Fundamentals of Engineering Electromagnetics

Sunil Bhooshan is currently Professor and Head of Department in Jaypee University of Information Technology (JUIT) at Waknaghat near Shimla which is a part of the group of educational institutions of the Jaypee group of industries. The author graduated from IIT Delhi, and completed his MS and Ph D degrees from the University of Illinois at Urbana-Champaign, USA. Dr Bhooshan has a balanced background of industry and academics. He has worked in Hewlett Packard (now Agilent Technologies) at Santa Rosa, USA, as a Member of Technical Staff. He taught briefly at IIT Kanpur and was a consultant to various companies in India where he helped develop parabolic dish antennas and other microwave components. He has more than fifty research papers published in reputed journals and presented in international conferences. He is a member of IEEE (Institute ofElectrical and Electronics Engineers) and WSEAS (World Scientific and Engineering Academy and Society) societies.

• FREQUENTLY USED REFERENCE MATERIAL ; 0.1. TABLE OF FUNDAMENTAL CONSTANTS ; 0.2. UNITS ; 0.3. THE GREEK ALPHABET ; 0.4. SI PREFIXES ; 0.5. DIELECTRIC CONSTANTS OF MATERIALS ; 0.6. RELATIVE PERMEABILITIES OF MATERIALS ; I. INTRODUCTORY MATERIAL ; 1. SCALARS AND VECTORS ; 1.1. INTRODUCTION ; 1.2. SCALARS ; 1.2.1. RULES TO MANIPULATE SCALARS ; 1.2.2. KEEPING TRACK OF CALCULATIONS ; 1.2.3. ORDER OF MAGNITUDE OF CALCULATIONS ; 1.2.4. APPROXIMATIONS ; 1.3. VECTORS ; 1.3.1. THE UNIT VECTOR ; 1.3.2. VECTOR ADDITION ; 1.3.2.1. A HANDY TECHNIQUE ; 1.3.2.2. CALCULATIONS WITH VECTOR ADDITION ; 1.3.3. DOT PRODUCT OR SCALAR PRODUCT ; 1.3.3.1. WORK AND SCALAR PRODUCT ; 1.3.3.2. SCALAR PRODUCTS OF ORTHOGONAL UNIT VECTORS ; 1.3.4. CROSS PRODUCT OR VECTOR PRODUCT ; 1.3.4.1. CROSS PRODUCTS OF ORTHOGONAL UNIT VECTORS ; 1.3.4.2. CROSS PRODUCT IN RECTANGULAR COORDINATES ; 1.3.4.3. MEMORIZING CROSS-PRODUCT CALCULATIONS ; 1.3.4.4. SCALAR TRIPLE PRODUCT ; 1.4. UNITS AND DIMENSIONS ; 1.5. POINTS TO REMEMBER ; 1.6. PRACTICE PROBLEMS AND SELF ASSESSMENT ; 2. COORDINATE SYSTEMS AND FIELDS ; 2.1. INTRODUCTION ; 2.2. SCALAR AND VECTOR FIELDS ; 2.2.1. SCALAR FIELDS ; 2.2.2. VECTOR FIELDS ; 2.3. THE RECTANGULAR COORDINATE SYSTEM ; 2.3.1. DISTANCE BETWEEN TWO POINTS ; 2.3.2. DIRECTION COSINES ; 2.3.3. VECTOR EQUATION OF A STRAIGHT LINE ; 2.3.4. EQUATION OF A PLANE ; 2.4. CYLINDRICAL COORDINATE SYSTEM ; 2.4.1. EQUATIONS OF SURFACES AND LINES IN CYLINDRICAL COORDINATES ; 2.5. THE SPHERICAL COORDINATE SYSTEM ; 2.6. POINTS TO REMEMBER ; 2.7. PRACTICE PROBLEMS AND SELF ASSESSMENT ; 3. VECTOR CALCULUS 143 ; 3.1. CHAPTER GOALS ; 3.2. BASIC 3-DIMENSIONAL CALCULUS ; 3.2.1. DIFFERENTIAL ELEMENT OF A LINE ; 3.2.2. LINE INTEGRAL ; 3.2.3. DIFFERENTIAL ELEMENT OF A SURFACE ; 3.2.4. SURFACE INTEGRAL ; 3.2.5. THE VOLUME INTEGRAL ; 3.3. DIFFERENTIAL CALCULUS CONCEPTS ; 3.3.1. THE DEL OR NABLA OPERATOR ; 3.3.2. GRADIENT ; 3.3.3. THE CURL ; 3.3.4. DIVERGENCE ; 3.4. MAXWELL'S EQUATIONS ; 3.5. UNITS AND DIMENSIONS OF EM FIELDS ; 3.6. LIST OF FORMULAE ; 3.7. PRACTICE PROBLEMS AND SELF ASSESSMENT ; II. ELECTROSTATICS ; 4. THE ELECTRIC FIELD AND GAUSS'S LAW ; 4.1. CHAPTER GOALS ; 4.2. ELECTROSTATICS: AN INTRODUCTION ; 4.3. CHARGE ; 4.3.1. THE DIRAC DELTA FUNCTION ; 4.4. COULOMB'S LAW AND THE ELECTRIC FIELD ; 4.5. THE ELECTRIC FIELD DUE TO A SYSTEM OF POINT CHARGES ; 4.5.1. ELECTRIC DIPOLE ; 4.5.2. ELECTRIC FIELD DUE TO ANY NUMBER OF POINT CHARGES ; 4.6. ELECTRIC FIELD DUE TO CONTINUOUS CHARGE DISTRIBUTIONS ; 4.6.1. INFINITE LINE CHARGE ; 4.6.2. INFINITE SHEET CHARGE ; 4.7. ELECTRIC DISPLACEMENT ? AND FLUX DENSITY D ; 4.8. GAUSS'S LAW ; 4.9. GAUSS'S LAWAPPLIED TO CASES OF SPHERICAL SYMMETRY ; 4.9.1. GAUSS'S LAW APPLIED TO A POINT CHARGE ; 4.9.2. GAUSS'S LAW APPLIED TO A CHARGED SPHERE ; 4.10. GAUSS'S LAW APPLIED TO CASES OF CYLINDRICAL SYMMETRY ; 4.11. GAUSS'S LAWAPPLIED TO CASES OF RECTANGULAR SYMMETRY ; 4.12. LIST OF FORMULAE ; 4.13. PRACTICE PROBLEMS AND SELF ASSESSMENT ; 5. ENERGY AND POTENTIAL ; 5.1. CHAPTER GOALS ; 5.2. POTENTIAL DUE TO A POINT CHARGE ; 5.3. EQUIPOTENTIAL SURFACES ; 5.4. POTENTIAL ENERGY ; 5.5. POTENTIAL DUE TO A SYSTEM OF POINT CHARGES ; 5.5.1. FAR FIELDS FOR AN ELECTRIC DIPOLE ; 5.6. POTENTIAL DUE ANY CONTINUOUS CHARGE DISTRIBUTION ; 5.7. LIST OF FORMULAE ; 5.8. PRACTICE PROBLEMS AND SELF ASSESSMENT ; 6. THE ELECTRIC FIELD AND MATERIAL MEDIA ; 6.1. CHAPTER GOALS ; 6.2. CURRENT AND CURRENT DENSITY ; 6.3. CONTINUITY EQUATION ; 6.4. CONDUCTORS, SEMICONDUCTORS AND DIELECTRICS ; 6.4.1. CONDUCTORS AND RESISTANCE ; 6.4.2. RELAXATION TIME FOR CONDUCTORS ; 6.4.3. THE METHOD OF IMAGES ; 6.4.4. SEMICONDUCTORS ; 6.4.5. DIELECTRICS ; 6.5. CAPACITANCE ; 6.5.1. PARALLEL PLATE CAPACITOR ; 6.5.2. COAXIAL LINE ; 6.5.3. TWO CONDUCTOR LINE ; 6.6. RELATION BETWEEN CAPACITANCE AND RESISTANCE ; 6.7. BOUNDARY CONDITIONS FOR ELECTROSTATIC FIELDS ; 6.8. ENERGY STORED IN THE ELECTRIC FIELD ; 6.9. LIST OF FORMULAE ; 6.10. PRACTICE PROBLEMS AND SELF ASSESSMENT ; 7. LAPLACE'S AND POISSON'S EQUATIONS ; 7.1. CHAPTER GOALS ; 7.2. INTRODUCTION ; 7.3. UNIQUENESS THEOREM ; 7.4. LAPLACE'S EQUATION ; 7.4.1. SOME ONE DIMENSIONAL SOLUTIONS ; 7.4.1.1. LAPLACE'S EQUATION, APPLIED TO INFINITE PARALLEL PLANES ; 7.4.1.2. LAPLACE'SEQUATION,APPLIEDTOCONCENTRIC CYLINDERS ; 7.4.1.3. LAPLACE'SEQUATION,APPLIEDTOCONCENTRIC SPHERES ; 7.4.1.4. LAPLACE'SEQUATIONAPPLIEDTOTWO COAXIAL CONES ; 7.4.2. TWODIMENSIONAL SOLUTIONS TOLAPLACE'SEQUATION ; 7.4.2.1. ANALYTIC FUNCTIONS ; 7.4.3. SEPARATION OF VARIABLES ; 7.4.4. NUMERICAL TECHNIQUES ; 7.5. POISSON'S EQUATION ; 7.5.1. ONE DIMENSIONAL SOLUTIONS ; 7.6. LIST OF FORMULAE ; 7.7. PRACTICE PROBLEMS AND SELF ASSESSMENT ; III. MAGNETOSTATICS ; 8. THE STEADY MAGNETIC FIELD ; 8.1. CHAPTER GOALS ; 8.2. INTRODUCTION ; 8.3. THE BIOT-SAVART LAW ; 8.3.1. BIOT-SAVART LAW APPLIED TO A TINY FILAMENTARY CURRENT ; 8.4. TYPES OF CURRENT ; 8.4.1. BIOT-SAVARTLAWAPPLIEDTO AN INFINITELYLONG STRAIGHT WIRE ; 8.4.2. MAGNETIC FIELD LINES OF A LONG STRAIGHT WIRE ; 8.4.3. BIOT-SAVART LAW APPLIED TO A SHORT STRAIGHT WIRE ; 8.5. AMPERE'S LAW ; 8.5.1. AMPERE'S LAW APPLIED TO A LONG STRAIGHT WIRE ; 8.5.2. AMPERE'S LAW APPLIED TO A WIRE OF RADIUS A ; 8.5.3. AMPERE'S LAW APPLIED TO AN INFINITE SOLENOID ; 8.5.4. AMPERE'S LAW APPLIED TO A WINDING AROUND A TORUS ; 8.6. THE MAGNETIC FIELD-SOME CALCULATIONS ; 8.6.1. LOOP OF WIRE CARRYING A CURRENT ; 8.6.2. MAGNETIC FIELD DUE TO A CURRENT SHEET ; 8.6.3. MAGNETIC FIELD IN THE INTERIOR OF AN INFINITE SOLENOID ; 8.6.4. MAGNETIC FIELD IN THE INTERIOR OF A FINITE SOLENOID ; 8.6.5. MAGNETIC FIELD ON THE AXIS OF A ROTATING CHARGED DISK ; 8.7. THE MAGNETIC SCALAR POTENTIAL ; 8.7.1. SCALAR POTENTIAL IN THE INTERIOR OF AN INFINITE SOLENOID ; 8.8. THE VECTOR POTENTIAL AND THE MAGNETIC FLUX DENSITY ; 8.8.1. CALCULATION OF THE VECTOR POTENTIAL ; 8.8.2. VECTOR POTENTIAL OF A CIRCULAR LOOP ; 8.9. THE BIOT-SAVART LAW-REVISITED ; 8.10. VARIOUS RESULTS ; 8.10.1. VECTORPOENTIAL FOR ACURRENTCARRYING STRAIGHT CONDUCTOR ; 8.10.2. TWO CURRENT CARRYING STRAIGHT CONDUCTORS ; 8.11. FAR FIELD APPROXIMATION ; 8.11.1. SQUARE CURRENT LOOP AND MAGNETIC DIPOLE ; 8.12. LIST OF FORMULAE ; 8.13. PRACTICE PROBLEMS AND SELF ASSESSMENT ; 9. MAGNETIC FORCES, INDUCTANCE AND MAGNETISATION ; 9.1. CHAPTER GOALS ; 9.2. THE LORENTZ FORCE ; 9.3. ELECTRON MOVING IN A STEADY MAGNETIC FIELD ; 9.4. A STRAIGHT WIRE CARRYING A CURRENT IN A MAGNETIC FIELD ; 9.5. OTHER FORMULATIONS ; 9.6. LOOP CARRYING A CURRENT IN A CONSTANT MAGNETIC FIELD ; 9.7. TORQUE ON LOOP CARRYING A CURRENT IN A CONSTANT MAGNETIC FIELD ; 9.7.1. THE MAGNETIC DIPOLE AND TORQUE ON AN ARBITRARY LOOP ; 9.8. FORCE BETWEEN TWO CURRENT ELEMENTS ; 9.9. INDUCTANCE ; 9.9.1. INDUCTANCE OF A COIL ; 9.9.2. INDUCTANCE OF A COAXIAL LINE ; 9.9.3. MAGNETIC ENERGY ; 9.9.4. INDUCTANCE OF A CIRCULAR LOOP ; 9.9.5. MUTUAL INDUCTANCE ; 9.10. MAGNETIC MATERIALS AND MAGNETIC CIRCUITS ; 9.10.1. MAGNETISATION ; 9.10.2. MAGNETIC CIRCUITS ; IV. TIME VARYING FIELDS, RADIATION AND PROPAGATION ; 10.TIME DEPENDANT FIELDS ; 10.1. CHAPTER GOALS ; 10.2. LIST OF FORMULAE ; 10.3. FARADAY'S LAW ; 10.4. A MAXWELL EQUATION FROM FARADAY'S LAW ; 10.5. THE DISPLACEMENT CURRENT DENSITY ; 10.6. TIME-DEPENDENTMAXWELL'S EQUATIONS ; 10.6.1. POINT FORM OF THE EQUATIONS ; 10.7. INTEGRAL FORM OF MAXWELL'S EQUATIONS ; 10.8. THE FUNDAMENTALEQUATIONS OFRADIATION AND PROPAGATION ; 10.9. TIME DOMAIN WAVE EQUATION ; 10.10.FREQUENCY DOMAIN WAVE EQUATION ; 10.10.1.PHASORS ; 10.11.THE WAVE EQUATION ; 10.12.CHAPTER SUMMARY ; 10.13.SHORT ANSWER QUESTIONS ; 10.14.PROBLEMS ; 11.ELECTROMAGNETIC WAVES ; 11.1. UNIFORM PLANE WAVE ; 11.2. WAVE POLARISATION ; 11.2.1. CIRCULAR POLARISATION ; 11.2.2. ELLIPTICAL POLARISATION ; 11.3. WAVE PROPAGATION IN CONDUCTING MEDIA ; 11.3.1. LOW CONDUCTIVITY MATERIALS ; 11.3.2. HIGH CONDUCTIVITY MATERIALS ; 11.4. BOUNDARY CONDITIONS ; 11.5. REFLECTION AND REFRACTION OF WAVES ; 11.5.1. REFLECTION FROM A METAL SURFACE ; 11.5.1.1. NORMAL INCIDENCE ; 11.5.2. REFRACTION FROM A DIELECTRIC SURFACE ; 11.6. POYNTING VECTOR AND THE FLOW OF POWER ; 11.6.1. POYNTING'S THEOREM ; 11.6.2. POYNTING VECTOR ; 12.TRANSMISSION LINES ; 12.1. TIME DOMAIN EQUATION ; 12.2. FREQUENCY DOMAIN EQUATION ; 12.3. SOLUTIONS TO THE TRANSMISSION LINE EQUATION ; 12.3.1. POWER CONSIDERATIONS ; 12.3.2. REFLECTIONS FROM DISCONTINUITIES ; 12.3.3. STANDINGWAVE RATIO ; 12.3.4. INPUT IMPEDANCE ANYWHERE ALONG THE LINE ; 12.4. TRANSMISSION LINE CHARTS ; 12.5. TRANSFORMER MATCHING ; 12.6. REFERENCES ; 13.WAVEGUIDES ; 13.1. THE PARALLEL PLATE WAVEGUIDE ; 13.2. TEM MODE WAVEGUIDES ; 13.3. THE RECTANGULARWAVEGUIDE ; 13.4. THE CIRCULARWAVEGUIDE ; 14.RADIATION FROM CURRENTS ; 14.1. WAVE EQUATION DUE TO CHARGES AND CURRENTS ; 14.2. RADIATION FROM A CURRENT ELEMENT ; 14.3. THE HALF-WAVE DIPOLE ANTENNA ; 14.4. BASIC ANTENNA CONCEPTS ; 14.5. DIRECTIVITY ; 14.5.1. DIRECTIVITY FROM THE BEAM PATTERN ; 14.6. EFFECTIVE APERTURE AND FRIIS' TRANSMISSION FORMULA ; 15. INTRODUCTION TO ANTENNAS ; 15.1. CHAPTER GOALS ; 15.2. INTRODUCTION ; 15.3. LINEAR ANTENNA ARRAYS ; 15.4. LINEAR ARRAY WITH EQUAL CURRENTS ; 15.4.1. THE ARRAY FACTOR ; 15.4.2. NULLS AND SIDELOBES ; 15.4.3. BEAM POINTING ANGLE ; 15.5. FARFIELD PATTERN ; 15.6. APERTURE ANTENNAS ; 15.7. HORN ANTENNAS ; 15.7.1. INTRODUCTION ; 15.8. PARABOLIC REFLECTOR ; 15.9. LIST OF FORMULAE ; 15.10.PRACTICE PROBLEMS AND SELF ASSESSMENT ; 16.RADIO WAVE PROPAGATION ; 16.1. INTRODUCTION ; 16.2. GROUND WAVE PROPAGATION ; 16.3. EARTH REFLECTION ; 16.4. THE SURFACE WAVE ; 16.4.1. THE SURFACE WAVE FOR THE VERTICAL DIPOLE ; 16.4.2. WAVE TILT OF THE SURFACE WAVE ; 16.5. SURFACE WAVE FOR A HORIZONTAL DIPOLE ; 16.6. APPROXIMATIONS FOR GROUND WAVE PROPAGATION ; 16.7. TROPOSPHERIC PROPAGATION ; 16.7.1. SPHERICAL EARTH CONSIDERATIONS ; 16.7.2. TROPOSPHERIC WAVES ; 16.8. IONOSPHERIC PROPAGATION ; 16.8.1. THE IONOSPHERE ; 16.8.1.1. PLASMA OSCILLATIONS ; 16.8.1.2. WAVE PROPAGATION IN A PLASMA ; A. LIST OF SYMBOLS ; A.1. COMMONLY USE SYMBOLS AND NOMENCLATURE ; B. COORDINATE SYSTEMS ; B.1. RECTANGULAR TO CYLINDRICAL, CYLINDRICAL TO RECTANGULAR ; B.2. RECTANGULAR TO SPHERICAL, SPHERICAL TO RECTANGULAR ; B.3. SPHERICAL AND CYLINDRICAL COORDINATES ; B.4. GRAD, DIV, CURL AND LAPLACIAN IN DIFFERENT COORDINATE SYSTEMS ; B.4.1. CARTESIAN COORDINATE ; B.4.2. CYLINDRICAL COORDINATES ; B.4.3. SPHERICAL COORDINATES ; C. MATHEMATICAL REFERENCE ; C.1. GENERAL ; C.1.1. IMPORTANT CONSTANTS ; C.1.2. TAYLOR'S SERIES EXPANSION ; C.1.3. C.2. VECTOR IDENTITIESDINATE SYSTEMS ; C.2.1. GENERAL ; C.2.2. GRADIENT ; C.2.3. CURL ; C.2.4. DIVERGENCE ; C.2.5. DOUBLE ; C.3. COMPLEX VARIABLES ; C.3.1. GENERAL ; C.3.2. INEQUALITIES ; C.3.3. COMPLEX CONJUGATES ; C.3.4. EULER'S IDENTITY ; C.4. TRIGONOMETRY ; C.4.1. BASIC FORMULAE ; C.4.2. SUM AND DIFFERENCE FORMULAE ; C.4.3. DOUBLE ANGLE FORMULAE ; C.4.4. HALF ANGLE FORMULAE ; C.4.5. PRODUCT TO SUM FORMULAE ; C.4.6. SUM AND DIFFERENCE TO PRODUCT ; C.4.7. TRIANGLE FORMULAE ; C.4.8. POWERS OF THE TRIGONOMETRIC FUNCTIONS ; C.5. DIFFERENTIATION ; C.5.1. RULES ; C.5.2. DIFFERENTIATION OF FUNCTIONS ; C.6. INTEGRATION ; C.6.1. COMMON SUBSTITUTIONS ; C.6.2. INDEFINITE INTEGRALS ; BIBLIOGRAPHY