INTRODUCTORY ELECTROMAGNETICS
CONTENTS 1 ELECTROSTATICS I REVIEW OF F = MA ENTER ELECTRICITY COULOMB’S LAW PROPERTIES OF CHARGE SUPERPOSITION PRINCIPLE VERIFYING COULOMB’S LAW THE RATIO OF GRAVITATIONAL TO ELECTRIC FORCES COULOMB’S LAW FOR CONTINUOUS CHARGE DENSITY 2 THE ELECTRIC FIELD REVIEW OF KEY IDEAS DIGRESSION ON NUCLEAR FORCES THE ELECTRIC ?ELD E VISUALIZING THE ?ELD FIELD OF A DIPOLE FAR ?ELD OF DIPOLE: GENERAL CASE RESPONSE TO A ?ELD DIPOLE IN A UNIFORM ?ELD 3 GAUSS’S LAW I FIELD OF AN IN?NITE LINE CHARGE FIELD OF AN IN?NITE SHEET OF CHARGE SPHERICAL CHARGE DISTRIBUTION: GAUSS’S LAW DIGRESSION ON THE AREA VECTOR DA COMPOSITION OF AREAS AN APPLICATION OF THE AREA VECTOR GAUSS’S LAW THROUGH PICTURES CONTINUOUS CHARGE DENSITY 4 GAUSS’S LAW II: APPLICATIONS APPLICATIONS OF GAUSS’S LAW FIELD INSIDE A SHELL FIELD OF AN IN?NITE CHARGED WIRE, REDUX FIELD OF AN IN?NITE PLANE, REDUX CONDUCTORS FIELD INSIDE A PERFECT CONDUCTOR IS ZERO THE NET CHARGE ON A CONDUCTOR WILL RESIDE AT THE SURFACE A CONDUCTOR WITH A HOLE INSIDE FIELD ON THE SURFACE OF A CONDUCTOR 5 THE COULOMB POTENTIAL CONSERVATIVE FORCES AND POTENTIAL ENERGY IS THE ELECTROSTATIC ?ELD CONSERVATIVE? PATH INDEPENDENCE THROUGH PICTURES POTENTIAL AND ?ELD OF A DIPOLE 6 CONDUCTORS AND CAPACITORS CASES WHERE COMPUTING V FROM E IS EASIER VISUALIZING V EQUIPOTENTIALS METHOD OF IMAGES PROOF OF UNIQUENESS (OPTIONAL SECTION) ADDITIONAL PROPERTIES OF THE POTENTIAL V(R) CAPACITORS ENERGY STORED IN A CAPACITOR ENERGY OF A CHARGE DISTRIBUTION 7 CIRCUITS AND CURRENTS ENERGY IN THE ELECTRIC ?ELD CIRCUITS AND CONDUCTIVITY CIRCUITS THE BATTERY AND THE EMF E THE RC CIRCUIT WITH A BATTERY MISCELLANEOUS CIRCUITS 8 MAGNETISM I EXPERIMENTS POINTING TO MAGNETISM EXAMPLES OF THE LORENTZ FORCE, THE CYCLOTRON LORENTZ FORCE ON CURRENT-CARRYING WIRES THE MAGNETIC DIPOLE THE DC MOTOR 9 MAGNETISM II: BIOT-SAVART LAW PRACTICE WITH BIOT-SAVART: ?ELD OF A LOOP MICROSCOPIC DESCRIPTION OF A BAR MAGNET MAGNETIC ?ELD OF AN IN?NITE WIRE AMP`ERE’S LAW MAXWELL’S EQUATIONS (STATIC CASE) 10 AMP`ERE II, FARADAY, AND LENZ FIELD OF AN IN?NITE WIRE, REDUX FIELD OF A SOLENOID FARADAY AND LENZ OPTIONAL DIGRESSION ON FARADAY’S LAW 11 MORE FARADAY BETATRON GENERATORS INDUCTANCE MUTUAL INDUCTANCE SELF-INDUCTANCE ENERGY IN THE MAGNETIC ?ELD 12 AC CIRCUITS REVIEW OF INDUCTORS THE LC CIRCUIT DRIVEN LC CIRCUIT THE LCR CIRCUIT REVIEW OF COMPLEX NUMBERS SOLVING THE LCR EQUATION VISUALIZING Z COMPLEX FORM OF OHM’S LAW 13 LCR CIRCUITS AND DISPLACEMENT CURRENT ANALYSIS OF LCR RESULTS TRANSIENTS AND THE COMPLEMENTARY SOLUTION POWER OF THE COMPLEX NUMBERS DISPLACEMENT CURRENT 14 ELECTROMAGNETIC WAVES THE WAVE EQUATION RESTRICTED MAXWELL EQUATIONS IN VACUUM MAXWELL EQUATIONS INVOLVING IN?NITESIMAL CUBES MAXWELL EQUATIONS INVOLVING IN?NITESIMAL LOOPS THE WAVE! SINUSOIDAL SOLUTION TO THE WAVE EQUATION ENERGY IN THE ELECTROMAGNETIC WAVE ORIGIN OF ELECTROMAGNETIC WAVES MAXWELL EQUATIONS—THE GENERAL CASE (OPTIONAL) CONSEQUENCES FOR THE RESTRICTED E AND B FROM MICROSCOPIC TO MACROSCOPIC (OPTIONAL) MAXWELL EQUATIONS INVOLVING CUBES MAXWELL EQUATIONS INVOLVING LOOPS 15 ELECTROMAGNETISM AND RELATIVITY MAGNETISM FROM COULOMB’S LAW AND RELATIVITY RELATIVISTIC INVARIANCE OF ELECTRODYNAMICS REVIEW OF LORENTZ TRANSFORMATIONS IMPLICATIONS FOR NEWTONIAN MECHANICS SCALAR AND VECTOR ?ELDS THE DERIVATIVE OPERATOR LORENTZ SCALARS AND VECTORS THE FOUR-CURRENT J CHARGE CONSERVATION AND THE FOUR-CURRENT J THE FOUR-POTENTIAL A GAUGE INVARIANCE WAVE EQUATION FOR THE FOUR-VECTOR A WHY WORK WITH V AND A? 1510 THE ELECTROMAGNETIC TENSOR F 15101 TENSORS 15102 THE ELECTROMAGNETIC ?ELD TENSOR F 16 OPTICS I: GEOMETRIC OPTICS REVISITED GEOMETRIC OR RAY OPTICS BRIEF HISTORY OF C SOME HIGHLIGHTS OF GEOMETRIC OPTICS THE LAW OF RE?ECTION FROM FERMAT’S PRINCIPLE SNELL’S LAW FROM FERMAT’S PRINCIPLE RE?ECTION OFF A CURVED SURFACE BY FERMAT ELLIPTICAL MIRRORS AND FERMAT’S PRINCIPLE PARABOLIC MIRRORS 17 OPTICS II: MORE MIRRORS AND LENSES SPHERICAL APPROXIMATIONS TO PARABOLIC MIRRORS IMAGE FORMATION: GEOMETRIC OPTICS A MIDLIFE CRISIS IMAGE FORMATION BY FERMAT’S PRINCIPLE TRICKY CASES FERMAT’S PRINCIPLE FOR VIRTUAL FOCAL POINTS RAY OPTICS FOR VIRTUAL IMAGES LENSES `A LA FERMAT PRINCIPLE OF LEAST ACTION THE EYE 18 WAVE THEORY OF LIGHT INTERFERENCE OF WAVES ADDING WAVES USING REAL NUMBERS ADDING WAVES WITH COMPLEX NUMBERS ANALYSIS OF INTERFERENCE DIFFRACTION GRATING SINGLE-SLIT DIFFRACTION UNDERSTANDING RE?ECTION AND CRYSTAL DIFFRACTION LIGHT INCIDENT ON AN OIL SLICK NORMAL INCIDENCE OBLIQUE INCIDENCE 19 QUANTUM MECHANICS: THE MAIN EXPERIMENT DOUBLE-SLIT EXPERIMENT WITH LIGHT TROUBLE WITH MAXWELL DIGRESSION ON PHOTONS PHOTOELECTRIC EFFECT COMPTON EFFECT MATTER WAVES PHOTONS VERSUS ELECTRONS THE HEISENBERG UNCERTAINTY PRINCIPLE THERE ARE NO STATES OF WELL-DE?NED POSITION AND MOMENTUM HEISENBERG MICROSCOPE LET THERE BE LIGHT THE WAVE FUNCTION ? COLLAPSE OF THE WAVE FUNCTION 1910 SUMMARY 20 THE WAVE FUNCTION AND ITS INTERPRETATION PROBABILITY IN CLASSICAL AND QUANTUM MECHANICS GETTING TO KNOW ? STATISTICAL CONCEPTS: MEAN AND UNCERTAINTY 21 QUANTIZATION AND MEASUREMENT MORE ON MOMENTUM STATES SINGLE-VALUEDNESS AND QUANTIZATION OF MOMENTUM QUANTIZATION THE INTEGRAL OF ?P(X) MEASUREMENT POSTULATE: MOMENTUM AN EXAMPLE SOLVABLE BY INSPECTION USING A NORMALIZED ? FINDING A(P) BY COMPUTATION MORE ON FOURIER’S THEOREMS MEASUREMENT POSTULATE: GENERAL MORE THAN ONE VARIABLE 22 STATES OF DE?NITE ENERGY FREE PARTICLE ON A RING ANALYSIS OF ENERGY LEVELS: DEGENERACY THINKING INSIDE THE BOX PARTICLE IN A WELL THE BOX: AN EXACT SOLUTION ENERGY MEASUREMENT IN THE BOX 23 SCATTERING AND DYNAMICS QUANTUM SCATTERING TUNNELING QUANTUM DYNAMICS A SOLUTION OF THE TIME-DEPENDENT SCHR¨ODINGER EQUATION DERIVATION OF THE PARTICULAR SOLUTION ?E(X,T) SPECIAL PROPERTIES OF THE PRODUCT SOLUTION GENERAL SOLUTION FOR TIME EVOLUTION TIME EVOLUTION: A MORE COMPLICATED EXAMPLE 24 SUMMARY AND OUTLOOK POSTULATES: ?RST PASS RE?NING THE POSTULATES TOWARD A COMPACT SET OF POSTULATES EIGENVALUE PROBLEM THE DIRAC DELTA FUNCTION AND THE OPERATOR X POSTULATES: ?NAL MANY PARTICLES, BOSONS, AND FERMIONS IDENTICAL VERSUS INDISTINGUISHABLE IMPLICATIONS FOR ATOMIC STRUCTURE ENERGY-TIME UNCERTAINTY PRINCIPLE WHAT NEXT? EXERCISES PROBLEM SET 1, FOR CHAPTERS 1 AND PROBLEM SET 2, FOR CHAPTERS 3 AND PROBLEM SET 3, FOR CHAPTERS 5 AND PROBLEM SET 4, FOR CHAPTER PROBLEM SET 5, FOR CHAPTERS 8 AND PROBLEM SET 6, FOR CHAPTER PROBLEM SET 7, FOR CHAPTERS 11, 12, AND PROBLEM SET 8, FOR CHAPTERS 14 AND PROBLEM SET 9, FOR CHAPTERS 16, 17, AND PROBLEM SET 10, FOR CHAPTERS 19 AND PROBLEM SET 11, FOR CHAPTERS 21 AND PROBLEM SET 12, FOR CHAPTERS 23 AND ANSWERS TO EXERCISES CONSTANTS