by Nannapaneni Narayana Rao Edward C. Jordan Professor Emeritus of Electrical and Computer Engineering University of Ill

1. Fundamentals of Electromagneticsfor Teaching and Learning:A Two-Week Intensive Course for Faculty inElectrical-, Electronics-, Communication-, and Computer- Related Engineering Departments in Engineering Colleges in India by Nannapaneni Narayana Rao Edward C. Jordan Professor Emeritus of Electrical and Computer Engineering University of Illinois at Urbana-Champaign, USA Distinguished Amrita Professor of Engineering Amrita Vishwa Vidyapeetham, India

2. Program for Hyderabad Area and Andhra Pradesh FacultySponsored by IEEE Hyderabad Section, IETE Hyderabad Center, and Vasavi College of EngineeringIETE Conference Hall, Osmania University CampusHyderabad, Andhra PradeshJune 3 – June 11, 2009Workshop for Master Trainer Faculty Sponsored byIUCEE (Indo-US Coalition for Engineering Education)Infosys Campus, Mysore, KarnatakaJune 22 – July 3, 2009

3. Module 5 • Materials and Wave Propagation in Material Media • 5.1 Conductors and dielectrics • 5.2 Magnetic materials • 5.3 Wave equation and solution • 5.4 Uniform waves in dielectrics and conductors • 5.5 Boundary conditions • 5.6. Reflection and transmission of uniform plane waves

4. Instructional Objectives • 31. Find the charge densities on the surfaces of infinite plane • conducting slabs (with zero or nonzero net surface charge • densities) placed parallel to infinite plane sheets of charge • 32. Find the displacement flux density, electric field intensity, • and the polarization vector in a dielectric material in the • presence of a specified charge distribution, for simple • cases involving symmetry • 33. Find the magnetic field intensity, magnetic flux density, • and the magnetization vector in a magnetic material in the • presence of a specified current distribution, for simple • cases involving symmetry

5. Instructional Objectives (Continued) • 34. Determine if the polarization of a specified • electric/magnetic field in an anisotropic • dielectric/magnetic material of permittivity/permeability • matrix represents a characteristic polarization • corresponding to the material • 35. Write expressions for the electric and magnetic fields of a • uniform plane wave propagating away from an infinite • plane sheet of a specified sinusoidal current density, in a • material medium • 36. Find the material parameters from the propagation • parameters of a sinusoidal uniform plane wave in a • material medium • 37. Find the power flow, power dissipation, and the electric • and magnetic stored energies associated with electric and • magnetic fields in a material medium

6. Instructional Objectives (Continued) • 38. Determine whether a lossy material with a given set of • material parameters is an imperfect dielectric or good • conductor for a specified frequency • 39. Find the charge and current densities on a perfect • conductor surface by applying the boundary conditions • for the electric and magnetic fields on the surface • 40. Find the electric and magnetic fields at points on one side • of a dielectric-dielectric interface, given the electric and • magnetic fields at points on the other side of the interface • 41. Find the reflected and transmitted wave fields for a given • field of a uniform plane wave incident normally on a • plane interface between two material media

7. 5.1 Conductors • and Dielectrics • (EEE, Secs. 4.1, 4.2; FEME, Sec. 5.1)

8. Materials Materials contain charged particles that under the application of external fields respond giving rise to three basic phenomena known as conduction, polarization, and magnetization. While these phenomena occur on the atomic or “microscopic”scale, it is sufficient for our purpose to characterize the material based on “macroscopic” scale observations, that is, observations averaged over volumes large compared with atomic dimensions. 8

9. Material Media can be classified as • (1) Conductors • and Semiconductors • (2) Dielectrics • (3) Magnetic materials – magnetic property • Conductors and Semiconductors • Conductors are based upon the property of conduction, the phenomenon of drift of free electrons in the material with an average drift velocity proportional to the applied electric field. electric property

10. In semiconductors, conduction occurs not only by electrons but also by holes – vacancies created by detachment of electrons due to breaking of covalent bonds with other atoms. The conduction current density is given by Ohm’s Law at a point

11. The effect of conduction is taken into account explicitly by using J = Jc on the right side of Maxwell’s curl equation for H. conductors semiconductors

12. s Ohm’s Law Ohm’s Law Resistance

13. D4.1 (a) For cu, (b) 5-12

14. (c) From

15. Conductor in a static electric field

16. Plane conducting slab in auniform electric field rS0 E = – az –rS0 rS0 e0 5-15 5-15 rS = e0E0 rS = e0E0 rS = –e0E0 rS = e0E0 rS = –e0E0 rS = e0E0

17. P4.3 (a) 5-16

18. (b) 5-17 (1) (2) Write two more equations and solve for the four unknowns.

19. 5-18 Solving the four equations, we obtain

20. Dielectrics are based upon the property of polarization, which is the phenomenon of the creation of electric dipoles within the material. Electronic polarization: (bound electrons are displaced to form a dipole) Dipole moment p = Qd

21. Orientational polarization: (Already existing dipoles are acted upon by a torque) Direction into the paper. Ionic polarization: (separation of positive and negative ions in molecules)

22. The phenomenon of polarization results in a polarizationcharge in the material which produces a secondary E. 11

23. Plane dielectric slab in a uniform electric field

24. Polarization Current (in the time-varying case)

28. 5-27 The effect of polarization needs to be taken into account by adding the contributions from the polarization charges and the polarization current to the right sides of Maxwell’s equations. For free space,

29. 5-28 For dielectrics, Where Pis the polarization vector, or the dipole moment per unit volume. Rearranging, where now,

30. Thus, to take into account the effect of polarization, we define the displacement flux density vector, D, as vary with the material, implicitly taking into account the effect of polarization.

31. 5-30 As an example, consider Then, inside the material,

32. D4.3 For 0 < z < d, (a)

33. 5-32 (b) (c)

34. 5-33 Isotropic Dielectrics: D is parallel to E for all E. Anisotropic Dielectrics: D is not parallel to E in general. Only for certain directions (or polarizations) of E is D parallel to E. These are known as characteristic polarizations.

36. 5-35 D4.4 (a)

37. 5-36 (b)

38. 5-37 (c)

39. Review Questions • 5.1. Distinguish between bound electrons and free electrons • in an atom. • 5.2. Briefly describe the phenomenon of conduction. • 5.3. State Ohm’ law valid at a point, defining conductivity. • How is conduction current taken into account in • Maxwell’s equations? • 5.4. Discuss the formation of surface charge at the boundaries • of a conductor placed in a static electric field. • 5.5. Briefly describe the phenomenon of polarization in a • dielectric material. What are the different kinds of • polarization? • 5.6. What is an electric dipole? How is its strength defined?

40. Review Questions (Continued) • 5.7. Discuss the effect of polarization in a dielectric material, • involving polarization charge and polarization current. • 5.8. What is the polarization vector? How is it related to the • electric field intensity? • 5.9. Discuss how the effect of polarization in a dielectric • material is taken into account in Maxwell’s equations. • 5.10. Discuss the revised definition of the displacement flux • density and the permittivity concept. • 5.11. What is an anisotropic dielectric material? When can an • effective permittivity be defined for an anisotropic • dielectric material?

41. Problem S5.1. Finding the electric field due to a point charge in the presence of a conductor

42. Problem S5.1. Finding the electric field due to a point charge in the presence of a conductor (Continued)

43. Problem S5.2. Finding D, E, and P for a line charge surrounded by a cylindrical shell of dielectric material

44. Problem S5.3. Expressing an electric field in terms of the characteristic polarizations of an anisotropic dielectric

45. 5.2 Magnetic Materials(EEE, Sec. 4.3; FEME, Sec. 5.2)

46. Magnetic Materials are based upon the property of magnetization, which is the phenomenon of creation of magnetic dipoles within the material. Diamagnetism: A net dipole moment is induced by changing the angular velocities of the electronic orbits. Dipole moment m = IAan

47. Paramagnetism: Already existing dipoles are acted upon by a torque. Other:Ferromagnetism, antiferromagnetism, ferrimagnetism

48. The phenomenon of magnetization results in a magnetizationcurrent in the material which produces a secondary B.

50. Magnetization Current