Electromagnetism and Optics An introductory course Richard Fitzpatrick Professor of Physics The University of Texas at Austin Contents 1 Introduction 8 2 Vectors 9 2.1 Vector Algebra . 9 2.2 Vector Area . 12 2.3 The Scalar Product . 14 2.4 The Vector Product . 16 2.5 Vector Calculus . 19 2.6 Line Integrals . 20 2.7 Surface Integrals . 21 2.8 Volume Integrals . 22 3 Electricity 24 3.1 Historical Introduction . 24 3.2 Conductors and Insulators . 25 3.3 Electrometers and Electroscopes . 26 3.4 Induced Electric Charge . 27 3.5 Coulomb's Law . 29 3.6 Electric Fields . 31 3.7 Worked Examples . 33 4 Gauss' Law 37 4.1 Electric Field-Lines . 37 4.2 Gauss' Law . 38 2 4.3 Electric Field of a Spherical Conducting Shell . 39 4.4 Electric Field of a Uniformly Charged Wire . 41 4.5 Electric Field of a Uniformly Charged Plane . 42 4.6 Charged Conductors . 44 4.7 Worked Examples . 45 5 Electric Potential 46 5.1 Electric Potential Energy . 46 5.2 Electric Potential . 51 5.3 Electric Potential and Electric Field . 52 5.4 Electric Potential of a Point Charge . 56 5.5 Worked Examples . 57 6 Capacitance 63 6.1 Charge Storage . 63 6.2 Breakdown . 64 6.3 Capacitance . 67 6.4 Dielectrics . 68 6.5 Capacitors in Series and in Parallel . 71 6.6 Energy Stored by Capacitors . 74 6.7 Worked Examples . 76 7 Electric Current 81 7.1 Electric Circuits . 81 7.2 Ohm's Law . 83 7.3 Resistance and Resistivity . 85 3 7.4 Emf and Internal Resistance . 86 7.5 Resistors in Series and in Parallel . 88 7.6 Kirchhoff's Rules . 91 7.7 Capacitors in DC Circuits . 92 7.8 Energy in DC Circuits . 92 7.9 Power and Internal Resistance . 94 7.10 Worked Examples . 96 8 Magnetism 101 8.1 Historical Introduction . 101 8.2 Amp`ere's Experiments . 102 8.3 Amp`ere's Law . 105 8.4 The Lorentz Force . 107 8.5 Charged Particle in a Magnetic Field . 110 8.6 The Hall Effect . 113 8.7 Amp`ere's Circuital Law . 115 8.8 Magnetic Field of a Solenoid . 117 8.9 Origin of Permanent Magnetism . 118 8.10 Gauss' Law for Magnetic Fields . 122 8.11 Galvanometers . 123 8.12 Worked Examples . 128 9 Magnetic Induction 133 9.1 Faraday's Law . 133 9.2 Lenz's Law . 135 4 9.3 Magnetic Induction . 136 9.4 Motional Emf . 140 9.5 Eddy Currents . 143 9.6 The Alternating Current Generator . 145 9.7 The Direct Current Generator . 149 9.8 The Alternating Current Motor . 151 9.9 The Direct Current Motor . 154 9.10 Worked Examples . 157 10 Inductance 163 10.1 Mutual Inductance . 163 10.2 Self Inductance . 166 10.3 Energy Stored in an Inductor . 167 10.4 The RL Circuit . 169 10.5 The RC Circuit . 173 10.6 Transformers . 177 10.7 Impedance Matching . 182 10.8 Worked Examples . 183 11 Electromagnetic Waves 188 11.1 Maxwell's Equations . 188 11.2 Electromagnetic Waves . 193 11.3 Effect of Dielectric Materials . 197 11.4 Energy in Electromagnetic Waves . 197 11.5 Worked Examples . 199 5 12 Geometric Optics 201 12.1 Introduction . 201 12.2 History of Geometric Optics . 202 12.3 Law of Geometric Propagation . 203 12.4 Law of Reflection . 206 12.5 Law of Refraction . 207 12.6 Total Internal Reflection . 210 12.7 Dispersion . 213 12.8 Rainbows . 215 12.9 Worked Examples . 219 13 Paraxial Optics 222 13.1 Spherical Mirrors . 222 13.2 Image Formation by Concave Mirrors . ..