Problems in Classical Electromagnetism: 203 Exercises with Solutions

Preface to the Second Edition
Preface to the First Edition
Contents
1 Basics of Electrostatics
1.1 Overlapping Charged Spheres
1.2 Charged Sphere with Internal Spherical Cavity
1.3 Energy of a Charged Sphere
1.4 Plasma Oscillations
1.5 Mie Oscillations
1.6 Coulomb Explosions
1.7 Plane and Cylindrical Coulomb Explosions
1.8 Collision of Two Charged Spheres
1.9 Oscillations in a Positively Charged Conducting Sphere
1.10 Interaction Between a Point Charge and an Electric Dipole
1.11 Electric Field of a Charged Hemispherical Surface
1.12 The Electric Field of an Array of Charged Wires (1)
1.13 The Electric Field of an Array of Charged Wires (2)
1.14 Mean Value Property and the Force on a Spherical Charge
References
2 Electrostatics of Conductors
2.1 Metal Sphere in an External Field
2.2 Electrostatic Energy with Image Charges
2.3 Fields Generated by Surface Charge Densities
2.4 A Point Charge in Front of a Conducting Sphere
2.5 Dipoles and Spheres
2.6 Coulomb's Experiment
2.7 A Solution Looking for a Problem
2.8 Electrically Connected Spheres
2.9 A Charge Inside a Conducting Shell
2.10 A Charged Wire in Front of a Cylindrical Conductor
2.11 Hemispherical Conducting Surfaces
2.12 The Force Between the Plates of a Capacitor
2.13 Electrostatic Pressure on a Conducting Sphere
2.14 Conducting Prolate Ellipsoid
2.15 A Non-coaxial Cylindrical Capacitor
2.16 Induced Charge Density on a Conducting Plane
2.17 Charge Density on a Metal Sphere in Front of a Point Charge
3 Electrostatics of Dielectric Media
3.1 An Artificial Dielectric
3.2 Charge in Front of a Dielectric Half-Space
3.3 An Electrically Polarized Sphere
3.4 Dielectric Sphere in an External Field
3.5 Refraction of the Electric Field at a Dielectric Boundary
3.6 Contact Force Between a Conductor and a Dielectric
3.7 A Conducting Sphere Between Two Dielectrics
3.8 Measuring the Dielectric Constant of a Liquid
3.9 A Conducting Cylinder in a Dielectric Liquid
3.10 A Dielectric Slab in Contact with a Charged Conductor
3.11 A Transversally Polarized Cylinder
3.12 Force Between a Parallel-Plate Capacitor and a Dielectric Slab
3.13 A Cylindrical Quadrupole
Reference
4 Electric Currents
4.1 The Tolman-Stewart Experiment
4.2 Charge Relaxation in a Conducting Sphere
4.3 A Coaxial Resistor
4.4 Electrical Resistance Between Two Submerged Spheres (1)
4.5 Electrical Resistance Between Two Submerged Spheres (2)
4.6 Effects of Non-uniform Resistivity
4.7 Charge Decay in a Lossy Spherical Capacitor
4.8 Dielectric-Barrier Discharge
4.9 Charge Distribution in a Long Cylindrical Conductor
4.10 An Infinite Resistor Ladder
References
5 Magnetostatics
5.1 The Rowland Experiment
5.2 Pinch Effect in a Cylindrical Wire
5.3 A Magnetic Dipole in Front of a Magnetic Half-Space
5.4 Magnetic Levitation
5.5 Uniformly Magnetized Cylinder
5.6 Charged Particle in Crossed Electric and Magnetic Fields
5.7 Cylindrical Conductor with an Off-Centered Cavity
5.8 Conducting Cylinder in a Magnetic Field
5.9 Rotating Cylindrical Capacitor
5.10 Magnetized Spheres
5.11 A Transversally Magnetized Cylinder
5.12 A Rotating Charged Spherical Shell
5.13 Magnetic Field of a Polygonal Loop
5.14 Helmholtz Coils
6 Magnetic Induction and Time-Varying Fields
6.1 A Square Wave Generator
6.2 A Coil Moving in an Inhomogeneous Magnetic Field
6.3 A Circuit with ``Free-Falling'' Parts
6.4 The Tethered Satellite
6.5 Eddy Currents in a Solenoid
6.6 Feynman's ``Paradox''
6.7 Induced Electric Currents in the Ocean
6.8 A Magnetized Sphere as Unipolar Motor
6.9 Induction Heating
6.10 A Magnetized Cylinder as DC Generator
6.11 The Faraday Disk and a Self-Sustained Dynamo
6.12 Mutual Induction Between Circular Loops
6.13 Mutual Induction Between a Solenoid and an Internal Loop
6.14 Skin Effect and Eddy Inductance in an Ohmic Wire
6.15 Magnetic Pressure and Pinch Effect for a Surface Current
6.16 Magnetic Pressure on a Solenoid
6.17 A Homopolar Motor
6.18 A Magnetic Cylinder Sliding inside a Solenoid
6.19 Conducting Cylindrical Shell in a Magnetic Field
6.20 Electromagnetic Inertia of a Rotating Charged Ring
6.21 A Bar Sliding in a Magnetic Field
6.22 Magnetic Levitation of a Superconducting Ring
6.23 Electromagnetic Brake with Energy Recovery
6.24 A High Frequency Capacitor
References
7 Electromagnetic Oscillators and Wave Propagation
7.1 Coupled RLC Oscillators (1)
7.2 Coupled RLC Oscillators (2)
7.3 Coupled RLC Oscillators (3)
7.4 The LC Ladder Network
7.5 The CL Ladder Network
7.6 Non-dispersive Transmission Line
7.7 An ``Alternate'' LC Ladder Network
7.8 Resonances in an LC Ladder Network
7.9 Cyclotron Resonances (1)
7.10 Cyclotron Resonances (2)
7.11 A Quasi-Gaussian Wave Packet
7.12 A Wave Packet Along a Weakly Dispersive Line
8 Maxwell Equations and Conservation Laws
8.1 Poynting Vector(s) in an Ohmic Wire
8.2 Poynting Vector(s) in a Capacitor
8.3 Poynting's Theorem in a Solenoid
8.4 Poynting Vector in a Capacitor with Moving Plates
8.5 Radiation Pressure on a Perfect Mirror
8.6 A Light Beam
8.7 Intensity and Angular Momentum of a Light Beam
8.8 Feynman's Paradox solved
8.9 Magnetic Monopoles
8.10 An Interstellar Light Sail
8.11 Radiation Pressure at Oblique Incidence
8.12 A Square Law Detector
8.13 Poynting Vector for a Rotating Charged Spherical Shell
9 Relativistic Transformations of the Fields
9.1 The Fields of a Current-Carrying Wire
9.2 The Fields of a Plane Capacitor
9.3 The Fields of a Solenoid
9.4 The Four-Potential of a Plane Wave
9.5 The Force on a Magnetic Monopole
9.6 Reflection from a Moving Mirror
9.7 Oblique Incidence on a Moving Mirror
9.8 Pulse Modification by a Moving Mirror
9.9 Boundary Conditions on a Moving Mirror
9.10 Lorentz Transformations on a Coaxial Cable
9.11 Lorentz Transformations on a Rectangular Metal Pipe
9.12 Force on an Ohmic Wire
Reference
10 Radiation Emission and Scattering
10.1 Cyclotron Radiation
10.2 Atomic Collapse
10.3 Radiative Damping of the Elastically Bound Electron
10.4 Radiation Emitted by Orbiting Charges
10.5 Spin-Down Rate and Magnetic Field of a Pulsar
10.6 A Bent Dipole Antenna
10.7 A Receiving Circular Antenna
10.8 Polarization of Scattered Radiation
10.9 Polarization Effects on Thomson Scattering
10.10 Scattering and Interference
10.11 Optical Beats Generating a ``Lighthouse Effect''
10.12 Radiation Friction Force
10.13 Radiation of an Electron Falling on a Proton
10.14 Scattering by a Perfectly Conducting Sphere (1)
10.15 Scattering by a Perfectly Conducting Sphere (2)
References
11 Electromagnetic Waves in Matter
11.1 Wave Propagation in a Conductor at High and Low Frequencies
11.2 Energy Densities in a Free Electron Gas
11.3 Longitudinal Waves
11.4 Transmission and Reflection by a Thin Conducting Foil
11.5 Anti-reflection Coating
11.6 Birefringence and Waveplates
11.7 Magnetic Birefringence and Faraday Effect
11.8 Whistler Waves
11.9 Wave Propagation in a ``Pair'' Plasma
11.10 Surface Waves
11.11 Mie Resonance and a ``Plasmonic Metamaterial''
11.12 Wave Incident at Brewster's Angle
11.13 Electromagnetic Wave in a Conducting Medium
11.14 Wave Reflection at the Ionosphere
11.15 Waves in a Dipole Chain
Reference
12 Transmission Lines, Waveguides, Resonant Cavities
12.1 The Coaxial Cable
12.2 Electric Power Transmission Line
12.3 TEM and TM Modes in an ``Open'' Waveguide
12.4 Square and Triangular Waveguides
12.5 Waveguide Modes as an Interference Effect
12.6 Propagation in an Optical Fiber
12.7 Wave Propagation in a Filled Waveguide
12.8 Schumann Resonances
12.9 A One-Dimensional Cavity Fed by an Antenna (1)
12.10 A One-Dimensional Cavity Fed by an Antenna (2)
13 Further Problems
13.1 Electrically and Magnetically Polarized Cylinders
13.2 Oscillations of a Triatomic Molecule
13.3 Impedance of an Infinite Ladder Network
13.4 Discharge of a Cylindrical Capacitor
13.5 Fields Generated by Spatially Periodic Surface Sources
13.6 Energy and Momentum Flow Close to a Perfect Mirror
13.7 Laser Cooling of a Mirror
13.8 Radiation Pressure on a Thin Foil
13.9 Thomson Scattering in the Presence of a Magnetic Field
13.10 Undulator Radiation
13.11 Electromagnetic Torque on a Conducting Sphere
13.12 Surface Waves in a Thin Foil
13.13 The Fizeau Effect
13.14 Lorentz Transformations for Longitudinal Waves
13.15 Lorentz Transformations for a Transmission Cable
13.16 A Waveguide with a Moving End
13.17 A ``Relativistically'' Strong Electromagnetic Wave
13.18 Electric Current in a Solenoid
13.19 An Optomechanical Cavity
13.20 Radiation Pressure on an Absorbing Medium
13.21 Radiation and Scattering from a Linear Molecule
13.22 Radiation Drag Force
13.23 A Coaxial Cable with a Faraday Generator
13.24 Reflection and Transmission from a Moving Transparent Medium
13.25 The Electromotive Force in Two Different Frames
13.26 Electron Orbits in a Magnetic Field
13.27 A Parallel-Wire Metamaterial
13.28 Motion in an Inhomogeneous Magnetic Field
13.29 Solar Sail
13.30 Canonical Momentum
13.31 Classical Zeeman Effect
13.32 Force-Free Magnetic Field
13.33 Field Inside a Spherical Shell
13.34 Resonances in a Spherical Shell
References
Appendix S-1 Solutions for Chapter 1摥映數爠eflinkch:electrostatics11
S-1.1 Overlapping Charged Spheres
S-1.2 Charged Sphere with Internal Spherical Cavity
S-1.3 Energy of a Charged Sphere
S-1.4 Plasma Oscillations
S-1.5 Mie Oscillations
S-1.6 Coulomb Explosions
S-1.7 Plane and Cylindrical Coulomb Explosions
S-1.8 Collision of Two Charged Spheres
S-1.9 Oscillations in a Positively Charged Conducting Sphere
S-1.10 Interaction Between a Point Charge and an Electric Dipole
S-1.11 Electric Field of a Charged Hemispherical Surface
S-1.12 The Electric Field of an Array of Charged Wires (1)
S-1.13 The Electric Field of an Array of Charged Wires (2)
S-1.14 Mean Value Property and the Force on a Spherical Charge
Appendix S-2 Solutions for Chapter 2摥映數爠eflinkch:ECM22
S-2.1 Metal Sphere in an External Field
S-2.2 Electrostatic Energy with Image Charges
S-2.3 Fields Generated by Surface Charge Densities
S-2.4 A Point Charge in Front of a Conducting Sphere
S-2.5 Dipoles and Spheres
S-2.6 Coulomb's Experiment
S-2.7 A Solution Looking for a Problem
S-2.8 Electrically Connected Spheres
S-2.9 A Charge Inside a Conducting Shell
S-2.10 A Charged Wire in Front of a Cylindrical Conductor
S-2.11 Hemispherical Conducting Surfaces
S-2.12 The Force Between the Plates of a Capacitor
S-2.13 Electrostatic Pressure on a Conducting Sphere
S-2.14 Conducting Prolate Ellipsoid
S-2.15 A Non-coaxial Cylindrical Capacitor
S-2.16 Induced Charge Density on a Conducting Plane
S-2.17 Charge Density on a Metal Sphere in Front of a Point Charge
Appendix S-3 Solutions for Chapter 3摥映數爠eflinkch:EDM33
S-3.1 An Artificial Dielectric
S-3.2 Charge in Front of a Dielectric Half-Space
S-3.3 An Electrically Polarized Sphere
S-3.4 Dielectric Sphere in an External Field
S-3.5 Refraction of the Electric Field at a Dielectric Boundary
S-3.6 Contact Force Between a Conductor and a Dielectric
S-3.7 A Conducting Sphere Between Two Dielectrics
S-3.8 Measuring the Dielectric Constant of a Liquid
S-3.9 A Conducting Cylinder in a Dielectric Liquid
S-3.10 A Dielectric Slab in Contact with a Charged Conductor
S-3.11 A Transversally Polarized Cylinder
S-3.12 Force Between a Parallel-Plate Capacitor and a Dielectric Slab
S-3.13 A Cylindrical Quadrupole
Appendix S-4 Solutions for Chapter 4摥映數爠eflinkch:ElCurr44
S-4.1 The Tolman-Stewart Experiment
S-4.2 Charge Relaxation in a Conducting Sphere
S-4.3 A Coaxial Resistor
S-4.4 Electrical Resistance Between Two Submerged Spheres (1)
S-4.5 Electrical Resistance Between Two Submerged Spheres (2)
S-4.6 Effects of Non-uniform Resistivity
S-4.7 Charge Decay in a Lossy Spherical Capacitor
S-4.8 Dielectric-Barrier Discharge
S-4.9 Charge Distribution in a Long Cylindrical Conductor
S-4.10 An Infinite Resistor Ladder
Appendix S-5 Solutions for Chapter 5摥映數爠eflinkch:MagnStat55
S-5.1 The Rowland Experiment
S-5.2 Pinch Effect in a Cylindrical Wire
S-5.3 A Magnetic Dipole in Front of a Magnetic Half-Space
S-5.4 Magnetic Levitation
S-5.5 Uniformly Magnetized Cylinder
S-5.6 Charged Particle in Crossed Electric and Magnetic Fields
S-5.7 Cylindrical Conductor with an Off-Centered Cavity
S-5.8 Conducting Cylinder in a Magnetic Field
S-5.9 Rotating Cylindrical Capacitor
S-5.10 Magnetized Spheres
S-5.11 A Transversally Magnetized Cylinder
S-5.12 A Rotating Charged Spherical Shell
S-5.13 Magnetic Field of a Polygonal Loop
S-5.14 Helmholtz Coils
Appendix S-6 Solutions for Chapter 6摥映數爠eflinkch:MagnInduc66
S-6.1 A Square Wave Generator
S-6.2 A Coil Moving in an Inhomogeneous Magnetic Field
S-6.3 A Circuit with ``Free-Falling'' Parts
S-6.4 The Tethered Satellite
S-6.5 Eddy Currents in a Solenoid
S-6.6 Feynman's ``Paradox''
S-6.7 Induced Electric Currents in the Ocean
S-6.8 A Magnetized Sphere as Unipolar Motor
S-6.9 Induction Heating
S-6.10 A Magnetized Cylinder as DC Generator
S-6.11 The Faraday Disk and a Self-sustained Dynamo
S-6.12 Mutual Induction Between Circular Loops
S-6.13 Mutual Induction Between a Solenoid and an Internal Loop
S-6.14 Skin Effect and Eddy Inductance in an Ohmic Wire
S-6.15 Magnetic Pressure and Pinch Effect for a Surface Current
S-6.16 Magnetic Pressure on a Solenoid
S-6.17 A Homopolar Motor
S-6.18 A Magnetic Cylinder Sliding Inside a Solenoid
S-6.19 Conducting Cylindrical Shell in a Magnetic Field
S-6.20 Electromagnetic Inertia of a Rotating Charged Ring
S-6.21 A Bar Sliding in a Magnetic Field
S-6.22 Magnetic Levitation of a Superconducting Ring
S-6.23 Electromagnetic Brake with Energy Recovery
S-6.24 A High Frequency Capacitor
Appendix S-7 Solutions for Chapter 7摥映數爠eflinkch:oscillators77
S-7.1 Coupled RLC Oscillators (1)
S-7.2 Coupled RLC Oscillators (2)
S-7.3 Coupled RLC Oscillators (3)
S-7.4 The LC Ladder Network
S-7.5 The CL Ladder Network
S-7.6 A Non-dispersive Transmission Line
S-7.7 An ``Alternate'' LC Ladder Network
S-7.8 Resonances in an LC Ladder Network
S-7.9 Cyclotron Resonances (1)
S-7.10 Cyclotron Resonances (2)
S-7.11 A Quasi-Gaussian Wave Packet
S-7.12 A Wave Packet Traveling along a Weakly Dispersive Line
Appendix S-8 Solutions for Chapter 8摥映數爠eflinkch:MaxwCons88
S-8.1 Poynting Vector(s) in an Ohmic Wire
S-8.2 Poynting Vector(s) in a Capacitor
S-8.3 Poynting's Theorem in a Solenoid
S-8.4 Poynting Vector in a Capacitor with Moving Plates
S-8.5 Radiation Pressure on a Perfect Mirror
S-8.6 A Light Beam
S-8.7 Intensity and Angular Momentum of a Light Beam
S-8.8 Feynman's Paradox Solved
S-8.9 Magnetic Monopoles
S-8.10 An Interstellar Light Sail
S-8.11 Radiation Pressure at Oblique Incidence
S-8.12 A Square Law Detector
S-8.13 Poynting Vector for a Rotating Charged Spherical Shell
Appendix S-9 Solutions for Chapter 9摥映數爠eflinkch:relativistic99
S-9.1 The Fields of a Current-Carrying Wire
S-9.2 The Fields of a Plane Capacitor
S-9.3 The Fields of a Solenoid
S-9.4 The Four-Potential of a Plane Wave
S-9.5 The Force on a Magnetic Monopole
S-9.6 Reflection from a Moving Mirror
S-9.7 Oblique Incidence on a Moving Mirror
S-9.8 Pulse Modification by a Moving Mirror
S-9.9 Boundary Conditions on a Moving Mirror
S-9.10 Lorentz Transformations on a Coaxial Cable
S-9.11 Lorentz Transformations on a Rectangular Metal Pipe
S-9.12 Force on an Ohmic Wire
Appendix S-10 Solutions for Chapter 10摥映數爠eflinkch:radiation1010
S-10.1 Cyclotron Radiation
S-10.2 Atomic Collapse
S-10.3 Radiative Damping of the Elastically Bound Electron
S-10.4 Radiation Emitted by Orbiting Charges
S-10.5 Spin-Down Rate and Magnetic Field of a Pulsar
S-10.6 A Bent Dipole Antenna
S-10.7 A Receiving Circular Antenna
S-10.8 Polarization of Scattered Radiation
S-10.9 Polarization Effects on Thomson Scattering
S-10.10 Scattering and Interference
S-10.11 Optical Beats Generating a ``Lighthouse Effect''
S-10.12 Radiation Friction Force
S-10.13 Radiation of an Electron Falling on a Proton
S-10.14 Scattering by a Perfectly Conducting Sphere (1)
S-10.15 Scattering by a Perfectly Conducting Sphere (2)
Appendix S-11 Solutions for Chapter 11摥映數爠eflinkch:continuousmedia1111
S-11.1 Wave Propagation in a Conductor at High and Low Frequencies
S-11.2 Energy Densities in a Free Electron Gas
S-11.3 Longitudinal Waves
S-11.4 Transmission and Reflection by a Thin Conducting Foil
S-11.5 Anti-reflection Coating
S-11.6 Birefringence and Waveplates
S-11.7 Magnetic Birefringence and Faraday Effect
S-11.8 Whistler Waves
S-11.9 Wave Propagation in a ``Pair'' Plasma
S-11.10 Surface Waves
S-11.11 Mie Resonance and a ``Plasmonic Metamaterial''
S-11.12 Wave Incident at Brewster's Angle
S-11.13 Electromagnetic Wave in a Conducting Medium
S-11.14 Wave Reflection at the Ionosphere
S-11.15 Waves in a Dipole Chain
Appendix S-12 Solutions for Chapter 12摥映數爠eflinkch:lineswaveguides1212
S-12.1 The Coaxial Cable
S-12.2 Electric Power Transmission Line
S-12.3 TEM and TM Modes in an ``Open'' Waveguide
S-12.4 Square and Triangular Waveguides
S-12.5 Waveguide Modes as an Interference Effect
S-12.6 Propagation in an Optical Fiber
S-12.7 Wave Propagation in a Filled Waveguide
S-12.8 Schumann Resonances
S-12.9 A One-Dimensional Cavity Fed by an Antenna (1)
S-12.10 A One-Dimensional Cavity Fed by an Antenna (2)
Appendix S-13 Solutions for Chapter 13摥映數爠eflinkch:summary1313
S-13.1 Electrically and Magnetically Polarized Cylinders
S-13.2 Oscillations of a Triatomic Molecule
S-13.3 Impedance of an Infinite Ladder Network
S-13.4 Discharge of a Cylindrical Capacitor
S-13.5 Fields Generated by Spatially Periodic Surface Sources
S-13.6 Energy and Momentum Flow Close to a Perfect Mirror
S-13.7 Laser Cooling of a Mirror
S-13.8 Radiation Pressure on a Thin Foil
S-13.9 Thomson Scattering in the Presence of a Magnetic Field
S-13.10 Undulator Radiation
S-13.11 Electromagnetic Torque on a Conducting Sphere
S-13.12 Surface Waves in a Thin Foil
S-13.13 The Fizeau Effect
S-13.14 Lorentz Transformations for Longitudinal Waves
S-13.15 Lorentz Transformations for a Transmission Cable
S-13.16 A Waveguide with a Moving End
S-13.17 A ``Relativistically'' Strong Electromagnetic Wave
S-13.18 Electric Current in a Solenoid
S-13.19 An Optomechanical Cavity
S-13.20 Radiation Pressure on an Absorbing Medium
S-13.21 Radiation and Scattering from a Linear Molecule
S-13.22 Radiation Drag Force
S-13.23 A Coaxial Cable with a Faraday Generator
S-13.24 Reflection and Transmission from a Moving Transparent Medium
S-13.25 The Electromotive Force in Two Different Frames
S-13.26 Electron Orbits in a Magnetic Field
S-13.27 A Parallel-Wire Metamaterial
S-13.28 Motion in an Inhomogeneous Magnetic field
S-13.29 Solar Sail
S-13.30 Canonical Momentum
S-13.31 Classical Zeeman Effect
S-13.32 Force-Free Magnetic Field
S-13.33 Field Inside a Spherical Shell
S-13.34 Resonances in a Spherical Shell
Appendix A Mathematical Appendix
A.1 Gradient, Curl, Divergence and Laplacian
A.2 Vector Identities
A.3 Hyperbolic Functions
Index