Problems and Puzzles in Electric Fields

Preface
Acknowledgements
Contents
1 Introduction
	1.1 Purpose of This Book
	1.2 Composition of the Book
2 Notes
	2.1 Electrostatic and Quasi-electrostatic Fields
	2.2 Other Notes
3 Questions and Answers
	3.1 Basic Concepts in Electric Fields
		Subject A: Basics of Electric Fields
			Question A1: Simple Solution for Two-Dimensional Fields?
			Question A2: Superposition of Electric Fields
			Question A3: Magnitude of the Image Charge
			Question A4: Application of the Neumann Boundary Condition
			Answer A1
				Comment
			Answer A2
				Detailed Explanation
			Answer A3
			Answer A4
				Detailed Explanation
		Subject B: Lines of Electric Force and Electrostatic Capacitance
			Question B1: Lines of Electric Force on Rotation Axis in an Axisymmetric Configuration
			Question B2: Two Conductors at Different Potentials
			Question B3: Two Conductors at the Same Potential
			Question B4: Capacitance of an Isolated Conductor
			Question B5: Mutual Capacitance Between Two Conductors
			Answer B1
			Answer B2
				Detailed Explanation: Role of Electrostatic Capacitances
			Answer B3
				Detailed Explanation
			Answer B4
				Comment
				Application
			Answer B5
				Detailed Explanation
	3.2 Mono-dielectric Fields
		Subject C: Spherical Conductors
			Question C1: Maximum Electric Field in Two Configurations
			Question C2: Maximum Electric Field in Three Configurations
			Question C3: Sphere-to-Ground Versus Sphere-to-Sphere Configuration
			Answer C1
				Detailed Explanation
				Comment
				Application 1: Sphere Gap
				Application 2: Utilization Factor
			Answer C2
				Detailed Explanation
				Comment
				Application 1: Breakdown (Sparkover) Voltage of a Non-uniform Gap in Air
				Application 2: Optimal Shape Design
				Application 3: Designing Discharge Gaps
			Answer C3
				Detailed Explanation
		Subject D: Electric Field at a Conductor Wedge Tip
			Question D1: Electric Field at a Sharp Conductor Wedge Tip
			Question D2: Zero Field at a Conductor Wedge Tip
			Question D3: Infinitely High Field at a Conductor Pit
			Answer D1
			Answer D2
				Detailed Explanation: Numerical Field Calculation
				Comment 1
				Comment 2
			Answer D3
				Detailed Explanation
		Subject E: Electric Field for a Conducting Needle or a Foil on a Grounded Plane
			Question E1: Needle on a Grounded Plane Under a Uniform Field
			Question E2: Thin Foil Standing on a Grounded Plane Under a Uniform Field
			Answer E1
				Detailed Explanation
				Application
			Answer E2
				Detailed Explanation
		Subject F: Electrode Configurations and Electric Fields
			Question F1: Electric Field Decreasing Radially on a Plane
			Question F2: Uniform Field-Forming Electrodes 1: Square Electrodes
			Question F3: Uniform Field-Forming Electrodes 2: Why Is the Borda Profile Not Utilized in Practice?
			Answer F1
				Detailed Explanation
				Application
			Answer F2
				Detailed Explanation
				Application
			Answer F3
				Comment: Borda profile
	3.3 Electric Charge, Space Charge, and Drifting Charge
		Subject G: Charges and Electric Fields
			Question G1: Electric Field on a Single Sheet of Charge
			Question G2: Electric Field on a Conductor Surface
			Question G3: Laplace’s Equation and Poisson’s Equation
			Answer G1
			Answer G2
			Answer G3
				Detailed Explanation
				Application: Space Charge in Atmospheric Air
		Subject H: Electric Current Caused by Drifting Charge
			Question H1: Ion Current in a Uniform Field
			Question H2: Ion Current in a Non-uniform Field
			Question H3: Current Based on the Energy Balance
			Answer H1
				Detailed Explanation
				Application: Current Caused by the Continuous Flow of Ion Pairs
			Answer H2
				Detailed Explanation
			Answer H3
				Comment
	3.4 Composite Dielectrics
		Subject I: Polarization Charge and Accumulated Charge on a Dielectric Surface
			Question I1: What Is Polarization Charge?
			Question I2: The λ Function in Probe Measurement
			Question I3: Solid Supporting Dielectric 1
			Question I4: Solid Supporting Dielectric 2
			Answer I1
				Detailed Explanation
				Comment
				Application: Field Calculation Including a Floating Conductor (Ref. I1-1)
			Answer I2
				Comment
			Answer I3
			Answer I4
				Comment: Floating Conductor
				Application: Field Strength Meter
		Subject J: Triple-Junction Effect
			Question J1: Triple Junction 1: Finite Contact Angle (Takagi Effect)
			Question J2: Sharp Wedge-Shaped Tip of a Solid Dielectric
			Question J3: Sharp Dielectric Pit
			Question J4: Triple-Junction Effect 2: Zero Contact Angle
			Answer J1
				Detailed Explanation
				Comment: The Takagi Effect
				Application: Significance of the Takagi Effect
			Answer J2
				Comment: Cone-Shaped Interface of a Solid Dielectric
			Answer J3
				Detailed Explanation
				Application: Electric Field When the Dielectric Constant of a Solid is Sufficiently High
			Answer J4
				Detailed Explanation
				Comment 1: Analysis Using the Variable Separation Method
				Comment 2: Application of an Equivalent Circuit
				Application 1: Solid Dielectric Supports
				Application 2: Electrorheological Fluid
		Subject K: Electric Fields Including Conduction
			Question K1: Ohmic Conduction and Ion Flow
			Question K2: What Is Surface Conduction?
			Question K3: Proposal for Field Calculations Including Surface Conduction
			Question K4: Comparison of Electric Fields for DC and AC Applications
			Question K5: Electric Fields with and Without Conduction
			Answer K1
				Detailed Explanation
				Application: Calculation of Ion Flow Fields
			Answer K2
				Detailed Explanation
				Comment: Infinitely High Conductivity
			Answer K3
			Answer K4
				Detailed Explanation
			Answer K5
				Comment
	3.5 Other Topics
		Subject L: Electric Force
			Question L1: Force on a Charge in an Electric Field
			Question L2: Significant Force Caused by Balanced Forces?
			Question L3: Electric Field and Force on a Charged Spherical Dielectric Shell
			Question L4: Holding a Charge with Electrostatic Force 1: Surrounding Point or Line Charges
			Question L5: Holding a Charge with Electrostatic Force 2: A Cage with Uniform Surface Charge
			Answer L1
				Detailed Explanation: Example of an Induced Field
				Application 1: Effect of Induced Charge in Gas Discharge
				Application 2: Floating Force
			Answer L2
				Detailed Explanation
				Comment: Charge and Potential of a Spherical Conductor
			Answer L3
			Answer L4
			Answer L5
				Detailed Explanation
				Comment: Problem Setting in the Journal of the Institute of Electrical Engineers of Japan
		Subject M: Induction on the Human Body
			Question M1: Shaking Hands Under Atmospheric Electricity
			Question M2: Induction on a Falling Body
			Question M3: Induction from a Power-Frequency High-Voltage Source
			Question M4: Induction from a High-Voltage DC Source
			Question M5: Boundary Conditions for Calculating Induced Current
			Answer M1
				Comment
			Answer M2
				Comment
			Answer M3
				Detailed Explanation
				Application 1: Calculation of Induced Current Inside a Human Body
				Application 2: Induction by an AC Transmission Line
			Answer M4
				Application: Current Induced by the Magnetic Field of a DC Transmission Line
			Answer M5
				Detailed Explanation
4 Three Simple Questions Not Related to Electric Fields
5 Fundamentals of Electrostatic and Quasi-electrostatic Fields
	5.1 Governing Equations
	5.2 Uniqueness Theorem in Electrostatic Fields
	5.3 Boundary Conditions for Composite Dielectric Fields
	5.4 Basic Equations for Capacitive–Resistive 	(Mixed) Fields
	5.5 Boundary Conditions for Mixed Fields
	5.6 Summary of Equations in Mixed Fields
6 Supplementary Explanations
	6.1 Image Charge Method (in Answer A3)
	6.2 Critical Comment on Answer C2
	6.3 Variable Separation Method Applied to Question D1
	6.4 Field Behavior Near a Sharp Conical Tip (in Sect. 6.3)
	6.5 Ellipsoidal Coordinates Applied to Question E1
	6.6 Ellipsoidal Coordinates Applied to Question E2
	6.7 Electric Field for a Semi-infinite Plane Electrode Above a Grounded Plane (in Answer F2)
	6.8 Relationship Between the Surface Shape of an Electrode and the Electric Field (in Answer F3)
	6.9 Comparison of Electric Fields Between Two-Dimensional and Axisymmetric Configurations (in Answer F3)
	6.10 Axisymmetric Uniform Field-Forming Electrodes in Practice (in Answer F3)
	6.11 Application of Gauss’s Theorem (in Answer G1)
	6.12 Electric Field in a Uniform Ion Flow Field (in Answer G3)
	6.13 Estimation of Threshold Space Charge in a Non-uniform Field Condition (in Answer G3)
	6.14 Green’s Reciprocity Theorem (in Answers H1, H3 and I2)
	6.15 Ion Current in Concentric-Sphere Configuration (in Answer H2)
	6.16 Electrostatic Capacitances in Fig. I2-1
	6.17 Refraction Law for a Line of Electric Force (in Answer J1)
	6.18 Analysis of the Field in Fig. J1-1 by the Variable Separation Method
	6.19 Contact of Three Dielectrics with Straight Interfaces (in Answer J1)
	6.20 Analysis of the Configuration in Fig. J2-1 Using the Variable Separation Method
	6.21 Analysis of the Field for a Cone-Shaped Dielectric Interface (in Answer J2)
	6.22 Analysis of the Axisymmetric Configuration in Question J4 Using the Successive Image Charge Method
	6.23 Analysis of the Two-Dimensional Case in Question J4 Using the Successive Image Charge Method
	6.24 Contact-Point Electric Fields (in Answer J4)
	6.25 Hemispherical Solid Dielectric on a Grounded Plane Under a Uniform Field (in Answers K5 and M5)
	6.26 Examples of Induced Charge and Floating Force (in Answer L1)
	6.27 Induced Charge and Floating Force for a Hemispherical Conductor on a Grounded Plane (in Sect. 6.26)
	6.28 Force on a Charged Spherical Shell Above a Grounded Plane (in Answer L3)
	6.29 Force or Electric Field Exerted on a Charged Particle in the Two Configurations Shown in Fig. L4-1
References
Index