[Japanese/English]

Electromagnetic Theory

Takuichi Hirano, Japan

1. Polarization, standing wave, reflection and transmission

Differential Forms in Electromagnetic Theory

Brigham Young University
Department of Electrical and Computer Engineering
459 Clyde Building, Provo, Utah 84602

Richard H. Selfridge, David V. Arnold and
Karl F. Warnick

The differential forms research group at BYU is investigating the use of the calculus of differential forms in teaching and research. Differential forms have been used to express Maxwell’s laws since early in this century, but many of the advantages of forms as a tool for applied electromagnetics have only recently been discovered. Relative to the usual vector analysis treatment, differential forms make elementary electromagnetics clearer, simpler, and more intuitive. At the same time, differential forms are a powerful tool for research, and open the way for the application of powerful tools of modern differential geometry to electromagnetics. The purpose of this website is to make available publications and course materials to those interested in differential forms and their use in research and teaching.

Download the latest EM theory course notes, also available in pdf form.

Electromagnetics using differential forms with problems and solutions: K. Warnick and P. Russer, Problem Solving in Electromagnetics, Microwave Circuit, and Antenna Design for Communications Engineering, Norwood, MA: Artech House, 2006.

Teaching/Course Materials | Research | Publications For more information, contact warnick@ee.byu.edu.
Last revised Sep. 21, 2006

Polarization

Animation of polarization

Condition for a circularly polarized wave radiation by two linearly polarized waves (in Japanese)

Condition to realize a circularly polarized wave by two linearly polarized waves

Standing wave

Animation of standing wave

Reflectin and transmission

Reflection and transmission of a plane wave, reflection law (Fermart’s principle), refraction law (Snell’s law), Fresnel’s reflection and transmission coefficients, etc.

2. Radiation from the source

Electric dipole

Animation of electric force lines of electric dipole

Small dipole antenna

Animation of electromagnetic field radiated from the small dipole

Half-wavelength dipole antenna

Animation of electromagnetic field radiated from the half-wavelength dipole antenna
(Method of Moments analysis)

1.5-wavelength antenna

Animation of electromagnetic field radiated from the 1.5-wavelength antenna
(Method of Moments analysis)

Radiation Pattern of a Dipole Antenna As a Function of Dipole Length

Current distribution is approximated by sine

Electrostatic field and electromagnetic field

Comparison between electrostatic field and electromagnetic field

Field Equivalence Theorem (in Japanese)

Field Equivalence Theorem

3. Diffraction by a half-infinite ground plane

Diffraction by a half-infinite ground plane

Animation of diffraction by a half-infinite ground plane (FDTD analysis)

4. Radiation from the small dipole (transient)

Radiation from the small dipole (transient)

Animation of radiation from the small dipole (transient) (FDTD analysis)

5. Modal Analysis

Modal Analysis

Modal Analysis for waveguides

6. Microwave Circuits

Scatterers in a waveguide and its equivalent electric circuit model

Mechanism of a choke and stub

7. Analysis Methods for Electromagnetics

Method of Moments (MoM), Moment Method

Spectral Domain Approach (SDA) (PDF)

8. Antenna

Array Antennas

9. Signal Processing of Measured Field

• Transformation of Observation Plane by Decomposition of Field into Plane Wave Spectrum (in Japanese) (PDF)
  • Example of Mathematica Programming (PDF)

Electromagnetic Interactions Fundamental electromagnetic interactions occur between any two particles that have electric charge. These interactions involve the exchange or production of photons. Thus, photons are the carrier particles of electromagnetic interactions. Electromagnetic decay processes can often be recognized by the fact that they produce one or more photons (also known as gamma particles). They proceed less rapidly than strong decay processes with comparable mass differences, but more rapidly than comparable weak decays. Forces Within Atoms Electromagnetic interactions are responsible for the binding force that causes negatively charged electrons to combine with positively charged nuclei to form atoms. Forces Between Atoms Residual electromagnetic interactions between electrically neutral atoms are responsible for the binding of atoms to form molecules and most of the forces (apart from gravity) that we experience in everyday life. Molecular binding effects result from atoms sharing and/or exchanging electrons.  The rigidity of the floor supporting you, the friction between your feet and the floor that allows you to walk, the pull of a rubber band on your finger, and the feel of the wind in your faces are all due to residual electromagnetic interactions.  Forces such as these result from the changes in energy due to repositioning of electrons or atoms as material is deformed by contact with other material. Electromagnetic Fields and Electromagnetic Waves Electromagnetic interactions are also responsible for electric and magnetic field formation around electric charges and electric currents, and for traveling electromagnetic waves such as light, radio-waves, x-rays, and microwaves. All these phenomena are electromagnetic waves and differ only in wavelength. In the quantum field theory, any changing electromagnetic fields or electromagnetic waves can be described in terms of photons. When there are many photons involved, the effects are equally correct (and more simply) given by the earlier non-quantum theory, namely Maxwell’s equations. Photons produced in radioactive decays are also called (”gamma”) particles, originally called x-rays.

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