# Electromagnetic Fields in 3D

By Dr. Sohel Rana   |   SASI Institute of Technology & Engineering, Tadepalligudem
Learners enrolled: 3969
This course related to electromagnetic fields is useful for many universities' syllabus . Animations in this  course  are self-explanatory. . Here are some points considered while making this course.

1.   This subject is considered as one of the toughest subjects in electrical as well as electronics engineering. What I observed was that we need to adapt methods differently for understanding the problem. Explaining mathematical expressions physically in three dimensions was a nice solution.

2.  Topic selection was on the basis of actual requirement of the student for understanding the subject core very clearly. This led me to not confining it to a specific university pattern but something which is essential for every university.

3.  It is observed by many teachers that hours allotted to this subject are very less compared to its actual requirement. Which I tried to reduce by making the imagination process broader and simple.

4. This course stresses on removing fear of this subject by explaining it in a simple language with necessary examples rather than including multiple examples. This course focuses on making students competent to solve numerical problems by gaining the actual 3-D situation.
Summary
 Course Status : Upcoming Course Type : Core Duration : Self Paced Category : Multidisciplinary Credit Points : 4 Level : Undergraduate

### Course layout

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.

Syllabus
UNIT -1) 3-D’s

PART-A:ESSENTIALS OF VECTOR CALCULUS

1.1) INTRODUCTION
1.2)  THE MAGNITUDE!
1.3)  THE DIRECTION (UNIT VECTOR)
1.3.1) DOT PRODUCT OF UNIT VECTORS
1.3.2) DEFINING A PLANE USING DIRECTION COMPONENTS
1.4)   DOT PRODUCT
1.5)    THE CROSS PRODUCT

PART B: COORDINATE SYSTEM

1.1)         INTRODUCTION TO COORDINATE SYSTEM
1.2)         CARTESIAN COORDINATE SYSTEM
1.2.1) DEFINING POINT ‘P’ IN CARTESIAN COORDINATE SYSTEM
1.3) CONSTANT PLANES
1.4) DIFFERENTIAL VOLUME IN SPACE
1.5) VECTORS IN CARTESIAN
1.6) CYLINDRICAL COORDINATE SYSTEM
1.6.1) FINDING POINT 'P' IN CYLINDER
1.7) CONSTANT PLANE
1.8) INTRODUCTION TO COORDINATE SYSTEM
1.9) SPHERICAL COORDINATE SYSTEM
1.10) CONSTANT PLANES
1.11) LOCATING POINT 'P' IN SPHERICAL COORDINATE SYSTEM
1.12) DIFFERENTIAL VOLUME IN SPHERICAL SYSTEM
1.13) RELATION BETWEEN VARIOUS COORDINATE SYSTEMS
1.13.1) CONVERSION OF RECTANGULAR COORDINATES TO SPHERICAL COORDINATES
1.13.2) CONVERSION OF SPHERICAL COORDINATE TO CARTESIAN COORDINATE SYSTEM

PART–C: THE INTEGRALS AND Del OPERATOR

1.1)         LINE, SURFACE AND VOLUME INTEGRALS
1.2)         VOLUME INTEGRALS
1.3)         INTEGRAL CALCULUS
1.4)         TRIPLE INTEGRAL FOR VOLUME
1.5)         ALL ABOUT THE DEL OPERATOR
1.7)         DIVERGENCE OF VECTOR FIELD
1.8)         CURL
1.9)        FUNDAMENTAL THEOREMS
1.9.1)      STROKES THEOREM
1.9.2)      DIVERGENCE THEOREM

UNIT 2) ELECTROSTATICS ELECTRO's )

12.1) INTRODUCTION
2.1.1) WHAT IS ELECTROSTATICS?
2.2) COULOMB’S LAW
2.2.1) MORE ABOUT CONSTANT OF PROPORTIONALITY
2.2.2) COULOMB’S LAW IN VECTOR FORMAT
2.
3) ELECTRIC FIELD INTENSITY ‘E’
2.3.1) VARIOUS CHARGE DISTRIBUTION
2.4)    'E' DUE TO VARIOUS CHARGE DISTRIBUTIONS
2.4.1)    'E' DUE TO A POINT CHARGE
2.4.2) 'E'  DUE TO LINE CHARGE DISTRIBUTION
2.4.3)    'E' DUE TO FINITE LENGTH LINE
2.4.4) 'E'  DUE TO INFINITE LINE CHARGE
2.4.5)    'E' DUE TO CIRCULAR RING
2.4.6)     'E' DUE TO SURFACE CHARGE DISTRIBUTION
2.5) GAUSS’S LAW AND ITS APPLICATIONS
2.5.1) ELECTRIC FLUX
2.5.2) VARIOUS RELATIONS REATED TO GAUSS LAW
2.6) GAUSS LAW
2.6.1) WHAT IS GAUSSIAN SURFACE!
2.7) APPLICATIONS OF GAUSS’S LAW
2.7.1) PROOF OF GAUSS’S LAW FROM COULOMB'S LAW (IN CASE OF POINT CHARGE)
2.7.2)  ELCTRIC FLUX DENSITY DUE TO INFINITE LONG CONDUCTOR
2.7.3)  ELCTRIC FLUX DENSITY DUE TO A SHEET OF CHARGE
2.8) DIVERGENCE OF ELECTRIC FLUX DENSITY

UNIT 3) ELECTROE’S II

3.1) INTRODUCTION
3.2) CURRENT
3.2.1) CURRENT IN CONDUCTORS
3.2.2) CONDUCTIVITY OF MATERIAL
3.2.3) VARIOUS RELATIONS OF CONDUCTIVITY
3.2.3) CONTINUITY EQUATION
3.2.4) RELAXATION TIME
3.3) DIELECTRIC MATERIALS
3.3.1) ELECTRIC DIPOLE
3.3.2) DIPOLE IN UNIFORM FIELD
3.3.3) PROPERTIES OF DIELECTRIC MATERIALS
3.3.4) DIELECTRIC CONSTANT
3.3.5) ISOTROPIC, HOMOGENEOUS & LINEAR DIELECTRICS
3.4) POTENTIAL
3.4.1) DEFINITION OF ELECTRIC POTENTIAL
3.4.2) POTENTIAL DIFFERENCE AND ABSOLUTE POTENTIAL
3.4.3) ABSOLUTE POTENTIAL
3.4.4) RELATION BETWEEN 'E' & 'V'
3.4.5) CONSERVATIVE FIELD FOR MAXWELL’S EQUATION
3.4.6) UNIT OF ‘E’ & MORE DETAIL ABOUT E & V
3.4.7) VOLTAGE DUE TO VARIOUS CHARGES DISTRIBUTION
3.5) CAPACITOR
3.5.1) PARALLEL PLATECAPACITOR
3.5.2) SPHERICALCAPACITOR-CAPACITANCE OF TWO CONCENTRIC CONDUCTING SPHERES
3.5.3) CAPACITANCE FOR COAXIAL CABLE
3.6) ENERGY DENSITY
3.7) POISON’S & LAPLACE’S EQUATION
3.8) MAXWELLS TWO EQUATIONS

UNIT 4 ) MAGNETOSTATICS (MAGNETO'S-I)

4.1) INTRODUCTION
4.1.1)    MAGNETIC FLUX
4.1.2)    MAGNETIC FIELD INTENSITY (H)
4.1.3)    MAGNETIC FLUX DENSITY
4.2) BIOT-SAVART’S LAW
4.2.1) 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 ELEMENT
4.2.3) CASE 3: MAGNETIC FIELD INTENSITY AT THE CENTRE OF SQUARE CURRENT LOOP
4.2.4) 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 LAW
4.4) APPLICATIONS OF AMPERE'S CIRCUITAL LAW
4.4.1) CASE 1: MAGNETICFIELD INTENSITY DUE TO LONG FILAMENTARY CONDUCTOR
4.4.2) CASE 2: MAGNETIC FIELD INTENSITY DUE TO A COAXIAL TRANSMISSION LINE
4.4.3) CASE 3: CURL OF MAGNETIC FIELD INTENSITY AND DIFFERENCE BETWEEN CURL ANDDIVERGENCE
4.4.4) CASE 4: STROKES THEOREM FOR MAGNETIC FIELD INTENSITY

UNIT 5 )

5.1) THE MAGNET
5.2) FORCE ON A MOVINGCHARGE AND DIFFERENTIAL CURRENT ELEMENT
5.2.1) LORENTZ FORCE EQUATION
5.3) FORCE ON DIFFERENTIAL CURRENT ELEMENT
5.4) EXAMPLE: FORCE BETWEEN LINE CURRENTS
5.5) FORCE AND TORQUE ON A CURRENT LOOP OR FORCE AND TORQUE ON A CLOSED CIRCUIT
5.5.1) MAGNETIC MOMENT
5.6) MAGNETIZATION
5.7) MAGNETIC MATERIALS
5.7.1) ELECTROMAGNETS AND ITS IMPORTANT USES
5.7.2) CLASSIFICATION OF MAGNETIC MATERIALS ACCORDING TO THEIR ALIGNMENT OF MAGNETIC MOMENT
5.8) MAGNETIC BOUNDARY CONDITIONS:THE BORDERS!

CHAPTER 6)  THE WAVE’S : TRANSMISSION LINES & ANTENNA'S

6.1) INTRODUCTION
6.1.1) WHAT IS TRANSVERSE WAVE?
6.1.2) LONGITUDINAL WAVE
6.1.3) THE PROBLEM
6.2)          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 POLARIZATION
6.5) TYPES OF WAVES
6.6)          WAVE EQUATIONS
6.6.1)       WAVE EQUATIONS FOR GOOD CONDUCTORS
6.7)     RELATIONBETWEEN ‘E’ AND ‘H’ ,THE CHARACTERISTIC OR INTRINSIC IMPEDANCE OF THE FREE SPACE OR TRANSVERSE NATURE OF WAVE
6.8)         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 MATERIALS
6.8.3)      REFLECTION AT THE SURFACE OF A CONDUCTING MEDIUM – NORMAL INCIDENCE
6.6)        POYNTING VECTOR AND POWER FLOW INELECTROMAGNETIC FIELDS
6.7)       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 SIGNIFICANCE
6.8)       INTRODUCTION TO ELECTROMAGNETICS & ANTENNAS.
6.9)       INTRODUCTION TO ELECTROMAGNETICS & WIRELESS COMMUNICATIONS.

### Dr. Sohel Rana

SASI Institute of Technology & Engineering, Tadepalligudem
Course Coordinator : Dr. Sohel Rana ( BE, M-tech, Phd ) received Bachelors of Engineering degree from Dr. BAMU, Aurangabad, India and M-Tech in VLSI & Embedded System from JNTU, Hyderabad, India. His teaching interests include the study of Electromagnetic fields, VLSI and Energy Harvesting, IOT, Embedded Systems etc. He has published two textbooks..