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Electromagnetics
Mojtaba Dehmollaian
Introduction
In this course, we study the following topics
• Vector analysis
• Electrostatics
• Special techniques
• Electric fields in matter
• Magnetostatics
• Magnetic fields in matters
discussed in the first 7 chapters of the following text books
• D. K. Cheng Field and Wave Electromagnetics, 2nd ed., Addition Wesley, 1989,
• D. J. Griffiths, Introduction to Electrodynamics, 3rd ed., Prentice Hall, 1999,
and the first thirteen chapters of
• M. H. Nayfeh and M. K. Brussel, Electricity and Magnetism, John Wiley and
Sons, 1985.
Further excellent references are
• W.R. Smythe, Static and Dynamic Electricity, McGraw-Hill, 1950.
• J. D. Jackson, Classical Electrodynamics, 3rd edition, John Wiley and Sons, 1999.
• E. M. Purcell, Electricity and Magnetism, Berkeley Physics Course Vol. 2, 2nd
ed., 1965.
The total (20-point) grade is calculated by adding
• 7 points of midterm,
• 8 points of final, and
• 5 points of (11) homework assignments and (6) quizzes.
Notes:
• HW assignments are assigned almost every week and due the following week.
• HW assignments may involve writing a computer program with MATLAB.
• Although midterm and final exams’ questions are divided into electricity and
magnetism, respectively, the theories behind the questions are closely related.
The following is a tentative outline, presented in order.
Vector Analysis
1. * Electric field, electric potential, curvilinear transformations, differential
calculus; gradient, divergence, curl, null identities.
2. Helmholtz theorem, uniqueness theorem, Dirac delta function. HW#1
Electrostatics
3. Potential of a localized charge distribution and multipole expansion.
4. Multipole expansion (cont.), work and energy in electrostatics, conductors, and
uniqueness theorem in a system of conductors. HW#2
5. Conductors (cont. with examples), calculation of field lines for a set of point
charges in a row.
6. Quiz 1
7. Conductors (surface charge density and force on a conductor), Ohm’s law
(resistors), continuity equation, boundary condition of current distribution, and
power dissipation and Joule’s law. HW#3
8. Quiz 2, uniqueness of Laplace’s equation, image method (conducting infinite
plane and conducting sphere)
9. Image method (conducting cylinder), examples of image methods (i.e., infinite
ground plane and conducting sphere). HW#4
Special Techniques
10. *More examples on image theory (conducting cylinder), Laplaces’s equation in
Cartesian and cylindrical coordinates, separation of variables.
11. Laplace’s equation in spherical coordinates, solution of electrostatic boundary
value problems with dielectrics. HW#5
Electric Fields in Matter
12. Dielectrics, induced dipoles, polarization, bound charges, physical interpretation
of bound charges, the field inside dielectrics, electric displacement, electrostatic
boundary conditions.
13. Quiz 3, Electric flux density, Gauss’s law in the presence of dielectrics,
(susceptibility, permittivity, dielectric constant), boundary value problems
(dielectric sphere in presence of uniform electric fields), energy in dielectric
systems, and forces in dielectrics. HW#6
14. Electrostatic forces, energy stored in a capacitor(s), system of conducting bodies.
15. Midterm
Magnetostatics
16. Magnetic fields, Ampere’s law, magnetic vector potential, the Biot-Savart law,
the Lorentz force law. HW#7
17. Examples (applications of Ampere’s law, computing magnetic vector potential),
magnetic dipole.
18. Multipole expansion of the vector potential, magnetic force and torque,
G
magnetization vector M . HW#8
Magnetic Fields in Matter
19. The field of a magnetized object, bond currents, physical interpretation of bound
currents, magnetic field inside matter, auxiliary field H, scalar magnetic potential,
equivalent magnetic charges.
20. Examples on computing fields using magnetic currents and/or magnetic charges,
examples on Laplace’s equation in magnetostatic problems. HW#9
21. Quiz 4, *Magnetic materials, boundary conditions, solving boundary problems
using Laplace’s equation and image theory.
22. Magnetic circuits, inductances, coaxial cable. HW#10
23. Magnetic energy, Faraday’s induction law, mutual inductances L12 = L21 , magnetic
energy in terms of fields, magnetic force on a current loop.
24. Magnetic torques and forces. HW#11
25. Quiz 5, Faraday’s induction law, stationary/moving circuits in stationary/moving
magnetic fields.
26. Ferromagnetic transformer, eddy currents, examples and review.
27. Quiz 6
*
Powerpoint presentation