Electric Field Analysis: 1st Edition (Hardback) book cover

Electric Field Analysis

1st Edition

By Sivaji Chakravorti

CRC Press

568 pages | 261 B/W Illus.

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Hardback: 9781482233360
pub: 2015-03-16
eBook (VitalSource) : 9781315215273
pub: 2017-12-19
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Electric Field Analysis is both a student-friendly textbook and a valuable tool for engineers and physicists engaged in the design work of high-voltage insulation systems. The text begins by introducing the physical and mathematical fundamentals of electric fields, presenting problems from power and dielectric engineering to show how the theories are put into practice. The book then describes various techniques for electric field analysis and their significance in the validation of numerically computed results, as well as:

  • Discusses finite difference, finite element, charge simulation, and surface charge simulation methods for the numerical computation of electric fields
  • Provides case studies for electric field distribution in a cable termination, around a post insulator, in a condenser bushing, and around a gas-insulated substation (GIS) spacer
  • Explores numerical field calculation for electric field optimization, demonstrating contour correction and examining the application of artificial neural networks
  • Explains how high-voltage field optimization studies are carried out to meet the desired engineering needs

Electric Field Analysis is accompanied by an easy-to-use yet comprehensive software for electric field computation. The software, along with a wealth of supporting content, is available for download with qualifying course adoption.


"… very useful to teachers and students in classes on applications of the theory, numerical analyses, and practice of using the electric field for practical electric power applications that benefit mankind, such as avoiding electrical breakdown in high-voltage systems. … The book begins at the senior undergraduate level in developing the fundamentals of electric field physics and applications, … [and] then continues on to advanced numerical methods valuable to graduate students and practitioners."

—Markus Zahn, Massachusetts Institute of Technology, Cambridge, USA

"… gives clear and precise description of the state of the art in electric field analysis. … the book comes along with software for the computation of capacitive as well as capacitive-resistive electric fields."

Prof. Dr.-Ing. Josef Kindersberger, Technische Universität München, Institute for High Voltage Engineering and Switchgear Technology

"A unique book for understanding electric fields and its computation with particular emphasis to problems and configurations typically encountered by high voltage engineers while designing and building power apparatus and electric insulation systems. The coverage is comprehensive, up to date, and spans the entire spectrum thus making it an ideal book for both undergraduate and graduate students."

—Professor L. Satish, HV Lab, Dept of Electrical Engineering, Indian Institute of Science, Bangalore

"This is a very intriguing book, because it adds a great deal of practical insight into otherwise cold and lifeless equations and theory. It was a pleasure to review it and enjoy many of the applied examples using the theory presented in the first part of the book."

IEEE Electrical Insulation Magazine, May/June 2016

Table of Contents

Fundamentals of Electric Field


Electric Charge

Electric Fieldlines

Coulomb’s Law

Electric Field Intensity

Electric Flux and Electric Flux Density

Electric Potential

Field due to Point Charge

Field due to a Uniformly Charged Line

Field due to a Uniformly Charged Ring

Field due to a Uniformly Charged Disc

Objective Type Questions


Gauss’s Law and Related Topics


Useful Definitions and Integrals

Integral Form of Gauss’s Law

Differential Form of Gauss’s Law

Divergence Theorem

Poisson’s and Laplace’s Equations

Field due to a Continuous Distribution of Charge

Steps to Solve Problems Using Gauss’s Law

Objective Type Questions

Orthogonal Coordinate Systems

Basic Concepts

Cartesian Coordinate System

Cylindrical Coordinate System

Spherical Coordinate System

Generalized Orthogonal Curvilinear Coordinate System

Vector Operations

Objective Type Questions

Single-Dielectric Configurations


Displacement Current

Parallel Plate Capacitor

Energy Stored in Electric Field

Two Concentric Spheres with Homogeneous Dielectric

Two Co-Axial Cylinders with Homogeneous Dielectric

Field Factor

Objective Type Questions

Dielectric Polarization


Field due to an Electric Dipole and Polarization Vector


Field due to a Polarized Dielectric

Electric Displacement Vector

Classification of Dielectrics

Frequency Dependence of Polarizabilities

Mass-Spring Model of Fields in Dielectrics

Dielectric Anisotropy

Objective Type Questions

Electrostatic Boundary Conditions


Boundary Conditions between a Perfect Conductor and a Dielectric

Boundary Conditions between Two Different Dielectric Media

Objective Type Questions

Multi-Dielectric Configurations


Parallel Plate Capacitor

Co-Axial Cylindrical Configurations

Objective Type Questions

Electrostatic Pressures on Boundary Surfaces


Mechanical Pressure on a Conductor-Dielectric Boundary

Mechanical Pressure on a Dielectric-Dielectric Boundary

Two Dielectric Media in Series between a Parallel Plate Capacitor

Two Dielectric Media in Parallel between a Parallel Plate Capacitor

Objective Type Questions

Method of Images


Image of a Point Charge with Respect to an Infinitely Long Conducting Plane

Image of a Point Charge with Respect to a Grounded Conducting Sphere

Image of an Infinitely Long Line Charge with Respect to an Infinitely Long Conducting Plane

Two Infinitely Long Parallel Cylinders

Salient Features of Method of Images

Objective Type Questions

Sphere or Cylinder in Uniform External Field


Sphere in Uniform External Field

Cylinder in Uniform External Field

Objective Type Questions

Conformal Mapping


Basic Theory of Conformal Mapping

Concept of Complex Potential

Procedural Steps in Solving Problems Using Conformal Mapping

Applications of Conformal Mapping in Electrostatic Potential Problems

Objective Type Questions

Graphical Field Plotting


Experimental Field Mapping

Field Mapping Using Curvilinear Squares

Field Mapping in Multi-Dielectric Media

Field Mapping in Axi-Symmetric Configuration

Objective Type Questions


Numerical Computation of Electric Field


Methods of Determination of Electric Field Distribution

Uniqueness Theorem

Procedural Steps in Numerical Electric Field Computation

Objective Type Questions

Numerical Computation of High-Voltage Field by Finite Difference Method


FDM Equations in 3D System for Single-Dielectric Medium

FDM Equations in Axi-Symmetric System for Single-Dielectric Medium

FDM Equations in 3D System for Multi-Dielectric Media

FDM Equations in Axi-Symmetric System for Multi-Dielectric Media

Simulation Details

FDM Examples

Objective Type Questions


Numerical Computation of High-Voltage Field by Finite Element Method


Basics of FEM

Procedural Steps in FEM

Variational Approach towards FEM Formulation

Features of Discretization in FEM

Solution of System of Equations in FEM

Advantages of FEM

FEM Examples

Objective Type Questions


Numerical Computation of High-Voltage Field by Charge Simulation Method


CSM Formulation for Single-Dielectric Medium

CSM Formulation for Multi-Dielectric Media

Types of Fictitious Charges

CSM with Complex Fictitious Charges

Capacitive-Resistive Field Computation by CSM

Field Computation by CSM under Transient Voltage

Accuracy Criteria

Other Development in CSM

Comparison of CSM with FEM

Hybrid Method Involving CSM and FEM

CSM Examples

Objective Type Questions


Numerical Computation of High-Voltage Field by Surface Charge Simulation Method


SCSM Formulation for Single-Dielectric Medium

Surface Charge Elements in 2D and Axi-Symmetric Configurations

SCSM Formulation for Multi-Dielectric Media

SCSM Formulation in 3D System

Capacitive-Resistive Field Computation by SCSM

SCSM Examples

Objective Type Questions


Numerical Computation of Electric Field in High-Voltage System - Case Studies


Benchmark Models for Validation

Electric Field Distribution in the Cable Termination

Electric Field Distribution around a Post-Type Insulator

Electric Field Distribution in a Condenser Bushing

Electric Field Distribution around a Gas-Insulated Substation Spacer

Objective Type Questions


Electric Field Optimization


Review of Published Works

Field Optimization Using Contour Correction Techniques

ANN-Based Optimization of Electrode and Insulator Contours

ANN-Aided Optimization of 3D Electrode-Insulator Assembly

Objective Type Questions


About the Author

Sivaji Chakravorti holds bachelor’s, master’s, and Ph.D degrees from Jadavpur University, Kolkata, India. Dr. Chakravorti has nearly 30 years of teaching experience and is currently a full professor in electrical engineering at Jadavpur University, where he teaches electric field analysis at the undergraduate and postgraduate levels. Previously, he worked in various capacities at the Indian Institute of Science, Bangalore; Technical University of Munich, Germany; Siemens AG, Berlin, Germany; ABB Corporate Research, Ladenburg, Germany; Advanced Research Institute of Virginia Tech, Alexandria, USA; and Technical University Hamburg-Harburg, Germany. Dr. Chakravorti is highly decorated, widely published, and an active member of IEEE.

Subject Categories

BISAC Subject Codes/Headings:
TECHNOLOGY & ENGINEERING / Power Resources / Electrical