 # Electromagnetic Theory

#### Features Includes:

• 180 - 3D/2D Animation
• 880 Pages of Content
• 60 Lecture Hours
• 165 Solved Problems
• 150 Quiz
• Suitable for All Technical University Syllabus

#### Course Description

This course provides an exhaustive coverage of Electrostatics, Conductor, Dielectrics, Magnetostatics, Maxwell's equations of Electrodynamic fields and Electromagnetic waves.

#### OBJECTIVES:

• To introduce the basic mathematical concepts related to electromagnetic vector fields
• To impart knowledge on the concepts of electrostatics, electrical potential, energy density and their applications
• To impart knowledge on the concepts of magnetostatics, magnetic flux density, scalar and vector potential and its applications
• To impart knowledge on the concepts of Faraday’s law, induced emf and Maxwell’s equations
• To impart knowledge on the concepts of Concepts of electromagnetic waves and Pointing vector.
###### UNIT I - VECTOR ANALYSIS AND ELECTROSTATICS

Sources and effects of electromagnetic fields - Introduction, Sources and effects of electromagnetic fields. Coordinate systems and vector fields - Introduction of scalar and vector,Cartesian or rectangular coordinate system, Representing a point in Rectangular coordinate system, Problem based on cartesian coordinate system, Differential elements in cartesian coordinate system, Problem based on cartesian coordinate system, Cylindrical coordinate system, Differential elements in cylindrical coordinate system, Problem based on cylindrical coordinate system, Spherical coordinate system, Differential elements in spherical coordinate system, Problem based on spherical coordinate system. Vector multiplication - Scalar or dot product of vectors, Properties of dot product, Applications of dot product, Vector or cross product of vectors, Properties of cross product, Applications of cross product, Products of three vectors. Transformation of vectors - Transformation of vectors from cartesian to cylindrical, Transformation of vectors from cylindrical to Cartesian, Problem based on cartesian to cylindrical and cylindrical to Cartesian, Transformation of vectors from cartesian to spherical, Transformation of vectors from spherical to Cartesian, Problem based on cartesian to spherical and spherical to Cartesian, Transformation of vectors from spherical to cylindrical, Transformation of vectors from cylindrical to spherical, Problem based on spherical to cylindrical and cylindrical to spherical,Distances in all coordinate systems. Types of integrals - Types of integral related to electromagnetic theory. Gradient, Divergence and Curl – Gradient, Divergence, Divergence Theorem, Problem based on divergence theorem, Applications of Divergence,Curl, Application of Curl, Types of Vector Fields, Problem based on divergence and curl of a vector, Problem based on curl, Problem based on vector field, Stoke’s Theorem, Problem based on stokes theorem. Coulomb’s law - Introduction to Coulomb's law and electric field intensity, Coulomb's law, Statement of Coulomb's law, Vector form of Coulomb's law, Force due to n number of charges, Steps to solve problems on Coulomb's law, Problem based on Coulomb's law. Electric field intensity - Electric field intensity, Method of obtaining E in cartesian system, Problem based on electric field intensity, Point charge, Line charge, Surface charge, Volume charge, Electric field Intensity due to various charge distributions. Electric field intensity using Coulomb’s law - Electric field due to infinite line charge, Problems on Coulomb's law, Electric field due to charged circular ring, Electric field due to infinite sheet of charge, To find surface area (dS), Problem based on Coulomb's law. Electric flux - Electric Flux, Properties of Flux lines, Electric Flux density, Vector Form of Electric Flux Density, Differential surface area due to a point charge, Electric Flux density for various charge distributions, Problem based on various charge distributions. Gauss’s law - Mathematical Representation of Gauss's Law, Special Gaussian Surfaces, Applications of Gauss's Law, To find electric flux density and electric field intensity using gauss’s law. Electric field intensity using Gauss’s law - Electric field due to infinite line charge using Gauss's law, Electric field due to infinite sheet of charge using Gauss's Law, Electric field intensity due to uniformly charged sphere, Electric field intensity due to spherical shell of charge, Gauss's Law Applied to Differential Volume Element, Problem based on gauss's law.

###### UNIT II - CONDUCTOR, DIELECTRIC AND CAPACITANCE

Electrical potential - Introduction, Work done, The line integral, Problem based on workdone, Potential difference, Potential due to point charge, Concept of absolute potential, Potential due to point charge not at origin, Potential due to several point charges, Problems on electric potential. Potential due to a line charge - Problems on potential due to a line charge, Potential due to volume charge, Problems on potential due to volume charge, Potential difference due to infinite line charge. Electrical field and Equipotential plots - Equipotential surfaces, Potential gradient, Relation between electric field and potential, Properties of gradient of a scalar, Problem based on electric field intensity, An electric dipole, Expression for electric field intensity due to electric dipole, Dipole moment, Utilization factor, Methode of images. Conductors - Current and current density, Relation between current density and volume charge density, Continuity equation, Resistance of a conductor, Properties of conductor, Relaxation time, Problem based on charge density. Dielectrics - Dielectric polarization, Mathematical expression for polarization, Properties of delectric materials. Dielectric strength - Dielectric strength, Problems on dielectric strength. Boundary conditions - Boundary conditions between conductor and free space, Electric field intensity at the boundary, Electric flux density at the boundary, Problem based on boundary conditions between conductor and free space, Boundary Conditions Between Two Perfect Dielectrics, Refraction of Electric flux density at the boundary. Capacitance - Classification of capacitor, Capacitors in series, Capacitors connected in parallel, Energy stored in a capacitor, Problem based on energy stored in capacitor, Capacitors with two dielectrics, Capacitance of a parallel plate capacitor with uniform dielectric, Capacitance of co-axial cable, Capacitance of co-axial cable with two dielectrics, Capacitance of spherical capacitor, Capacitance of an isolated spheres, Parallel conductor, Equipotential surface. Poisson’s and Laplace’s equations - Introduction, Poisson’s and laplace equations, Operation in different coordinate systems, Problem based on laplace equation, Uniqueness Theorem, Procedure for Solving Laplace's Equation, Problem based on laplace equation. Energy density - Energy density, Problem based on energy density, Applications.

###### UNIT III – MAGNETOSTATICS

Introduction - Magnetic field and its properties, Magnetic field due to current carrying conductor, Magnetic field intensity. Biot-Savart law - Biot-Savart law, Biot-Savart law interms of Distributed sources, Problem based on Biot-Savart law. Magnetic field intensity using Biot Savart law - Magnetic field intensity (H) due to infinitely long straight conductor, Magnetic field intensity (H) due to straight conductor of finite length, Magnetic field intensity (H) at the centre of a circular conductor, Magnetic field intensity (H) on the axis of a circular loop, Problem based on Magnetic field intensity using Biot Savart law. Magnetic field intensity using Ampere circuital law - Ampere circuital law, Steps to apply Ampere’s circuital law, H due to infinitely long straight conductor, Magnetic field intensity H due to a co-axial cable using ampere circuit law, Magnetic field intensity H due to a infinite sheet of current using ampere's circuital law, H due to cylindrical conductor, Problem based on Magnetic field intensity using Ampere circuital law. Curl in magnetostatics - Curl in various coordinate system, Physical significance of a Curl, Problem based on Curl in magnetostatics. Stoke’s Theorem - Problem based on stoke's theorem, Magnetic Flux and Flux density, Maxwell’s equation for static Electromagnetic Fields, Application of flux density and flux to co-axial cable. Magnetic scalar and vector potential - Magnetic scalar and vector potential, Laplace’s equation for scalar magnetic potential. Problems based on magnetic scalar and vector potential - Problems based on magnetic scalar and vector potential. Magnetization - Magnetization and Permeability, Problem based on magnetization and permeability. Nature of Magnetic materials - Origin of Magnetic Dipole Moment in the Material, Classification of Magnetic Materials, Comparison between different types of magnetic materials. Boundary conditions - Magnetic boundary conditions, Boundary conditions for normal component, Boundary conditions for tangential component, Problem based on Magnetic boundary conditions. Poisson’s Equation - Poisson's Equation for Magnetic Field. Magnetic Force - Introduction, Force on a moving point charge, Problem based on force on a moving point charge, Force on a differential current element, Force between Two Parallel Conductors. Magnetic torque - Magnetic torque and magnetic dipole moment, Magnetic moment of a planer coil, Magnetic dipole moment, Magnetic dipole, Problem based on Magnetic torque and magnetic dipole. Inductance - Introduction, Self inductance, Mutual inductance, Coefficient of coupling between two circuits, Inductance of a solenoid, Inductance of a toroid, Inductance of a co-axial cable, Mutual inductance between a long, straight wire and rectangular loop laying in same plane. Energy density - Magnetic energy, Problem based on energy density. Applications - Applications of Magnetic material, Ferrite cores, Magnetic recording, Principle of Tape recorders, Methods of recording, Direct recording, Frequency Modulation recording, Magnetic Shielding, Magnetic stripe in credit and debit cards, Magnetic levitation transport.

###### UNIT IV - ELECTRODYNAMIC FIELDS

Magnetic circuits - Introduction, Analogy between the electric circuit and magnetic circuit, Dissimilarities between the electric and magnetic circuit, Static fields and dynamic fields. Faraday’s Law - Introduction, Statement of Faraday's law and Lenz’s law. Transformer and motional EMF - A Stationary loop in a time varying magnetic field – Transformer E.M.F., A moving loop in a static magnetic field – Motional E.M.F., Moving closed path in a time varying magnetic field, Faraday's disc generator, Problem based on induced emf. Displacement current - Displacement current density and displacement current, Physical significance of displacement current, Problem based on displacement current density and displacement current, Equation of continuity for time varying fields, Inconsistency of Ampere’s circuit law. Maxwell’s equations - Introduction, Maxwell's equations for static fields, Maxwell’s equations for time varying fields, Maxwell’s equations for free space, Maxwell's equations for good conductor, Maxwell's equations for harmonically varying fields, Boundary conditions for time varying fields, Retarded potentials, Phasor representation of a vector. Relation between field theory and circuit theory - Comparison between field theory and circuit theory. Applications - Applications of Electrodynamics Fields, Transformers, Magnetic brake, Induction heating, Magnetic levitation, Electromagnetic propulsion of ships and submarines, Electromagnetic launcher, Electromagnetic forming, Eddy current testing of materials, Magneto hydrodynamic (MHD) generator.

###### UNIT V - ELECTROMAGENTIC WAVES

Electromagnetic wave generation and equations – Introduction, General wave equation, Uniform plane waves in free space. Wave parameters - velocity, intrinsic impedance,propagation constant - Phase velocity, Relationship between E and H in free space - Concept of Intrinsic Impedance, Propagation constant, Wavelength, Equations describing propagation of electromagnetic waves, Equations describing propagation of electromagnetic waves. Waves in free space - Electromagnetic wave equations in phasor form, Problem based on electromagnetic wave equations, Uniform plane waves in perfect (or Lossless) dielectric, Problem based on Uniform plane waves in perfect (or Lossless) dielectric. Lossy dielectrics - Uniform plane waves in lossy dielectric. Lossless dielectrics - Uniform plane wave in practical dielectric, Problem based on Lossless dielectrics. Waves in Conductors - Uniform plane waves in good conductor, Problem based on uniform plane waves in good conductor. Poynting vector - Poynting vector and poynting theorem, Average power density (Pavg), Integral and point forms of poynting theorem, Power flow in Co-axial cable, Instantaneous, Average and Complex poynting vector, Power loss in a plane conductor, Problem based on power loss. Plane wave reflection and refraction - Polarization of uniform plane waves, Linear polarization, Elliptical polarization, Circular polarization, Conditions for the polarization of a sinusoidal wave, Reflection of uniform plane waves, Normal incidence at plane dielectric boundary, Normal incidence at plane conducting boundary, Standing Wave Ratio (SWR), Oblique incidence of uniform plane waves, Direction cosines, Oblique incidence at a plane conducting boundary, Vertical polarization, Oblique Incidence at a plane dielectric boundary, Total reflection, Horizontal polarization (Perpendicular polarization), Vertical polarization (Parallel polarization). Problems on Plane wave reflection and refraction - Problems on Plane wave reflection and refraction. Applications - Superconducting Power Transmission, Fiber Optic Magnetometer.