 Oscillations . . . . . . . . . . 172 A.3 Voltage and Current . . . . . . . 175 A.4 Decay. . . . . . . . . . . . . 179 The RC circuit, 179.The RL circuit, 180. A.5 Impedance. . . . . . . . . . . 182 Problems . . . . . . . . . . . . . 185 Appendix 1: Exercises 186 Appendix 2: Photo Credits 201 Appendix 3: Hints and Solutions 203 11 9. 12 10. Chapter 1 Electricity and the Atom Where the telescope ends, the microscope begins. Which of the two has the grander view? Victor Hugo His father died during his mothers pregnancy. Rejected by her as a boy, he was packed o to boarding school when she remarried. He himself never married, but in middle age he formed an intense relationship with a much younger man, a relationship that he ter- minated when he underwent a psychotic break. Following his early scientic successes, he spent the rest of his professional life mostly in frustration over his inability to unlock the secrets of alchemy. The man being described is Isaac Newton, but not the triumphant Newton of the standard textbook hagiography. Why dwell on the sad side of his life? To the modern science educator, Newtons life- long obsession with alchemy may seem an embarrassment, a distrac- tion from his main achievement, the creation the modern science of mechanics. To Newton, however, his alchemical researches were nat- urally related to his investigations of force and motion. What was radical about Newtons analysis of motion was its universality: it succeeded in describing both the heavens and the earth with the same equations, whereas previously it had been assumed that the sun, moon, stars, and planets were fundamentally dierent from earthly objects. But Newton realized that if science was to describe all of nature in a unied way, it was not enough to unite the human scale with the scale of the universe: he would not be satised until 13 11. he t the microscopic universe into the picture as well. It should not surprise us that Newton failed. Although he was a rm believer in the existence of atoms, there was no more experimen- tal evidence for their existence than there had been when the ancient Greeks rst posited them on purely philosophical grounds. Alchemy labored under a tradition of secrecy and mysticism. Newton had already almost single-handedly transformed the fuzzyheaded eld of natural philosophy into something we would recognize as the modern science of physics, and it would be unjust to criticize him for failing to change alchemy into modern chemistry as well. The time was not ripe. The microscope was a new invention, and it was cutting-edge science when Newtons contemporary Hooke discovered that living things were made out of cells. 1.1 The quest for the atomic force Newton was not the rst of the age of reason. He was the last of the magicians. John Maynard Keynes Nevertheless it will be instructive to pick up Newtons train of thought and see where it leads us with the benet of modern hind- sight. In uniting the human and cosmic scales of existence, he had reimagined both as stages on which the actors were objects (trees and houses, planets and stars) that interacted through attractions and repulsions. He was already convinced that the objects inhab- iting the microworld were atoms, so it remained only to determine what kinds of forces they exerted on each other. His next insight was no less brilliant for his inability to bring it to fruition. He realized that the many human-scale forces friction, sticky forces, the normal forces that keep objects from occupying the same space, and so on must all simply be expressions of a more fundamental force acting between atoms. Tape sticks to paper because the atoms in the tape attract the atoms in the paper. My house doesnt fall to the center of the earth because its atoms repel the atoms of the dirt under it. Here he got stuck. It was tempting to think that the atomic force was a form of gravity, which he knew to be universal, fundamental, and mathematically simple. Gravity, however, is always attractive, so how could he use it to explain the existence of both attractive and repulsive atomic forces? The gravitational force between ob- jects of ordinary size is also extremely small, which is why we never notice cars and houses attracting us gravitationally. It would be hard to understand how g