# Electromagnetic Fields in 3-D

Por: Swayam . en: ,

Course Objectives

• To provide the foundation and rudiments of Electromagnetic theory essential to subsequent courses of radiation, microwave and wireless communications.• To expose the learners to basic laws of electrostatics, magnetostatics leading to the Maxwell Equations for static and dynamic fields.• To familiarize the learners with the basic principles of Uniform Plane waves, antennas and transmission line theory, and wireless communication.• The main focus will be on the physical interpretation of mathematical formulations in 3-Dimensions.
SyllabusUNIT -1) 3-D’s

PART-A:ESSENTIALS OF VECTOR CALCULUS

1.1) INTRODUCTION1.2) THE MAGNITUDE!1.3) THE DIRECTION (UNIT VECTOR)1.3.1) DOT PRODUCT OF UNIT VECTORS1.3.2) DEFINING A PLANE USING DIRECTION COMPONENTS1.4) DOT PRODUCT1.5) THE CROSS PRODUCT

PART B: COORDINATE SYSTEM

1.1) INTRODUCTION TO COORDINATE SYSTEM1.2) CARTESIAN COORDINATE SYSTEM1.2.1) DEFINING POINT ‘P’ IN CARTESIAN COORDINATE SYSTEM1.3) CONSTANT PLANES1.4) DIFFERENTIAL VOLUME IN SPACE1.5) VECTORS IN CARTESIAN1.6) CYLINDRICAL COORDINATE SYSTEM1.6.1) FINDING POINT 'P' IN CYLINDER1.7) CONSTANT PLANE1.8) INTRODUCTION TO COORDINATE SYSTEM1.9) SPHERICAL COORDINATE SYSTEM1.10) CONSTANT PLANES1.11) LOCATING POINT 'P' IN SPHERICAL COORDINATE SYSTEM1.12) DIFFERENTIAL VOLUME IN SPHERICAL SYSTEM1.13) RELATION BETWEEN VARIOUS COORDINATE SYSTEMS1.13.1) CONVERSION OF RECTANGULAR COORDINATES TO SPHERICAL COORDINATES1.13.2) CONVERSION OF SPHERICAL COORDINATE TO CARTESIAN COORDINATE SYSTEM
PART–C: THE INTEGRALS AND Del OPERATOR

1.1) LINE, SURFACE AND VOLUME INTEGRALS1.2) VOLUME INTEGRALS1.3) INTEGRAL CALCULUS1.4) TRIPLE INTEGRAL FOR VOLUME1.5) ALL ABOUT THE DEL OPERATOR1.6) GRADIENT OF A SCALAR1.7) DIVERGENCE OF VECTOR FIELD1.8) CURL1.9) FUNDAMENTAL THEOREMS1.9.1) STROKES THEOREM1.9.2) DIVERGENCE THEOREM
UNIT 2) ELECTROSTATICS (ELECTRO's )
12.1) INTRODUCTION2.1.1) WHAT IS ELECTROSTATICS?2.2) COULOMB’S LAW2.2.1) MORE ABOUT CONSTANT OF PROPORTIONALITY2.2.2) COULOMB’S LAW IN VECTOR FORMAT
2.3) ELECTRIC FIELD INTENSITY ‘E’2.3.1) VARIOUS CHARGE DISTRIBUTION2.4) 'E' DUE TO VARIOUS CHARGE DISTRIBUTIONS2.4.1) 'E'DUE TO A POINT CHARGE2.4.2) 'E'DUE TO LINE CHARGE DISTRIBUTION2.4.3) 'E'DUE TO FINITE LENGTH LINE2.4.4) 'E'DUE TO INFINITE LINE CHARGE2.4.5) 'E'DUE TO CIRCULAR RING2.4.6) 'E'DUE TO SURFACE CHARGE DISTRIBUTION2.5) GAUSS’S LAW AND ITS APPLICATIONS2.5.1) ELECTRIC FLUX2.5.2) VARIOUS RELATIONS REATED TO GAUSS LAW2.6) GAUSS LAW2.6.1) WHAT IS GAUSSIAN SURFACE!2.7) APPLICATIONS OF GAUSS’S LAW2.7.1) PROOF OF GAUSS’S LAW FROM COULOMB'S LAW (IN CASE OF POINT CHARGE)2.7.2) ELCTRIC FLUX DENSITYDUE TO INFINITE LONG CONDUCTOR2.7.3) ELCTRIC FLUX DENSITYDUE TOA SHEET OF CHARGE
2.8) DIVERGENCE OF ELECTRIC FLUX DENSITY
UNIT 3) ELECTROE’S II
3.1) INTRODUCTION3.2) CURRENT3.2.1) CURRENT IN CONDUCTORS3.2.2) CONDUCTIVITY OF MATERIAL3.2.3) VARIOUS RELATIONS OF CONDUCTIVITY3.2.3) CONTINUITY EQUATION3.2.4) RELAXATION TIME3.3) DIELECTRIC MATERIALS3.3.1) ELECTRIC DIPOLE3.3.2) DIPOLE IN UNIFORM FIELD3.3.3) PROPERTIES OF DIELECTRIC MATERIALS3.3.4) DIELECTRIC CONSTANT3.3.5) ISOTROPIC, HOMOGENEOUS & LINEAR DIELECTRICS3.4) POTENTIAL3.4.1) DEFINITION OF ELECTRIC POTENTIAL3.4.2) POTENTIAL DIFFERENCE AND ABSOLUTE POTENTIAL3.4.3) ABSOLUTE POTENTIAL3.4.4) RELATION BETWEEN 'E' & 'V'3.4.5) CONSERVATIVE FIELD FOR MAXWELL’S EQUATION3.4.6) UNIT OF ‘E’ & MORE DETAIL ABOUT E & V3.4.7) VOLTAGE DUE TO VARIOUS CHARGES DISTRIBUTION3.5) CAPACITOR3.5.1) PARALLEL PLATECAPACITOR3.5.2) SPHERICALCAPACITOR-CAPACITANCE OF TWO CONCENTRIC CONDUCTING SPHERES3.5.3) CAPACITANCE FOR COAXIAL CABLE3.6) ENERGY DENSITY3.7) POISON’S & LAPLACE’S EQUATION3.8) MAXWELLS TWO EQUATIONS
UNIT 4 ) MAGNETOSTATICS (MAGNETO'S-I)
4.1) INTRODUCTION4.1.1) MAGNETIC FLUX4.1.2) MAGNETIC FIELD INTENSITY (H)4.1.3) MAGNETIC FLUX DENSITY4.2) BIOT-SAVART’S LAW4.2.1) CASE 1: MAGNETIC FIELD INTENSITY DUE TO INFINITE LONG STRAIGHT FILAMENT ON POINT 'P'4.2.2) CASE 2: MAGNETIC FIELD INTENSITY DUE TO FINITE LENGTH CURRENT ELEMENT4.2.3) CASE 3: MAGNETIC FIELD INTENSITY AT THE CENTRE OF SQUARE CURRENT LOOP4.2.4) CASE 4: 'H' DUE TO CIRCULAR CONDUCTING FILAMENT ON POINTP:4.2.5) CASE 5: RELATION BETWEEN MAGNETIC FIELD INTENSITY (H), VOLUME CURRENT DENSITY (J) AND SURFACECURRENT DENSITY (K)4.3) AMPERE'S CIRCUITALLAW {OR} AMPERES WORKS LAW4.4) APPLICATIONS OF AMPERE'S CIRCUITAL LAW4.4.1) CASE 1: MAGNETICFIELD INTENSITY DUE TO LONG FILAMENTARY CONDUCTOR4.4.2) CASE 2: MAGNETIC FIELD INTENSITY DUE TO A COAXIAL TRANSMISSION LINE4.4.3) CASE 3: CURL OF MAGNETIC FIELD INTENSITY AND DIFFERENCE BETWEEN CURL ANDDIVERGENCE4.4.4) CASE 4: STROKES THEOREM FOR MAGNETIC FIELD INTENSITY
UNIT 5 )
5.1) THE MAGNET5.2) FORCE ON A MOVINGCHARGE AND DIFFERENTIAL CURRENT ELEMENT5.2.1) LORENTZ FORCE EQUATION5.3) FORCE ON DIFFERENTIAL CURRENT ELEMENT5.4) EXAMPLE: FORCE BETWEEN LINE CURRENTS5.5) FORCE AND TORQUE ON A CURRENT LOOP OR FORCE AND TORQUE ON A CLOSED CIRCUIT5.5.1) MAGNETIC MOMENT5.6) MAGNETIZATION5.7) MAGNETIC MATERIALS5.7.1) ELECTROMAGNETS AND ITS IMPORTANT USES5.7.2) CLASSIFICATION OF MAGNETIC MATERIALS ACCORDING TO THEIR ALIGNMENT OF MAGNETIC MOMENT5.8) MAGNETIC BOUNDARY CONDITIONS:THE BORDERS!
CHAPTER 6) THE WAVE’S : TRANSMISSION LINES & ANTENNA'S
6.1) INTRODUCTION6.1.1) WHAT IS TRANSVERSE WAVE?6.1.2) LONGITUDINAL WAVE6.1.3) THE PROBLEM6.2) WHATIS PROPAGATION?6.2.1) LIGHTING THE WAVE!….AND LIGHT WAS THERE.
6.3) WHAT IS LIGHT ANDWHAT IS FREQUENCY? (WAAAAVE!)6.3.1) FREQUENCY AND WAVE!6.4) CONCEPT OF POLARIZATION6.5) TYPES OF WAVES6.6) WAVE EQUATIONS6.6.1) WAVE EQUATIONS FOR GOOD CONDUCTORS6.6.2) WAVE EQUATIONS FOR FREE SPACE6.7) RELATIONBETWEEN ‘E’ AND ‘H’ ,THE CHARACTERISTIC OR INTRINSIC IMPEDANCE OF THE FREE SPACE OR TRANSVERSE NATURE OF WAVE6.8) BOUNCING A WAVE!
6.8.1) NORMAL INCIDENCEAT A PLANE BOUNDARY OF GOOD CONDUCTING MATERIALS (STANDING WAVE)6.8.2) NORMAL INCIDENCEAT A PLANE BOUNDARY OF TWO PERFECT DIELECTRIC MATERIALS6.8.3) REFLECTION AT THE SURFACE OF A CONDUCTING MEDIUM – NORMAL INCIDENCE6.6) POYNTING VECTOR AND POWER FLOW INELECTROMAGNETIC FIELDS6.7) ELECTROMAGNETICS & TRANSMISSION LINES: OVERVIEW OF T AND Π NETWORKS.
6.7.1) TWO WIRE TRANSMISSION LINES,
6.7.2) PRIMARY AND SECONDARY CONSTANTS.
6.7.3) TRANSMISSION LINE EQUATIONS. INFINITE LINE AND CHARACTERISTIC IMPEDANCE- OPEN AND SHORT CIRCUIT LINES AND THEIR SIGNIFICANCE6.8) INTRODUCTION TO ELECTROMAGNETICS & ANTENNAS.6.9) INTRODUCTION TO ELECTROMAGNETICS & WIRELESS COMMUNICATIONS.