**Electromagnetic Theory I**

**Textbook**: *Classical Electrodynamics*, 3rd edition by J.D. Jackson

Lecture Notes Homework and Solution

- Lecture 1 – From Coulomb to Maxwell: charge, Coulombs law, the electric field, differential and integral form of Maxwell’s equations for electrostatics
- Lecture 2 – From Coulomb to Maxwell: Lorentz force, the magnetic field, current density, charge conservation and the definition of magnetostatics, Maxwell’s equations for magnetostatics, Faraday’s Law, Maxwell’s correction to Ampere’s Law, EM waves
- Lecture 3 – Systems of units, scalar and vector potentials, gauge invariance, Lorentz gauge, Coulomb gauge
- Lecture 4 – Longitudinal and transverse parts of a vector function, review Fourier transforms, physical meaning of the electrostatic potential, Green’s function, conductors in electrostatics
- Lecture 5 – Coulomb problem as a boundary value problem, electric field at a charged surface, Dirichlet vs Neumann boundary condition, examples, Green’s identities and uniqueness

Green’s functions, part II – Greens functions for Dirichlet and Neumann boundary conditions – we will not go over this in lecture.

- Lecture 6 – The image charge method for a charge in front of an infinite plane, and in front of a conducting sphere
- Lecture 7 – Separation of variables method in rectangular and polar coordinates
- Lecture 8 – Separation of variables method in spherical coordinates, Legendre polynomials

Green’s functions, part III – Eigenfunction expansion for the Greens function – we did not go over this in lecture, but it provides some of the theoretical basis for why the separation of variables method works

- Lecture 9 – Multipole expansion: monopole, dipole and quadrupole moments
- Lecture 10 – Multipole expansion continued, magnetostatics, magnetic dipole approximation
- Lecture 11 – Magnetostatic scalar potential, boundary conditions at a sheet current, examples
- Lecture 12 – Symmetry under parity transformations, Macroscopic Maxwell’s equations: dielectrics
- Lecture 13 – Macroscopic Maxwell’s equations: polarization density, electric dispacement field
**D**, magnetic materials, paramagnetism and diamagnetism, bound currents - Lecture 14 – Macroscopic Maxwell’s equations: magnetization density,
**H**field, bound surface current, conservation of bound charge, boundary conditions - Lecture 15 – Linear Materials: electric and magnetic susceptibilities, dielectric constant, magnetic permeability, atomic polarizability and the Clausius-Mossotti equation, boundary condition problems
- Lecture 16 – Point charge in a dielectric sphere, bar magnets, electromagnetism and conservation of energy
- Lecture 17 – Electromagnetic energy density, Poynting vector, conservation of momentum, Maxwell stress tensor, force on a conducting surface
- Lecture 18 – Capacitance matrix, inductance matrix, electromagnetic waves in a vacuum

Supplement – Force, torque, and interaction energy for electric and magnetic dipoles in an external field – we did not go over this in lecture.

- Lecture 19 – Energy and momentum in electromagntic waves, frequency dependent atomic polarizability, frequency dependent dielectric function
- Lecture 20 – Electromagnetic waves in a dielectric: transparent propagation, resonant absorption, total reflection
- Lecture 21 – Electromagnetic waves in conductors: frequency dependent conductivity, low frequency “good” conductors, skin depth, high frequencies, longitudinal modes and plasma oscillations
- Lecture 22 – Linear, circular and elliptical polarization, waves at interfaces, angles of incidence, reflection and transmission
- Lecture 23 – Snell’s law for transparent and dissipative media, total internal reflection, coefficient of reflection
- Lecture 24 -Total reflection, Brewster’s angle, Kramers-Kronig relation, Green’s function for the wave equation
- Lecture 25 – Lienard-Weichert potentials for a moving charged particle, potentials from a particle moving with constant velocity, radiation from a source oscillating with simple harmonic motion
- Lecture 26 – Electric dipole, magnetic dipole, and electric quadrupole radiation; fields, Poynting vector and radiated power
- Lecture 27 – Radiation from a general time dependent source, Larmor’s formula for radiation from an accelerating charge, special relativity, Lorentz transformation, 4-vectors
- Lecture 28 – Proper time, 4-velocity, 4-gradient, 4-current, 4-potential, field strength tensor and Maxwell’s equations
- Lecture 29 – Energy-momentum 4-vector, Lorentz force, relativistic Larmor’s formula

**ELECTROMAGNETIC THEORY II (Spring 2013)**

**Textbook:** Classical Electrodynamics (3rd Edition) by J. D. Jackson

**Lecture Notes, Homework Answers and Exam Solutions**

- Maxwell equations, plane vectors, polarization, Stokes parameters, Jones vector, reflection, refraction, Brewster’s angle, total internal reflection
- Complex permmitivity, resonant absorption, conductivity, plasma frequency
- Superposition of waves, group velocity, pulse spreading, dispersion, Kramers-Kronig relation
- Fields at the surface of an imperfect conductor, waveguide equations
- Rectangular waveguides, cutoff Frequency, resonant cavities, Q-factor
- Radiation, long-wavelength approximation, far-field waves, dipole radiation
- Linear antennas
- Long-wavelength scattering, polarization-dependent cross-sections, scattering by a small dielectric sphere, scattering matrix
- Scattering by a conducting sphere, atmospheric scattering
- Galilean relativity, ether, Einstein’s postulates
- Einstein’s principle of relativity, Lorentz transformations, Four-vectors
- Velocity addition in special relativity, relativistic momentum and energy
- Covariant geometry, covariant Maxwell’s equations

## electromagnetic waves

Introduction to Electromagnetics

**Text Book: **F.T. Ulaby, Fundamentals of Applied Electromagnetics, Prentice Hall 2009

*Lectures Video **The University of UTAH- Fall 2012*

**Course Material: **Introduction to electromagnetics. Fundamentals of wave propagation, transmission lines, impedance matching, electrostatics, magnetostatics, Maxwell’s equations, plane waves in free space, lossy media, and reflections from planar interfaces, wireless communication systems. Electromagnetic safety. Applications include wireless communication systems, high speed digital circuits, electromagnetic sensors, and bioelectromagnetics.

Textbook: *University Physics*, by Hugh D.Young, Roger Freedman and Lewis Ford, 13th edition

*Lectures Slides* – *LEHIGH University *1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28

* Homework Solutions*

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28

Course Materials

General Information

Schedule and Assignments

Equation Sheet

Handout on Optics

Handout on Waves

Coulomb’s Law with Vectors

Line Integrals

Integrals

Gauss’s Law

First Exam

information about the exam practice exam solution exam solution

Second Exam

information about the exam, a practice exam, and the solution to the practice exam. exam solution.

study guide, some practice problems on optics, and their solution

Electromagnetic fields and energy

*Electromagnetic* Fields and Waves

*Electromagnetic*Fields and Waves

Textbook: Electromagnetic Waves by David H. Staelin, Ann W. Morgenthaler, Jin A. Kong

### Lecture notes

Applications of electromagnetic fields and waves in industry and research.

Maxwell’s equations in integral and differential forms, electrostatics and magnetostatics, electroquasistatics and magnetoquasistatics.

Electrostatics, applications of Gauss’ Law in problem solving, applications of the superposition principle in problem solving, some simple charge distributions.

Electric scalar potential, Poisson equation, Laplace equation, superposition principle, problem solving.

Electrical conduction and perfect metals in electroquasistatics, solution of Laplace and Poisson equations with metal electrodes, boundary conditions, dielectric relaxation, image charges and method of images.

Capacitance, problems in Cartesian, Cylindrical and Spherical coordinates.

Material polarization, polarization charge and current densities, mathematics of polarization in electromagnetism, dielectrics vs conductors, boundary conditions.

Problems and examples involving material polarization, dielectrics, and boundary conditions.

Magnetoquasistatics, Ampere’s law, the vector potential, the vector Poisson equation, Biot-Savart law, magnetic fields of some simple current distributions, magnetic flux and the vector potential.

Magnetoquasistatics in the presence of perfect metals, boundary conditions, method of images, inductance, inductances of some simple structures.

Faraday’s Law and electromagnetic Induction, non-uniqueness of voltages in magnetoquasistatics, current-charge continuity equation in electromagnetism, power-energy continuity equation in electromagnetism, Poynting’s vector, electromagnetic energy and power flow and connection with electrical circuit theory

Energy, forces, and work in electromagnetics, forces between charged dielectrics and conductors, electromagnetic energy, forces, and work in closed systems and systems connected to voltage sources.

Electromagnetic wave equation, uniform plane wave solutions, Poynting vector.

Time-harmonic electromagnetic fields, phasors, complex version of Maxwell’s equations, complex Poynting vector.

Polarization states of plane waves, linearly polarized waves, circularly polarized waves, elliptically polarized waves, left-hand and right-hand circularly (or elliptically) polarized waves.

Wave propagation in isotropic media – dielectrics and conductors.

Wave propagation in isotropic media – plasmas, dispersive media, wave packets, phase and group velocities.

Wave propagation in anisotropic media, biaxial media, uniaxial media, half-wave plates, quarter-wave plates, birefringence.

Wave reflection and transmission at media interfaces, reflection and transmission coefficients, standing waves and standing wave ratio.

Non-normal incidence of waves at media interfaces, phase matching condition, reflection, refraction, Snell’s law, critical angle and evanescent waves, Brewster’s angle.

Transmission lines, types of transmission lines, fields, voltages and currents on transmission lines, transmission line equations, transmission line dispersion relations, transmission line impedances

Impedance transformations in transmission line RF and microwave circuits, equivalent circuit models, short load, open load, matched load, Thevenin equivalent circuit models, power dissipation.

G-Plane and Smith Charts, load matching and stub tuning, quarter wave transformers.

Lecture 23 Lecture 23 addition

Reflection and transmission for multilayer structures, AR and HR coatings, 1-dimensional photonic bandgap structures, multilayer structures for non-normal incidence (TE and TM waves).

Time domain analysis of transmission lines, transients.

Guided waves in parallel plate metal waveguides, TE and TM modes, dispersion characteristics and cut-off frequencies.

Guided waves in dielectric slab waveguides, TE and TM modes, dispersion characteristics and cut-off frequencies.

Guided waves in rectangular metal waveguides, TE and TM modes, dispersion characteristics and cut-off frequencies.

Radiation by time-varying currents and charges, retarded potentials in time-domain and for time-harmonic fields, wave equations for vector and scalar potentials, Hertzian dipoles, near- and far-fields, Poynting vector.

Hertzian dipoles, near- and far-fields, Poynting vector, antenna gain, radiation pattern, radiation resistance.

Hertzian dipoles, superposition principle for more than one Hertzian dipoles, gain and radiation pattern for two-element array of Hertzian dipoles.

Radiation from linear wire antennas, short-dipole, half-wave dipole, three-half-wave dipole, radiation from wire loop antennas, electric vs magnetic dipole antennas.

Circuit properties of transmitting antennas, antenna self-impedance and trans-impedance, receiving and transmitting antennas, antenna effective area, reciprocity and antenna theorem.

Antenna arrays, element factor and array factor, linear antenna arrays, phase arrays, binomial arrays, radiation patterns.

Electromagnetic scattering, Rayleigh scattering, scattering from a dielectric sphere, scattering-cross section and scattered radiation, scattering of sunlight in the atmosphere (why the sky is blue), radars, radar range equation.

Aperture antennas and electromagnetic diffraction, Fraunhoffer diffraction, rectangular apertures – radiation pattern and gain.

Reflector antennas, dish antennas, parabolic dish antennas

### Homeworks and solutions

**Electromagnetic Wave Propagation – ***Lund University*

*Lectures Notes*

- Gerhard Kristensson: Modeling of Electromagnetic Interaction with Matter.
- Text book: Sophocles J. Orfanidis: Electromagnetic Waves and Antennas:

- The propagation, reflection, and transmission of plane waves, and the analysis and design of multilayer films.
- Waveguides, transmission lines, impedance matching, and S-parameters.
- Linear and aperture antennas, scalar and vector diffraction theory, antenna array design, and coupled antennas.

Review of Maxwell’s equations, Lorentz force, constitutive relations, boundary conditions, charge and energy conservation, Poynting’s theorem, simple models of dielectrics, conductors, and plasmas, relaxation time in conductors.

Uniform plane waves in lossless media, monochromatic waves, wave impedance, polarization, waves in lossy media, waves in weakly lossy dielectrics, propagation in good conductors, propagation in oblique directions, complex waves, propagation in negative-index media, Doppler effect.

Ch.3: Pulse Propagation in Dispersive Media

Propagation filter, front velocity and causality, exact medium response examples, transient and steady-state behavior, pulse propagation and group velocity, group velocity dispersion and pulse spreading, propagation and chirping, dispersion compensation, slow, fast, and negative group velocities, chirp radar and pulse compression.

Ch.4: Propagation in Birefringent Media

Linear and circular birefringence, uniaxial and biaxial media, chiral media, natural vs. Faraday rotation, gyrotropic media, linear and circular dichroism, oblique propagation in birefringent media.

Ch.5: Reflection and Transmission

Reflection and transmission at normal incidence, propagation and matching matrices, reflected and transmitted power, single and double dielectric slabs, reflectionless slab, time-domain reflection response, lattice diagrams, reflection by a moving boundary, such as a moving mirror.

Multiple dielectric slabs at normal incidence, antireflection coatings, dielectric mirrors, propagation bandgaps, narrow-band transmission filters, quarter-wave phase-shifted Fabry-Perot resonators, fiber Bragg gratings, equal travel-time multilayer structures, applications of layered structures, Chebyshev design of reflectionless multilayers.

Oblique incidence and Snel’s laws, transverse impedance, propagation and matching of transverse fields, Fresnel reflection coefficients, total internal reflection, Brewster angle, complex waves, lossy media, Zenneck surface wave, surface plasmons, oblique reflection by a moving interface, geometrical optics, Fermat’s principle of least time, ray tracing techniques in geometrical optics illustrated by several exactly solvable examples drawn from several applications, such as atmospheric refraction, mirages, ionospheric refraction, propagation in a standard atmosphere and the effect of Earth’s curvature, and propagation in graded-index optical fibers, Snel’s law in negative-index media.

Ch.8: Multilayer Film Applications (revised Oct.28, 2010)

Multilayer dielectric structures at oblique incidence, lossy multilayers, frustrated total internal reflection, surface plasmon resonance, perfect lenses in negative-index media, antireflection coatings at oblique incidence, omnidirectional dielectric mirrors, polarizing beam splitters, reflection and refraction in birefringent media, Brewster and critical angles in birefringent media, multilayer birefringent structures, giant birefringent optics.

Longitudinal-transverse decompositions of Maxwell’s equations, power transfer and attenuation in guiding systems, TEM, TE, TM modes, rectangular waveguides, higher TE and TM modes, operating bandwidth, power transfer, energy density, and group velocity in waveguides, power attenuation, reflection model of waveguide propagation, dielectric slab guides.

Ch.10: Transmission Lines (revised Nov.13, 2010)

General properties of TEM transmission lines, parallel-plate, microstrip, coaxial, and two-wire lines, distributed circuit model of a transmission line, wave impedance and reflection response, two-port equivalent circuits, terminated lines, power transfer from generator to load, open- and short-circuited lines, Thevenin and Norton equivalent circuits, standing wave ratio, determination of unknown load impedance, Smith chart. Transient Response.

Coupled transmission lines, even-odd mode decomposition for identical matched or unmatched lines, crosstalk between lines, weakly coupled lines with arbitrary terminations, coupled-mode theory, co-directional couplers, fiber Bragg gratings as examples of contra-directional couplers, quarter-wave phase-shifted fiber Bragg gratings as narrow-band transmission filters, and the Schuster-Kubelka-Munk theory of diffuse reflection and transmission as an example of contra-directional coupling.

Conjugate and reflectionless matching, multisection transmission lines, quarter-wavelength impedance transformers, two-section dual-band Chebyshev transformers, quarter-wavelength transformers with series sections and shunt stubs, two-section series impedance transformers, single-stub matching, balanced stubs, double- and triple-stub matching, L-, T-, and Pi-section lumped reactive matching networks and their Q-factors.

Scattering parameters, power flow, parameter conversions, input and output reflection coefficients, stability circles, transducer, operating, and available power gains, generalized S-parameters and power waves, simultaneous conjugate matching, power gain circles, unilateral gain circles, operating and available power gain circles, noise figure circles, design examples of low-noise high-gain microwave amplifiers and their microstrip matching circuits.

Currents and charges as sources of fields, retarded potentials, fields of a linear wire antenna, near and far fields of electric and magnetic dipoles, Ewald-Oseen extinction theorem of molecular optics, radiation fields, radiation field approximation, computing the radiation fields, radiation vector.

Ch.15: Transmitting and Receiving Antennas

Energy flux and radiation intensity from a radiating system, directivity, gain, and beamwidth of an antenna, effective area, gain-beamwidth product, antenna equivalent circuits, effective length and polarization and load mismatches, communicating antennas, Friis formula, antenna noise temperature, system noise temperature, limits on bit rates, satellite links, radar equation.

Ch.16: Linear and Loop Antennas

Linear antennas, Hertzian dipole, standing-wave antennas, half-wave dipole, monopole antennas, traveling wave antennas, vee and rhombic antennas, loop antennas, circular and square loops, dipole and quadrupole radiation.

Ch.17: Radiation from Apertures

Field equivalence principle, magnetic currents and duality, radiation fields from magnetic currents, radiation fields from apertures, Kottler’s formula, Huygens sources, directivity and effective area of apertures, uniform, rectangular, and circular apertures and their gain-beamwidth products, Rayleigh diffraction limit, vector diffraction theory, Stratton-Chu, Kottler, Franz, and Kirchhoff diffraction integral formulas, extinction theorem, vector diffraction from apertures, Fresnel diffraction, Knife-edge diffraction, Fresnel zones, geometrical theory of diffraction and Sommerfeld’s solution for a conducting half-plane, Rayleigh-Sommerfeld diffraction theory and its connection to the plane-wave spectrum representation and to the field equivalence principle, Fresnel diffraction and Fourier optics, lenses.

Open-ended waveguides, horn antennas, horn radiation fields, horn directivity, optimum horn design, microstrip antennas, parabolic reflector antennas, gain and beamwidth of reflector antennas, aperture-field and current-distribution methods, radiation patterns of reflector antennas, dual-reflector antennas, lens antennas.

Antenna arrays and translational phase shift, array pattern multiplication, one-dimensional arrays, visible region, grating lobes, uniform arrays, array directivity, steering, and beamwidth.

Schelkunoff’s zero-placement method, Fourier series design method with windowing, sector beam array design, Woodward-Lawson frequency-sampling design, discretization of continuous line sources, narrow-beam low-sidelobe designs, binomial arrays, Dolph-Chebyshev arrays, Taylor one-parameter source, prolate arrays, Taylor n-bar distribution, Villeneuve arrays, multi-beam arrays, emphasis on the connections to DSP methods of digital filter design and spectral analysis of sinusoids.

Ch.21: Currents on Linear Antennas

Hallen and Pocklington integral equations, delta-gap, frill generators, and plane-wave sources, solving Hallen’s equation, sinusoidal current approximation, reflecting and center-loaded receiving antennas, King’s three-term approximation, evaluation of the exact kernel using elliptic functions, method of moments, pulse, triangular, NEC, and delta-function bases, Hallen’s equation for arbitrary incident field, solving Pocklington’s equation.

Near fields of linear antennas, improved near-field calculation, self and mutual impedance, coupled two-element arrays, arrays of parallel dipoles, Yagi-Uda antennas, Hallen equations for coupled antennas.

Physical constants, electromagnetic frequency bands, vector identities and integral theorems, Green’s functions, coordinate systems, Fresnel integrals, stationary phase approximation, cosine integrals, Gauss-Legendre quadrature, Lorentz transformations, list of MATLAB functions.

**solutions manual**

*Dr. Joe McCullough*

### Lecture Notes

Example Problems

Pencasts

**Applets and Animations**

- Radio Waves and EM Fields
- EM Wave Animation
- EM Wave
- Electromagnetic Waves
- Color Vision
- Additive Colors
- Doppler Effect Explanation
- Doppler Wave Fronts
- Doppler Effect
- Circular Polarization
- Polarizer

University of Maryland – **Electromagnetic Wave Propagation**

**Textbook**: D. Cheng, Fields and Wave Electromagnetics Second Edition, Addison Wesley, 1992.

*Lecture Notes*

Lecture 1 | Lecture 6 | Lecture 11 | Lecture 15 |

Lecture 2 | Lecture 7 | Lecture 12 | Lecture 16 |

Lecture 3 | Lecture 8 | Lecture 13 | Lecture 17 |

Lecture 4 | Lecture 9 | Lecture 14 | Lecture 18 |

Lecture 5 | Lecture 10 |

**Electromagnetic Waves** – Arizona State University-Fulton Schools of Engineering

**Electromagnetic Waves**– Arizona State University

Textbook: **Cheng, *** Field and Wave Electromagnetics*.

**Course Topics:**

** Supporting Materials:**

**Fundamentals of Applied ***Electromagnetics *

*Electromagnetics*

**NEWS:**A wide range of applets on transmission lines, electromagnetic waves and antennas, which appear on this web site, have been re-designed and incorporated in the companion CD-ROM for the Text book: “** Fundamentals of Applied Electromagnetics **” 6th Edition, by Ulaby, Michielssen and Ravaioli, , Download JAVA

*Fields and Waves in Communication Electronics -*Electromagnetic II

**Text Book**: Fields and Waves in Communication Electronics , S.Ramo, J.R.Whinery and T.Van Duzer, J.Wiley Inc., 1994

*Microwave Engineering*

*Microwave Engineering*

Overview of pertinent electromagnetics. Telegrapher equations for transmission lines. Power flow. Telegrapher equations for transmission lines. Power flow.Phasor wave solutions to the telegrapher equations. Termination of TLs.TL input impedance, time average power, return and insertion losses. VSWR.Generator and load mismatches on TLs. The Smith chart.Transmission line matching using lumped L networks.Single-stub tuning. TEM, TE, and TM modes for waveguides. Rectangular waveguide. Vector network analyzer. Transmission (ABCD) matrix. And more **Labs Additional Course Materials **Smith **chartsColor**

**Physics-Video Lectures**

**Electric Charge**,Electric Force and Fields,Fields due to continuous charge distributions ,Electric Flux and **Gauss’s Law**,Electric potential,Potential distributions , Capacitors,Dielectrics, Electric Current,Conduction and Electric Power,DC Circuits,Applying Kirchoff’s rules, RC circuits,Electrostatics review, Magnetic Fields, Magnetic Force,**Applications of Magnetic Force Ampere’s Law**,Biot-Savart Law,Magnetic Materials,Electromagnetic Induction , *Applications of Induction*, Inductance, Electromagnetism Review,AC Circuits I,AC Circuits II,Maxwell’s Equations, **Electromagnetic Waves** ,Reflection, Refraction, Lenses, Optical Instruments ,Interference, From interference to diffraction ,Diffraction,Diffraction gratings and polarization.

**Stony Brook Physics-****Video Lectures**

**Electromagnetic Waves and ***Optics*

*Optics*

School of Physics and Astronomy, Queen Mary, University of London

**Exams & solution** Lecture notes Reference

### Textbook: *Optics* by Eugene Hecht, 4th Ed

*Optics*

Part I: Electromagnetic Waves & Physical Optics.

1. Maxwell’s Equations & the Electromagnetic Wave Equation.

a) Maxwell’s equations in free space.

b) Maxwell’s equations in simple media.

2. Dielectric Interface & Fresnel’s Equations.

3. Waveguides.

4. Polarisation.

5. Superposition.

6. Diffraction.

Part II: Geometrical Optics.

1. Reflection & Refraction.

2. Instruments.

Part III: Quantum Optics.

1. Einstein Coefficients and the two level systems.

** Classical Electromagnetism Lectures Notes Vectors** :Introduction,

**Vector**algebra , Vector areas, The scalar product, The vector product, Rotation, The scalar triple product, The vector triple product, Vector calculus, Line integrals, Vector line integrals, Surface integrals, Vector surface integrals, Volume integrals, Gradient, Divergence, The Laplacian, Curl. …

**Coulomb’s law,The electric scalar potential, Gauss’ law, Poisson’s equation, Ampère’s experiments, The Lorentz force, Ampère’s law,Magnetic monopoles, Ampère’s circuital law, Helmholtz’s theorem, The magnetic vector potential, The Biot-Savart law,Electrostatics and magnetostatics….**

*Time-independent Maxwell equations:***Faraday’s law,Electric scalar potential, Gauge transformations, The displacement current, Potential formulation, Electromagnetic waves, Green’s functions, Retarded potentials, Advanced potentials, Retarded fields, Summary ….**

*Time-dependent Maxwell’s equations:***Electrostatic energy, Ohm’s law,Conductors,Boundary conditions on the electric field ,Capacitors ,Poisson’s equation,The uniqueness theorem, One-dimensional solution of Poisson’s equation, The method of images,Complex analysis, Separation of variables ….**

*Electrostatics:***Polarization, Boundary ,conditions ,Boundary value problems with dielectrics, Energy density within a dielectric medium,Magnetization,Magnetic susceptibility and permeability, Ferromagnetism,Boundary conditions, Boundary value problems with ferromagnets, Magnetic energy ….**

*Dielectric and magnetic media:***The Hertzian dipole,Electric dipole radiation, Thompson scattering,Rayleigh scattering, Propagation in a dielectric medium,,,Reflection at a dielectric boundary, Wave-guides…**

*Magnetic induction,,, ..Electromagnetic energy and momentum,,,, ..Electromagnetic radiation:***The Lorentz transformation, Transformation of velocities, Tensors,The physical significance of tensors,,,,The current density 4-vector,The potential 4-vector.**

*Relativity and electromagnetism:***Text book**: ** ‘Electricity and Magnetism‘** by W J Duffin (McGraw-Hill), 4

^{th}edition,,,

**and electric field, Electric potential energy,**

*Coulomb’s law***and capacitance, The electric dipole,**

*electric potential***E**-field and Gauss’s law,

**Dielectrics**, Magnetic fields and forces, Electromagnetic induction, Magnetic materials, Maxwell’s equations and displacement current, Electromagnetic radiation,

**, Propagation of**

*Electromagnetic radiation***electromagnetic waves in materials**. .

**Tutorial questions, Problem,**Homework,

**Lecture material..**

**Electromagnetic Theory**

**Electromagnetic Theory**, David Bowler’s Teaching Preliminaries, Macroscopic Fields, Atomic Mechanisms, Ferromagnetism, Maxwell’s Equations and Electromagnetic Waves, Reflection and Refraction at a Plane Dielectric Surface, Waves in Conducting Media, Energy Flow and the Poynting Vector, Emission of Radiation, Relativistic Transformations of Electromagnetic Fields,* A hand-out containing the important equations and figures from the lecture*.

*A hand-out containing the important equations and figures from the lecture*

**Lecture Notes,** *Visualization Applications***,** **Homework Answers,** *Exam Solutions*

**Text Book:** *Classical Electrodynamics* (3rd Edition) by J. D. Jackson

Coulomb’s law, **Gauss’s law**, Surface charge density, electric potential, Green functions, energy density, computational approaches, Method of images, point charge in the presence of a sphere, **Fourier series**, Laplace equation in rectangular coordinates, Laplace equation in polar coordinates, Laplace equation in spherical coordinates, Legendre polynomials, azimuthal symmetry, **Spherical harmonics**, Laplace equation in cylindrical coordinates, Green functions in spherical coordinates, Multipole expansions, Electrostatic fields in dielectrics, **energy in dielectrics**, Biot-Savart law, Ampere’s law, magnetic force, **vector potential**, Magnetic dipole fields, magnetostatics in magnetic material, Magnetostatics sample problems, **Faraday’s law of induction**, Maxwell equations, **Wave equation**, potentials of electrodynamics, **Green functions for the wave equation,** conservation of energy.

**Advanced Electromagnetic Waves**

**Textbook:** Constantine Balanis, Advanced Engineering Electromagnetics*.* John Wiley & Sons,,** Homework Answers**

**Lecture Notes,** **Homework Answers,** *Exam Solutions*

*Textbook: **College Physics, 9th Editionby Serway & Vuille; *Electric Forces and Electric Fields, Electric Energy and Capacitance, Current and Resistance, Direct Current Circuits, Magnetism, *Induced Voltage and Inductance*, Vibrations and Waves, Sound, Electromagnetic Radiation (Photons), Interaction of Photons with Matter, **Reflection and Refraction of Light**, Mirrors and Lenses, Wave Optics, Optical Instruments.

** Text Book** :

**elements of electromagnetics**5th edition sadiku,

**Lecture Notes**,, Magnetic circuits, Faraday’s law of induction, Lenz’s law, Faraday’s law examples, Faraday’s law and moving circuits, Displacement current and Ampère’s law, Maxwell’s equations, boundary conditions, Sinusoidal steady state, phasors, Maxwell’s equations and electrical circuits, Non-ideal behavior of physical circuit elements, Skin effect, Ideal transformer, Transmission lines and distributed l and c, Time domain solutions to TL ave equations, Transmission line termination, reflections, Current waves, Bounce diagrams, Pulse propagation on transmission lines, Time domain reflectometry, Sinusoidal steady state excitation of lossless transmission lines, Termination of transmission lines, Load reflection coefficient, Input impedance of TLs, Excitation and source conditions, Generalized reflection coefficient, Crank diagram, VSWR, Lossy transmission lines, Dispersionless TLs, Special cases of general TLs, Smith chart, TL matching, Quarter-wave transformers, Resistive pads, Single-stub tuner I – Analytical solution, Single-stub tuner II – Smith chart solution, Uniform plane waves, Infinite current sheets, Plane waves in lossy materials, Skin depth, Poynting’s theorem, Power flow and plane waves, Uniform plane waves normally incident on a lossless half space, Example of a normally incident UPW on a lossless half space, Electromagnetic radiation and antennas, Hertzian dipole antenna, Near and far fields of the Hertzian dipole antenna, Radiation resistance, Antenna radiation patterns, Directivity and gain, Antenna effective aperture, The Friis equation.

**Antennas and their System Applications**

**Antennas and their System Applications**

** Lectures, Homework’s solution exams**; Introduction to Antennas: Gain, Directivity, Solid-angle, Impedance, Polarization, Friis Transmission and Radar Equations: Some System Examples, Plane waves, Polarization, Wave Impedance, Poynting Vector, Radiation and Free-Space Green’s function, Vector and Scalar Potentials, Dipoles and Loops, Impedance of dipoles and loops, Ground planes and Image Theory (introduce a bit arrays using image theory), Traveling-Wave Antennas (radio amateur antennas and near-horizon communications), Array Theory and Phased Arrays: Use signal processing techniques to analyze arrays (gain, tapered distribution, amplitude and phase error effects, 1-D and 2-D arrays, etc.), Mutual Impedance in Arrays: The emf method. Not a lot of coverage, but enough to understand it. Classic Antennas: Dual-Dipole over a ground plane (symmetric pattern, array theory), Dipole backed by a corner reflector (array theory), Yagi-Uda (mutual coupling effect),electromagnetic waves Log Periodic (endfire feeding), Helical antennas (traveling waves on a circle and end-fire feeding arrangement), Spiral antennas (wideband self-mapping), Inverted F-Antennas (cell phones), antennas for circular polarization (other than the helical antenna), Equivalence Principle and Slot Antennas (do not cover cavity backed slots), Microstrip Antennas: The two-slot model (do not cover cavity model), Microstrip antenna arrays. Miniature Antennas (Cell phone applications), System level applications of antennas (MIMO, Multi-Beam, Phased Arrays, etc.)

*Electromagnetism*

*Electromagnetism*

*Text Book**: Physics for Scientists and Engineers, a Strategic Approach*, By Randall D.Knight, 2nd edition, ;;Charge model, Coulomb’s law, Electric field, Gauss’s Law, Electric potential, Potential and Field, Current and resistance, Fundamentals of circuits, Electromagnetic induction, Electromagnetic waves, AC circuits.. **Lecture Notes , Homework , Workshops , Sample Exams , Exam Solutions .**

**Introduction to Electricity and Magnetism, Light and Sound**

**Text Book** : R. A. Serway and J. W. Jewett, Jr. ** Physics for Scientists & Engineers** 6th ed;; Electric Fields , Gauss’ , Electric Potential , Capacitance and Dielectrics ,Current and , Direct Current Circuits , Magnetic Fields , Sources of the Magnetic Field , Faraday’s Law , Inductance , Alternating Current Circuits , Wave Motion ,Superposition and Standing Waves ,Electromagnetic Waves , Light and Geometrical Optics , Image Formation ,Interference of Light Waves .

homework solution, Exams solution Practice Exams .

**Electro & Magneto – Statics , **Maxwell Equations** , Electromagnetic Wave Guides , **Electromagnetic Radiation**. Lectures Note.**

**Physics Lecture Notes**

Electric Charge, Electric Fields, Gauss’ Law, Electric Potential, Capacitance, Current & Resistance, Circuits, Magnetic Fields, B Fields Due to Currents, Induction, Magnets & Maxwell’s equations, EM Oscillations, EM Waves **Lecture Notes**

I seldom comment, but I browsed a few of the remarks here

Electromagnetic Waves. I actually do have some questions

for you if you do not mind. Could it be only me or does it look like a few of these remarks appear like they are left

by brain dead people? And, if you are posting at additional sites, I would like to keep up with everything new you have to post.

Would you post a list of all of all your social sites like your twitter feed, Facebook page or

linkedin profile?

Woah this blog is great i really like studying your articles. Stay up the great work! You know, lots of individuals are hunting around for this info, you could aid them greatly.