ELECTROMAGNETISM. Volume 2. Applications Magnetic Diffusion and Electromagnetic Waves ASHUTOSH PRAMANIK

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2 ELECTROMAGNETISM Volume 2 Applications Magnetic Diffusion and Electromagnetic Waves ASHUTOSH PRAMANIK Professor Emeritus, College of Engineering, Pune Formerly of Corporate Research and Development Division, BHEL (Senior Dy. General Manager) and The Universities of Birmingham and Leeds (Research Engineer and Lecturer) and D.J. Gandhi Distinguished Visiting Professor, IIT Bombay Delhi

3 ELECTROMAGNETISM VOLUME 2 (APPLICATIONS) Magnetic Diffusion and Electromagnetic Waves Ashutosh Pramanik 2014 by PHI Learning Private Limited, Delhi. All rights reserved. No part of this book may be reproduced in any form, by mimeograph or any other means, without permission in writing from the publisher. ISBN The export rights of this book are vested solely with the publisher. Published by Asoke K. Ghosh, PHI Learning Private Limited, Rimjhim House, 111, Patparganj Industrial Estate, Delhi and Printed by Rajkamal Electric Press, Plot No. 2, Phase IV, HSIDC, Kundli , Sonepat, Haryana.

4 To the revered memory of my parents Tarapada Pramanik and Renubala Pramanik whose encouragement and support for my professional career made this book possible and to my grandson Om S. Advant for his love and affection

5

6 Contents VOLUME 1 THEORY Preface xxvii Preface to the Second Edition Preface to the First Edition xxxi xxix 0. Vector Analysis Introduction Vectors and Vector Algebra Addition and Subtraction of Vectors Components of a Vector Multiplication of Vectors Three Orthogonal Coordinate Systems Rectangular Cartesian Coordinates (x, y, z) Cylindrical Polar Coordinate System (r, f, z) Spherical Polar Coordinate System (r, q, f) Vector Calculus Differentiation of Vectors Integration Line, Surface, and Volume Integrals The Vector Operator and Its Uses The Gradient of a Scalar The Divergence of a Vector The Curl of a Vector Some Integral Theorems of Vectors Gauss Theorem Stokes Theorem Green s Theorem Vector Analogue of Green s Theorem Applications of the Operator Del (= ) The Operator Div Grad 22 v

7 vi contents Divergence of a Vector Product Divergence and Curl of SA The Operator Curl Grad The Operator 2 with Vector Operand The Operator Grad Div The Operator Div Curl The Operator Curl Curl Gradient of a Scalar Product Curl of a Vector Product Types of Vector Fields Solenoidal and Irrotational Field (Lamellar) Irrotational but not Solenoidal Field Solenoidal but not Irrotational Field Neither Irrotational Nor Solenoidal Field Time Variation of Vectors Complex Representation of Time-harmonic Vectors Complex Representation of Rotating Vectors Magnitudes of Vectors in Complex Representation Complex Representation of a Vector Rotating in Cartesian Plane da A The Relationship between and dt t Conversion of a Vector from One Coordinate System to Another 39 Problems The Electrostatic Field in Free Space (in Absence of Dielectrics) Introduction The Law of Force between Charged Particles (Coulomb s Law) Four Fundamental Forces of Nature The Principle of Superposition The Electric Force (Per Unit Charge) and the Concept of Electric Field The Electric Field of Continuous Space Distribution of Charges (Gauss Theorem) The Flux of E Across a Surface Gauss Theorem An Alternative Proof of Gauss Theorem in Differential Form Electric Potential (or Electrostatic Potential) Electric Field and Electric Potential Potential Function and Flux Function Potential Field Expressed as Poisson and Laplace Equations Some Useful Examples of Calculation of Fields by Gauss Theorem and Potentials A Group of Charged Particles A Hollow Charged Sphere of Radius a, and Carrying a Charge Q Uniformly Distributed Charge on an Infinite Circular Cylinder Infinitely Long Straight Line Charge A Group of Parallel Line Charges 72

8 contents vii Charges Distributed Uniformly Over an Infinitely Plane Surface Electric Dipole 74 Problems Conductors and Insulators in Electrostatic Field Conductors and Insulators Conductors in the Electrostatic Field Relation between Electrostatic Potential and Charges on Conducting Bodies The Case of an Isolated Conductor The Case of Two Bodies with Equal Charges of Opposite Signs Methods of Evaluating Capacitance (C) The Behaviour of Insulators (or Dielectrics) in a Static Electric Field The Potential and Electric Field due to an Aggregate of Dipoles (Polarization Vector) Charge Distribution Equivalent to a Polarized Dielectric Generalized Form of Gauss Theorem Some Physical Properties of Dielectrics Dielectric Strength Dielectric Relaxation Triboelectricity Capacitance: Capacitors Calculation of Capacitance Parallel Plate Capacitor Concentric Cylinders Parallel Circular Cylinders Wire and Parallel Plane An Introductory Note on the Method of Images Capacitance between Two Spheres of Equal Diameter Capacitance between a Sphere and a Conducting Plane Capacitances in Parallel and in Series Field in a Region Containing Two Dielectric Materials: Boundary Conditions in Electrostatics Capacitors of Mixed Dielectrics and of Complex Shapes Parallel Plate Capacitor with Mixed Dielectrics Concentric Cylinders with Mixed Dielectrics Concentric Spheres with Single Dielectric Concentric Spheres with Mixed Dielectrics Capacitance of N Conductors 104 Problems Energy and Mechanical Forces in Electrostatic Fields Electrostatic Forces Energy of a System of Charged Conductors Energy Stored in the Electric Field An Alternative Derivation for the Field Energy 109

9 viii contents 3.4 Forces on Conductors and Dielectrics Forces and Pressures on Conductors Electrostatic Forces on Dielectrics General Method of Determining Forces in Electrostatic Fields Pressure on Boundary Surfaces Pressure on Surface of Charged Conductors Pressure on Boundary Surfaces of Two Dielectrics Stability of the Electrostatic System (Earnshaw s Theorem) 118 Problems Methods of Solving Electrostatic Field Problems Introduction Direct Solving of Laplace s Equation Introduction Boundary Surfaces and Conditions Coordinate Systems Separation of Variables in a Rectangular Cartesian System Separation of Variables in a Cylindrical Polar Coordinate System Potential Inside a Hollow Cylindrical Ring Separation of Variables in a Spherical Polar Coordinate System Electric Field within a Charged Hollow Sphere Green s Function Green s Function for a Two-dimensional Region Green s Function for a Rectangular Region with Poissonian Field Green s Function for an Infinite Conducting Plane Conformal Transformations and Complex Variables Functions of Complex Variables and Conjugate Functions Conformal Transformation Complex Potential W(z) Some Simple Examples Method of Images Line Charge Parallel to the Surface of a Semi-infinite Dielectric Block Point Charge Near an Infinite Grounded Conducting Plane Line Charge Near a Circular Boundary Point Charge Near a Conducting Sphere 166 Problems Approximate Methods of Solving Electrostatic Field Problems Introduction Graphical Method of Solving Electrostatic Problems A Note on Curvilinear Squares A Proof that the Potential Associated with a Field-plot Consisting of Curvilinear Rectangles Satisfies the Laplace s Equation 172

10 contents ix Plotting Technique Two-dimensional Multi-dielectric Fields Experimental Methods Electrolytic Tank Method Conducting Paper Analogue Elastic Membrane Method (Rubber Sheet Analogy) Hydrodynamic Analogy Numerical Methods Finite Difference Methods Finite Difference Representation Basic Equations for the Square and the Rectangular Meshes Reduction of the Field Problem into a Set of Simultaneous Equations Computational Methods Finite Element Method Functional and Its Extremum Functional in Two Variables Functional for Electrostatic Fields Functional and the Boundary Conditions Functional Minimization General Comments 204 Problems Steady Electric Current and Electric Field Introduction Electric Current and Current Density Electric Current and Electric Force The Conservation of Charge (The Equation of Continuity) Analogy between Electric Current and Electric Flux Electromotive Force Potential in the Electric Circuit Ohm s Law and Joule s Law Boundary Conditions Circuit Laws Series and Parallel Connection of Resistors 219 Problems Magnetic Field of Steady Currents in Free Space Introduction The Law of Magnetic Force between Two Small Moving Charges The Concept of the Magnetic Field (the Magnetic Flux Density) The Magnetic Field of an Electric Current Biot Savart s Law Magnetic Field of a Short Straight Length of Wire Magnetic Field on the Axis of a Square Coil Magnetic Field on the Axis of a Circular Coil 231

11 Electromagnetism - Applications (Magnetic Diffusion And Electromagnetic Waves): Volume 2 30% OFF Publisher : PHI Learning ISBN : Author : PRAMANIK, ASHUTOSH Type the URL : 4 Get this ebook

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