ALL 13 CHAPTERS COVERED
,Contents
1 Basics of Electrostatics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 Overlapping Charged Spheres . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.2 Charged Sphere with Internal Spherical Cavity . . . . . . . . . . . . . . 4
1.3 Energy of a Charged Sphere . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.4 Plasma Oscillations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.5 Mie Oscillations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.6 Coulomb Explosions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.7 Plane and Cylindrical Coulomb Explosions . . . . . . . . . . . . . . . . . 6
1.8 Collision of Two Charged Spheres . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.9 Oscillations in a Positively Charged Conducting Sphere . . . . . . . 7
1.10 Interaction Between a Point Charge and an Electric Dipole . . . . 7
1.11 Electric Field of a Charged Hemispherical Surface . . . . . . . . . . . 8
1.12 The Electric Field of an Array of Charged Wires (1) . . . . . . . . . . 8
1.13 The Electric Field of an Array of Charged Wires (2) . . . . . . . . . . 8
1.14 Mean Value Property and the Force on a Spherical Charge . . . . 9
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2 Electrostatics of Conductors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.1 Metal Sphere in an External Field . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.2 Electrostatic Energy with Image Charges . . . . . . . . . . . . . . . . . . . 12
2.3 Fields Generated by Surface Charge Densities . . . . . . . . . . . . . . . 12
2.4 A Point Charge in Front of a Conducting Sphere . . . . . . . . . . . . . 13
2.5 Dipoles and Spheres . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.6 Coulomb’s Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.7 A Solution Looking for a Problem . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.8 Electrically Connected Spheres . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.9 A Charge Inside a Conducting Shell . . . . . . . . . . . . . . . . . . . . . . . 15
2.10 A Charged Wire in Front of a Cylindrical Conductor . . . . . . . . . 16
2.11 Hemispherical Conducting Surfaces . . . . . . . . . . . . . . . . . . . . . . . 16
2.12 The Force Between the Plates of a Capacitor . . . . . . . . . . . . . . . . 17
2.13 Electrostatic Pressure on a Conducting Sphere . . . . . . . . . . . . . . . 17
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2.14 Conducting Prolate Ellipsoid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.15 A Non-coaxial Cylindrical Capacitor . . . . . . . . . . . . . . . . . . . . . . . 18
2.16 Induced Charge Density on a Conducting Plane . . . . . . . . . . . . . . 18
2.17 Charge Density on a Metal Sphere in Front of a Point
Charge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
3 Electrostatics of Dielectric Media . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
3.1 An Artificial Dielectric . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
3.2 Charge in Front of a Dielectric Half-Space . . . . . . . . . . . . . . . . . . 23
3.3 An Electrically Polarized Sphere . . . . . . . . . . . . . . . . . . . . . . . . . . 23
3.4 Dielectric Sphere in an External Field . . . . . . . . . . . . . . . . . . . . . . 24
3.5 Refraction of the Electric Field at a Dielectric Boundary . . . . . . 24
3.6 Contact Force Between a Conductor and a Dielectric . . . . . . . . . 25
3.7 A Conducting Sphere Between Two Dielectrics . . . . . . . . . . . . . . 25
3.8 Measuring the Dielectric Constant of a Liquid . . . . . . . . . . . . . . . 26
3.9 A Conducting Cylinder in a Dielectric Liquid . . . . . . . . . . . . . . . 26
3.10 A Dielectric Slab in Contact with a Charged Conductor . . . . . . . 27
3.11 A Transversally Polarized Cylinder . . . . . . . . . . . . . . . . . . . . . . . . 27
3.12 Force Between a Parallel-Plate Capacitor and a Dielectric
Slab . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
3.13 A Cylindrical Quadrupole . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
Reference . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
4 Electric Currents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
4.1 The Tolman-Stewart Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . 31
4.2 Charge Relaxation in a Conducting Sphere . . . . . . . . . . . . . . . . . . 31
4.3 A Coaxial Resistor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
4.4 Electrical Resistance Between Two Submerged
Spheres (1) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
4.5 Electrical Resistance Between Two Submerged
Spheres (2) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
4.6 Effects of Non-uniform Resistivity . . . . . . . . . . . . . . . . . . . . . . . . . 33
4.7 Charge Decay in a Lossy Spherical Capacitor . . . . . . . . . . . . . . . 33
4.8 Dielectric-Barrier Discharge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
4.9 Charge Distribution in a Long Cylindrical Conductor . . . . . . . . . 34
4.10 An Infinite Resistor Ladder . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
5 Magnetostatics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
5.1 The Rowland Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
5.2 Pinch Effect in a Cylindrical Wire . . . . . . . . . . . . . . . . . . . . . . . . . 41
5.3 A Magnetic Dipole in Front of a Magnetic Half-Space . . . . . . . . 42
5.4 Magnetic Levitation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
5.5 Uniformly Magnetized Cylinder . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
5.6 Charged Particle in Crossed Electric and Magnetic Fields . . . . . 43
5.7 Cylindrical Conductor with an Off-Centered Cavity . . . . . . . . . . 43
, Contents xiii
5.8 Conducting Cylinder in a Magnetic Field . . . . . . . . . . . . . . . . . . . 44
5.9 Rotating Cylindrical Capacitor . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
5.10 Magnetized Spheres . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
5.11 A Transversally Magnetized Cylinder . . . . . . . . . . . . . . . . . . . . . . 45
5.12 A Rotating Charged Spherical Shell . . . . . . . . . . . . . . . . . . . . . . . . 45
5.13 Magnetic Field of a Polygonal Loop . . . . . . . . . . . . . . . . . . . . . . . 45
5.14 Helmholtz Coils . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
6 Magnetic Induction and Time-Varying Fields . . . . . . . . . . . . . . . . . . . . 47
6.1 A Square Wave Generator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
6.2 A Coil Moving in an Inhomogeneous Magnetic Field . . . . . . . . . 48
6.3 A Circuit with “Free-Falling” Parts . . . . . . . . . . . . . . . . . . . . . . . . 49
6.4 The Tethered Satellite . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
6.5 Eddy Currents in a Solenoid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
6.6 Feynman’s “Paradox” . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
6.7 Induced Electric Currents in the Ocean . . . . . . . . . . . . . . . . . . . . . 51
6.8 A Magnetized Sphere as Unipolar Motor . . . . . . . . . . . . . . . . . . . 52
6.9 Induction Heating . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
6.10 A Magnetized Cylinder as DC Generator . . . . . . . . . . . . . . . . . . . 53
6.11 The Faraday Disk and a Self-Sustained Dynamo . . . . . . . . . . . . . 53
6.12 Mutual Induction Between Circular Loops . . . . . . . . . . . . . . . . . . 54
6.13 Mutual Induction Between a Solenoid and an Internal Loop . . . 55
6.14 Skin Effect and Eddy Inductance in an Ohmic Wire . . . . . . . . . . 55
6.15 Magnetic Pressure and Pinch Effect for a Surface Current . . . . . 56
6.16 Magnetic Pressure on a Solenoid . . . . . . . . . . . . . . . . . . . . . . . . . . 56
6.17 A Homopolar Motor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
6.18 A Magnetic Cylinder Sliding inside a Solenoid . . . . . . . . . . . . . . 57
6.19 Conducting Cylindrical Shell in a Magnetic Field . . . . . . . . . . . . 58
6.20 Electromagnetic Inertia of a Rotating Charged Ring . . . . . . . . . . 58
6.21 A Bar Sliding in a Magnetic Field . . . . . . . . . . . . . . . . . . . . . . . . . 59
6.22 Magnetic Levitation of a Superconducting Ring . . . . . . . . . . . . . 59
6.23 Electromagnetic Brake with Energy Recovery . . . . . . . . . . . . . . . 60
6.24 A High Frequency Capacitor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
7 Electromagnetic Oscillators and Wave Propagation . . . . . . . . . . . . . . . 63
7.1 Coupled R LC Oscillators (1) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
7.2 Coupled R LC Oscillators (2) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
7.3 Coupled R LC Oscillators (3) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
7.4 The LC Ladder Network . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
7.5 The C L Ladder Network . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
7.6 Non-dispersive Transmission Line . . . . . . . . . . . . . . . . . . . . . . . . . 66
7.7 An “Alternate” LC Ladder Network . . . . . . . . . . . . . . . . . . . . . . . 67
7.8 Resonances in an LC Ladder Network . . . . . . . . . . . . . . . . . . . . . 67
7.9 Cyclotron Resonances (1) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
7.10 Cyclotron Resonances (2) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
,Contents
1 Basics of Electrostatics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 Overlapping Charged Spheres . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.2 Charged Sphere with Internal Spherical Cavity . . . . . . . . . . . . . . 4
1.3 Energy of a Charged Sphere . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.4 Plasma Oscillations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.5 Mie Oscillations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.6 Coulomb Explosions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.7 Plane and Cylindrical Coulomb Explosions . . . . . . . . . . . . . . . . . 6
1.8 Collision of Two Charged Spheres . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.9 Oscillations in a Positively Charged Conducting Sphere . . . . . . . 7
1.10 Interaction Between a Point Charge and an Electric Dipole . . . . 7
1.11 Electric Field of a Charged Hemispherical Surface . . . . . . . . . . . 8
1.12 The Electric Field of an Array of Charged Wires (1) . . . . . . . . . . 8
1.13 The Electric Field of an Array of Charged Wires (2) . . . . . . . . . . 8
1.14 Mean Value Property and the Force on a Spherical Charge . . . . 9
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2 Electrostatics of Conductors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.1 Metal Sphere in an External Field . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.2 Electrostatic Energy with Image Charges . . . . . . . . . . . . . . . . . . . 12
2.3 Fields Generated by Surface Charge Densities . . . . . . . . . . . . . . . 12
2.4 A Point Charge in Front of a Conducting Sphere . . . . . . . . . . . . . 13
2.5 Dipoles and Spheres . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.6 Coulomb’s Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.7 A Solution Looking for a Problem . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.8 Electrically Connected Spheres . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.9 A Charge Inside a Conducting Shell . . . . . . . . . . . . . . . . . . . . . . . 15
2.10 A Charged Wire in Front of a Cylindrical Conductor . . . . . . . . . 16
2.11 Hemispherical Conducting Surfaces . . . . . . . . . . . . . . . . . . . . . . . 16
2.12 The Force Between the Plates of a Capacitor . . . . . . . . . . . . . . . . 17
2.13 Electrostatic Pressure on a Conducting Sphere . . . . . . . . . . . . . . . 17
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2.14 Conducting Prolate Ellipsoid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.15 A Non-coaxial Cylindrical Capacitor . . . . . . . . . . . . . . . . . . . . . . . 18
2.16 Induced Charge Density on a Conducting Plane . . . . . . . . . . . . . . 18
2.17 Charge Density on a Metal Sphere in Front of a Point
Charge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
3 Electrostatics of Dielectric Media . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
3.1 An Artificial Dielectric . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
3.2 Charge in Front of a Dielectric Half-Space . . . . . . . . . . . . . . . . . . 23
3.3 An Electrically Polarized Sphere . . . . . . . . . . . . . . . . . . . . . . . . . . 23
3.4 Dielectric Sphere in an External Field . . . . . . . . . . . . . . . . . . . . . . 24
3.5 Refraction of the Electric Field at a Dielectric Boundary . . . . . . 24
3.6 Contact Force Between a Conductor and a Dielectric . . . . . . . . . 25
3.7 A Conducting Sphere Between Two Dielectrics . . . . . . . . . . . . . . 25
3.8 Measuring the Dielectric Constant of a Liquid . . . . . . . . . . . . . . . 26
3.9 A Conducting Cylinder in a Dielectric Liquid . . . . . . . . . . . . . . . 26
3.10 A Dielectric Slab in Contact with a Charged Conductor . . . . . . . 27
3.11 A Transversally Polarized Cylinder . . . . . . . . . . . . . . . . . . . . . . . . 27
3.12 Force Between a Parallel-Plate Capacitor and a Dielectric
Slab . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
3.13 A Cylindrical Quadrupole . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
Reference . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
4 Electric Currents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
4.1 The Tolman-Stewart Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . 31
4.2 Charge Relaxation in a Conducting Sphere . . . . . . . . . . . . . . . . . . 31
4.3 A Coaxial Resistor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
4.4 Electrical Resistance Between Two Submerged
Spheres (1) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
4.5 Electrical Resistance Between Two Submerged
Spheres (2) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
4.6 Effects of Non-uniform Resistivity . . . . . . . . . . . . . . . . . . . . . . . . . 33
4.7 Charge Decay in a Lossy Spherical Capacitor . . . . . . . . . . . . . . . 33
4.8 Dielectric-Barrier Discharge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
4.9 Charge Distribution in a Long Cylindrical Conductor . . . . . . . . . 34
4.10 An Infinite Resistor Ladder . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
5 Magnetostatics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
5.1 The Rowland Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
5.2 Pinch Effect in a Cylindrical Wire . . . . . . . . . . . . . . . . . . . . . . . . . 41
5.3 A Magnetic Dipole in Front of a Magnetic Half-Space . . . . . . . . 42
5.4 Magnetic Levitation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
5.5 Uniformly Magnetized Cylinder . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
5.6 Charged Particle in Crossed Electric and Magnetic Fields . . . . . 43
5.7 Cylindrical Conductor with an Off-Centered Cavity . . . . . . . . . . 43
, Contents xiii
5.8 Conducting Cylinder in a Magnetic Field . . . . . . . . . . . . . . . . . . . 44
5.9 Rotating Cylindrical Capacitor . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
5.10 Magnetized Spheres . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
5.11 A Transversally Magnetized Cylinder . . . . . . . . . . . . . . . . . . . . . . 45
5.12 A Rotating Charged Spherical Shell . . . . . . . . . . . . . . . . . . . . . . . . 45
5.13 Magnetic Field of a Polygonal Loop . . . . . . . . . . . . . . . . . . . . . . . 45
5.14 Helmholtz Coils . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
6 Magnetic Induction and Time-Varying Fields . . . . . . . . . . . . . . . . . . . . 47
6.1 A Square Wave Generator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
6.2 A Coil Moving in an Inhomogeneous Magnetic Field . . . . . . . . . 48
6.3 A Circuit with “Free-Falling” Parts . . . . . . . . . . . . . . . . . . . . . . . . 49
6.4 The Tethered Satellite . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
6.5 Eddy Currents in a Solenoid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
6.6 Feynman’s “Paradox” . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
6.7 Induced Electric Currents in the Ocean . . . . . . . . . . . . . . . . . . . . . 51
6.8 A Magnetized Sphere as Unipolar Motor . . . . . . . . . . . . . . . . . . . 52
6.9 Induction Heating . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
6.10 A Magnetized Cylinder as DC Generator . . . . . . . . . . . . . . . . . . . 53
6.11 The Faraday Disk and a Self-Sustained Dynamo . . . . . . . . . . . . . 53
6.12 Mutual Induction Between Circular Loops . . . . . . . . . . . . . . . . . . 54
6.13 Mutual Induction Between a Solenoid and an Internal Loop . . . 55
6.14 Skin Effect and Eddy Inductance in an Ohmic Wire . . . . . . . . . . 55
6.15 Magnetic Pressure and Pinch Effect for a Surface Current . . . . . 56
6.16 Magnetic Pressure on a Solenoid . . . . . . . . . . . . . . . . . . . . . . . . . . 56
6.17 A Homopolar Motor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
6.18 A Magnetic Cylinder Sliding inside a Solenoid . . . . . . . . . . . . . . 57
6.19 Conducting Cylindrical Shell in a Magnetic Field . . . . . . . . . . . . 58
6.20 Electromagnetic Inertia of a Rotating Charged Ring . . . . . . . . . . 58
6.21 A Bar Sliding in a Magnetic Field . . . . . . . . . . . . . . . . . . . . . . . . . 59
6.22 Magnetic Levitation of a Superconducting Ring . . . . . . . . . . . . . 59
6.23 Electromagnetic Brake with Energy Recovery . . . . . . . . . . . . . . . 60
6.24 A High Frequency Capacitor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
7 Electromagnetic Oscillators and Wave Propagation . . . . . . . . . . . . . . . 63
7.1 Coupled R LC Oscillators (1) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
7.2 Coupled R LC Oscillators (2) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
7.3 Coupled R LC Oscillators (3) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
7.4 The LC Ladder Network . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
7.5 The C L Ladder Network . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
7.6 Non-dispersive Transmission Line . . . . . . . . . . . . . . . . . . . . . . . . . 66
7.7 An “Alternate” LC Ladder Network . . . . . . . . . . . . . . . . . . . . . . . 67
7.8 Resonances in an LC Ladder Network . . . . . . . . . . . . . . . . . . . . . 67
7.9 Cyclotron Resonances (1) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
7.10 Cyclotron Resonances (2) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
