Fall 2013 Notes 2 ECE 6340 Intermediate EM Waves Prof. David R. Jackson Dept. of ECE 1

Constitutive Relations Free Space: Since 1983, Also, (exact value) 2

Constitutive Relations Lorentz Force law (review): Particle Wire C The current i is the current flowing on the wire in the direction of the contour C. 3

Constitutive Relations (cont.) I I d FxFx Definition of I = 1 Amp: Hence x # 1 # 2 Two infinite wires carrying DC currents 4

Constitutive Relations (cont.) Phasor Domain: 5

Simple Linear Media Atomic picture: rr Dipoles -q q d Dipole moment of single molecule: 6 There is a simple linear relationship between the fields in the time domain, and there is thus no loss due to molecular or atomic friction.

Simple Linear Media (cont.) Applied electric field: Dipole moment per unit volume: Torque on dipole: rr Electric dipoles -q q E

Simple Linear Media (cont.) Simple linear media: so Then Definition of D vector: Dipole moment per unit volume: Note that usually  e > 0 Define: 8 Note: E is the average electric field inside the material (what we would use to calculate macroscopic voltage drop).

so a i Simple Linear Media (cont.) Magnetic media: Definition of H vector: Magnetic moment per unit volume: rr i Torque on dipole: Magnetic dipoles 9 Each magnetic dipole acts like a small bar magnet. N S

Simple linear media: so Simple Linear Media (cont.) or 10 Note: B is the average magnetic field inside the material.

Then Simple Linear Media (cont.) Define: 11

Summary Phasor Domain: 12 Simple Linear Media Note: For simple linear media the relative permittivity and permeability are real.

Generalized Linear Media Phasor Domain: Define: Then: Similarly: (complex) friction term 13 We still have a linear relationship in the phasor domain. This accounts for molecular or atomic friction, which results in material loss.

Anisotropic Media 14

Anisotropic Media (cont.) Isotropic: Uniaxial: Teflon Fibers 15

Anisotropic Media (cont.) Biaxial: Ferrite: is not symmetric! 16

Summary of Possible Media Simple: The permittivity is real. Generalized: The permittivity is complex. 17