Electromagnetic Wave Theory

1. Series: EMF Theory
Lecture: #0.00
Dr R S Rao
Professor, ECE
Electrostatic fields, steady magnetic fields, Dynamic fields, force, displacement/flux,
potentials, power, Maxwell’s equations, wave equations, UPWs, wave polarization.
Passionate
Teaching
Joyful
Learning

2. Electromagnetic
Field
Theory
2
• Electromagnetic Field Theory,
in short, Field Theory
• Electromagnetic Wave Theory,
in short, Wave Theory
Title:

3. Electromagnetic
Field
Theory
3
• Communications are mostly electrical,
• Electrical Communications are mostly wireless,
• Wireless Communications use antennas,
• Antennas functioning is based on EM radiation,
• EM radiation is property of dynamic fields.
Why Study Field/Wave Theory:
Hence, ECE students & engineers need to have solid grip
over EM Wave theory

4. Electromagnetic
Field
Theory
4
Circuit Theory:
• Easy but approximate
• Low frequencies validity
• 1D and scalar
• Voltage and currents
• Lumped elements
• Negligible Radiation
• No wave phenomenon
Circuit theory versus
Field theory

5. Electromagnetic
Field
Theory
5
Field/Wave Theory:
Circuit theory versus
Field theory
• Complex but exact
• All frequencies validity
• 3D and vector
• Electric and magnetic fields
• Distributed parameters
• Radiation taken into account
• Wave phenomenon

6. Electromagnetic
Field
Theory
6
• Vector Calculus:
 Gradient, Divergence and Curl
 Gradient theorem, Divergence theorem and
Curl theorems
• Coordinate systems:
 Rectangular, Cylindrical and Spherical
 Differential length, area and volume
Pre-requisites:

7. Electromagnetic
Field
Theory
7
Div and Curl:
Examples:
•Electrostatic field in charge free region is both solenoidal and irrotational.
•Steady magnetic field in a current carrying conductor is solenoidal but not
irrotational.
•Electrostatic field in charged region is not solenoidal but irrotational.
•Electric field in a charged region with a time varying magnetic field is neither
solenoidal nor irrotational.
Field F is solenoidal if .F=0 and irrotational if ×F=0.

8. Electromagnetic
Field
Theory
8
1. Static fields: Invariant with time
1.1.Electrostatic fields→ static charge distributions
1.2.Steady magnetic fields→ steady currents
2. Dynamic fields: Variant with time
2.1.Time varying fields → Time varying currents/
Acc. charges
2.2.EM Waves → Time varying fields
Parts in Field/Wave Theory:

9. Electromagnetic
Field
Theory
9
1.1.Electrostatic Field:
•Force → Coulomb’s law
→Field and Field Intensity
•Displacement → Gauss’ law, Field/flux lines
•Scalar Potential → Absolute & Relative
•Laplace Equation
•Energy storage
•Boundary conditions
•Materials: Conductors & Dielectrics
•Polarization
•Capacitance

10. Electromagnetic
Field
Theory
10
Charge Distributions:
•Charges are sources of electric fields…
•Two types: discrete and continuous types
Single/group of point charges belong to first
category.
Line charge, Surface charge and Volume charge
belong to the second category

11. Electromagnetic
Field
Theory
11
Charge Distributions:
Types of charge distributions.(a) Discrete, (b)line, (c) surface and(d) volume types.

12. Electromagnetic
Field
Theory
12
Line Charge:
•Shape of the charge is in the form of a thin line, it has only the length
dimension, with no area or volume.
•The charge per unit length, uniform or otherwise, is usually indicated by
symbol, λ (Lambda). Its units are Coulombs per meter or C/m.
•The charge within a differential length dl, called differential charge, dQ
becomes
dQ = λdl.
•The total charge within a length L can be obtained from the differential
charge using the relation
= λ
L
Q dl


13. Electromagnetic
Field
Theory
13
Surface Charge:
•Charge exists in the form of a thin sheet. This distribution has both length
and width dimensions but no thickness.
•The charge per unit area is usually indicated by symbol, σ (Sigma). It can
be non uniform and its units are Coulombs per sq. meter or C/m2.
•The differential charge, dQ charge within differential area da, which can
also be considered as a point charge because of its small size, becomes
dQ = σ da.
•The total charge with in an area A then is
= σ
A
Q da


14. Electromagnetic
Field
Theory
14
Volume Charge:
•The charge occurs in the form of a solid, having arbitrary shape but with a
finite volume. This distribution can have all the three dimensions: length,
width and thickness.
•The charge per unit volume is usually indicated by symbol, ρ (Rho). It may
be uniform or non-uniform and its dimensions are C/m3.
•The differential charge, dQ the charge within differential volume, dτ,
which can also be considered as a point charge because of its negligible
dimensions, becomes
dQ = ρdτ.
•The total charge with in a volume V then is
= ρ
V
Q d


15. Electromagnetic
Field
Theory
15
1.2.Steady Magnetic Fields:
•Force → Lorentz Force law
→Ampere’s Force law
•Field Intensity → Biot-Savart law
•Magnetic Flux → Ampere’s Circuital law
•Vector/Scalar Potentials
•Laplace Equation
•Boundary conditions
•Energy storage
•Magnetic materials: Dia, para and ferro
•Magnetization
•Inductance

16. Electromagnetic
Field
Theory
16
Current Distributions:
Currents are sources of magnetic fields…
These are three types:
Filamentary current: current is in the form of thin line,
Line current, I A
Surface current: current is in the form of thin sheet,
Surface current density K A/m
Volume current: current is in the form of solid rod
Volume current density J A/sq.m
       
1
n
i i
line surface volume
i
q dl da d

   
v I K J

17. Electromagnetic
Field
Theory
17
Current Distributions:
Various types of current distributions. (a) Line current, (b) sheet current and (c)
volume current.

18. Electromagnetic
Field
Theory
18
2.1.Time varying Fields:
•Maxwell’s Equations::Div and Curl of fields
Faraday’s law
Ampere’s law
Gauss’ law
No name
•Continuity Equation
•Retarded Potentials
•Boundary conditions
•Energy storage + power flow: Poynting theorem

19. Electromagnetic
Field
Theory
19
2.2.EM Waves:
•Wave Equations
•EM Waves, TEM and non-TEM
•Uniform plane waves
Depth of penetration
Surface impedance
•Wave polarization
Linear polarization
Non linear polarization and its sense
•Reflection & Refraction: Snell’s laws
Conductor surface
Dielectric surface

20. ENOUGH
FOR
TODAY
ENOUGH
FOR
TODAY
ENOUGH
FOR
TODAY
ENOUGH
FOR
TODAY
ENOUGH
FOR
TODAY
20