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PHYS1112 - Electricity and Magnetism Lecture Notes Dr. Jason Chun Shing Pun Department of Physics The University of Hong Kong January 2005 Contents 1 Vector Algebra 1 1.1 Definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Vector Algebra . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.3 Components of Vectors .
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  PHYS1112 - Electricity and MagnetismLecture Notes Dr. Jason Chun Shing Pun Department of PhysicsThe University of Hong Kong  January 2005  Contents 1 Vector Algebra 1 1.1 Definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Vector Algebra . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.3 Components of Vectors . . . . . . . . . . . . . . . . . . . . . . . . 21.4 Multiplication of Vectors . . . . . . . . . . . . . . . . . . . . . . . 41.5 Vector Field (Physics Point of View) . . . . . . . . . . . . . . . . 61.6 Other Topics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2 Electric Force & Electric Field 8 2.1 Electric Force . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82.2 The Electric Field . . . . . . . . . . . . . . . . . . . . . . . . . . . 92.3 Continuous Charge Distribution . . . . . . . . . . . . . . . . . . . 122.4 Electric Field Lines . . . . . . . . . . . . . . . . . . . . . . . . . . 182.5 Point Charge in E-field . . . . . . . . . . . . . . . . . . . . . . . . 212.6 Dipole in E-field . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 3 Electric Flux and Gauss’ Law 25 3.1 Electric Flux . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253.2 Gauss’ Law . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 283.3 E-field Calculation with Gauss’ Law . . . . . . . . . . . . . . . . . 283.4 Gauss’ Law and Conductors . . . . . . . . . . . . . . . . . . . . . 31 4 Electric Potential 36 4.1 Potential Energy and Conservative Forces . . . . . . . . . . . . . 364.2 Electric Potential . . . . . . . . . . . . . . . . . . . . . . . . . . . 404.3 Relation Between Electric Field E and Electric Potential V . . . . 454.4 Equipotential Surfaces . . . . . . . . . . . . . . . . . . . . . . . . 48 5 Capacitance and DC Circuits 51 5.1 Capacitors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 515.2 Calculating Capacitance . . . . . . . . . . . . . . . . . . . . . . . 515.3 Capacitors in Combination . . . . . . . . . . . . . . . . . . . . . . 545.4 Energy Storage in Capacitor . . . . . . . . . . . . . . . . . . . . . 55i  5.5 Dielectric Constant . . . . . . . . . . . . . . . . . . . . . . . . . . 575.6 Capacitor with Dielectric . . . . . . . . . . . . . . . . . . . . . . . 585.7 Gauss’ Law in Dielectric . . . . . . . . . . . . . . . . . . . . . . . 605.8 Ohm’s Law and Resistance . . . . . . . . . . . . . . . . . . . . . . 615.9 DC Circuits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 645.10 RC Circuits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 6 Magnetic Force 73 6.1 Magnetic Field . . . . . . . . . . . . . . . . . . . . . . . . . . . . 736.2 Motion of A Point Charge in Magnetic Field . . . . . . . . . . . . 756.3 Hall Effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 766.4 Magnetic Force on Currents . . . . . . . . . . . . . . . . . . . . . 78 7 Magnetic Field 81 7.1 Magnetic Field . . . . . . . . . . . . . . . . . . . . . . . . . . . . 817.2 Parallel Currents . . . . . . . . . . . . . . . . . . . . . . . . . . . 867.3 Amp`ere’s Law . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 887.4 Magnetic Dipole . . . . . . . . . . . . . . . . . . . . . . . . . . . . 927.5 Magnetic Dipole in A Constant B-field . . . . . . . . . . . . . . . 937.6 Magnetic Properties of Materials . . . . . . . . . . . . . . . . . . 94 8 Faraday’s Law of Induction 98 8.1 Faraday’s Law . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 988.2 Lenz’ Law . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 998.3 Motional EMF . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1008.4 Induced Electric Field . . . . . . . . . . . . . . . . . . . . . . . . 104 9 Inductance 107 9.1 Inductance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1079.2 LR Circuits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1109.3 Energy Stored in Inductors . . . . . . . . . . . . . . . . . . . . . . 1129.4 LC Circuit (Electromagnetic Oscillator) . . . . . . . . . . . . . . . 1139.5 RLC Circuit (Damped Oscillator) . . . . . . . . . . . . . . . . . . 115 10 AC Circuits 116 10.1 Alternating Current (AC) Voltage . . . . . . . . . . . . . . . . . . 11610.2 Phase Relation Between i,V  for R,L and C . . . . . . . . . . . . . 11710.3 Single Loop RLC AC Circuit . . . . . . . . . . . . . . . . . . . . . 11910.4 Resonance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12110.5 Power in AC Circuits . . . . . . . . . . . . . . . . . . . . . . . . . 12110.6 The Transformer . . . . . . . . . . . . . . . . . . . . . . . . . . . 123ii  11 Displacement Current and Maxwell’s Equations 125 11.1 Displacement Current . . . . . . . . . . . . . . . . . . . . . . . . . 12511.2 Induced Magnetic Field . . . . . . . . . . . . . . . . . . . . . . . . 12711.3 Maxwell’s Equations . . . . . . . . . . . . . . . . . . . . . . . . . 128iii
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