UNIVERSITY PHYSICS: HEAT, ELECTRICITY & MAGNETISM
1 Introduction 1 Page References 2 How to Use this Book 3 2 Graphical Facilities 5 Downloading the FlexPDE Program 5 The FlexPDE Editor 6 Plotting Functions of One Variable 7 Running the Problem Descriptor File 8 Plotting Functions of Two Variables 9 Help and Manual 15 3 “Curly” Velocity Fields 16 Liquid, Rotating as a Disk 16 Non-Constant ? 18 More General Velocity Fields 23 4 Fields of Gravitation 25 Earth and Moon as Point Masses 25 Planets of Finite Size 27 Divergence of g 32 5 Fields around Electric Charges 34 Field around Two Positive Point Charges 34 Positive and Negative Point Charges 36 The Dipole Field 37 Field around Charged Wires 39 Dipole of Charged Wires 41 The Gauss Integral 42 Positive and Negative Charges in (?, z) 43 6 Laplace and Poisson Equations 48 Known Values on Boundaries 48 Values and Derivatives on Boundaries 50 Multiplying through the PDE 51 Derivative Boundary Conditions Only 52 Solution Over a Quarter-Circle 53 The Poisson Equation 54 7 Electrostatic Fields in (x,y) Space 56 Metal Rod in a Metal Box 56 Metal Bar in a Tube 58 Metal Rod across a Parallel Field 60 8 Electrical Conduction in (x, y) Space 63 Conduction in a Rectangular Plate 64 Conduction in a Trapezoidal Plate 65 Checking the Solution 67 Radial Conduction in a Foil 68 Constricted Rectangular Plate 69 Plate Made of Two Different Metals 70 Plate with an Elliptic Insert 73 9 Dielectrics in (x, y) Space 76 Coaxial Cable 76 Capacitance 78 Parallel Plate Capacitor 78 Exploiting Symmetry 83 Glass Rod across a Parallel Field 84 Surface Charge of Polarization 87 10 Steady Fields in (?, z) Space 90 Electrical Conduction in a Cone 90 Plate Capacitor 93 Glass Ball in a Parallel Field 96 Charged, Conducting Ellipsoid 98 Spherical Capacitor 102 Charged Metal Balls in a Dielectric 101 Charged Dielectric 105 11 Electrostatic Force and Energy 108 Forces on a Parallel-Plate Capacitor 108 Oppositely Charged Metal Rods 109 Charged Metal Balls 111 Forces on a Dielectric 114 Metallic and Dielectric Rod across a Parallel Field 114 Metal Ball and Dielectric Ellipsoid 116 Electrostatic Energy 118 Field Energy of Metal Balls in Glass 119 Energy Minimum 121 12 Magnetostatics in (x, y) Space 124 Magnetic Field around a Wire 125 Field around Two Wires 128 Force between Two Wires 130 Two Wires inside a Magnetic Shield 132 Boundary Conditions for Magnetic Vectors 133 Force on a Magnetic Object 135 Force on a Magnetic Cylinder 136 Model of a Permanent Magnet 138 13 Magnetostatics in (?, z) Space 141 Magnetic Field around a Wire 141 Field along the (?, z) Plane 144 Simple Magnet Coil 145 Helmholtz Coil 147 Forces on Coils 149 Coil with a Magnetic Core 150 Force between a Coil and a Magnetic Ellipsoid 151 Magnetostatic Field Energy 153 Simple Model of a Permanent Magnet 155 Permanent Magnetization 156 Permanent Magnet as a Current Sheet 159 14 Heat Conduction in (x, y) Space 162 Two Hot-Water Tubes 163 Uniformly Heated, Semi-Circular Rod 165 Cooling by Forced Convection 167 Conduction in Anisotropic Wood 168 15 Heat Conduction in (?, z) Space 172 Radial Conduction in a Hollow Cylinder 172 Cooling by Forced Convection 174 Continuously Varying Thermal Conductivity 175 Steel Tube with Cooling Flanges 177 16 Non-Linear Heat Transfer 180 Temperature-Dependent Conductivity 180 Steel Foil Emitting Infrared Radiation 183 17 Simultaneous Electric and Thermal Conduction 186 Copper Block Heated by an Electric Current 187 Electrically Heated, Radiating Copper Foil 189 Semicircular Foil, Heated by an Electric Current 191 18 Transients in One Dimension 195 Iron Bar with a Temperature Step 195 Bar with a Temperature Step Halfway 198 Iron Bar, Soldered to a Copper Bar 199 Ramp Function at a Boundary 201 19 Transients in (x, y) and (?, z) Space 204 Internally Heated Steel Bar with a Loss 204 Capsule and Sample in a Scanning Calorimeter 206 Moving Heat Source 208 Stationary State for a Moving Heat Source 210 20 Time-Sinusoidal Problems 213 Oscillation Temperature in a Steel Block 214 Animation of an Oscillating Temperature 218 Sinusoidal Volume Heating of a Steel Foil 219 21 Electron and Hole Conduction 222 Steady-State Electron Current 222 One-Dimensional Conduction in a Metal 223 Field at a Metal-Vacuum Interface 224 Semiconductors 226 Semiconductors in One Dimension 227 Semiconductor in an Electric Field 228 Current through a Semiconductor 231 Model of a Silicon Junction Diode 232 Reverse Current 237 22 Fields in Three Dimensions 240 Two Point Charges of Different Signs 240 Non-Linear Set of Point Charges 243 Laplace Equation in 3D 244 Coin in a Metal Box 247 Improved Gridding around the Coin 251 Electrical Conduction in a Cone 251 Exploiting Symmetry 254 Glass Block in a Parallel Electric Field 255 Simple Magnet Coil 258 Steady Heat Conduction 261 Temperature Transients 264