1. Elements of electromagnetic field theory and guided waves
Joule’s law in differential and integral form
Time-varying current: Inductance
Time-varying currents: capacitance
Method of phasors (complex amplitudes)
Complex impedances
Maxwell’s equations for field phasors
Time-dependent wave equation
Helmholtz’ wave equation
Plane wave

2. Joule’s law Elemental volume dV=Sdl J 2 1 l Differential form
Area S
Elemental volume dV=Sdl J
Differential form 2 1 l
Integral form

3. Time-varying current. Capacitance
EMFext R 1 2
Process of recharging:

4. Time-varying current. InductanceBI
eext
Definition of L
Process of self-inductance
I(t)

5. Method of phasors Series LRC-circuit with external EMF e:
Let it be cos wt
Finally, one can find both amplitude
and phase of the real
current i(t)
So simple!

6. Complex impedances, Ohm’s and Kirchhoff laws for current and voltage phasors
ZL=jwL
ZC=1/jwC
ZR=R or
General
notation
Impedance
Notation r
V=IZ Es Z

7. Maxwell equations for field phasors

8. Wave equation for source-free regions (r=J=0)
Apply
axbxc=b(ac)-c(ab)
(Recall 3d Maxwell’s equation)
Time-harmonic case: k=w/u - wave number
Wave equation
For phasors it
is the so-called
Helmholtz’
equation
phase velocity

9. Plane wave in free space
Wave number in free space
Forward wave
Backward wave y
E=Ex
z=ct - wave front z
z=ray
t=0
t=p/2w