This document outlines the key topics to be covered in a lecture series on electromagnetic field (EMF) theory. The series will cover static and dynamic electric and magnetic fields, Maxwell's equations, electromagnetic waves, and key prerequisites like vector calculus. Static fields include electrostatic fields from charge distributions and steady magnetic fields from current distributions. Dynamic fields involve time-varying fields and EM waves. Maxwell's equations relate the divergence and curl of electric and magnetic fields. EM waves are analyzed using wave equations and concepts like uniform plane waves, polarization, and reflection/refraction. The goal is to provide students and engineers a solid understanding of EM wave theory, which is important for electrical communications that increasingly rely on wireless technologies using antennas.

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

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

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Theory
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• 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
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Theory
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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

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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

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• 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:

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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.

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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:

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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

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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

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

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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


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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


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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


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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

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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

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

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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

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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

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ENOUGH
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ENOUGH
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