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:
ď Gradient, Divergence and Curl
ď Gradient theorem, Divergence theorem and
Curl theorems
⢠Coordinate systems:
ď Rectangular, Cylindrical and Spherical
ď Differential length, area and volume
Pre-requisites:
7. Electromagnetic
Field
Theory
7
Div and Curl:
Examples:
â˘Electrostatic field in charge free region is both solenoidal and irrotational.
â˘Steady magnetic field in a current carrying conductor is solenoidal but not
irrotational.
â˘Electrostatic field in charged region is not solenoidal but irrotational.
â˘Electric field in a charged region with a time varying magnetic field is neither
solenoidal nor irrotational.
Field F is solenoidal if ďł.F=0 and irrotational if ďłĂF=0.
8. Electromagnetic
Field
Theory
8
1. Static fields: Invariant with time
1.1.Electrostatic fieldsâ static charge distributions
1.2.Steady magnetic fieldsâ steady currents
2. Dynamic fields: Variant with time
2.1.Time varying fields â Time varying currents/
Acc. charges
2.2.EM Waves â Time varying fields
Parts in Field/Wave Theory:
9. Electromagnetic
Field
Theory
9
1.1.Electrostatic Field:
â˘Force â Coulombâs law
âField and Field Intensity
â˘Displacement â Gaussâ law, Field/flux lines
â˘Scalar Potential â Absolute & Relative
â˘Laplace Equation
â˘Energy storage
â˘Boundary conditions
â˘Materials: Conductors & Dielectrics
â˘Polarization
â˘Capacitance
10. Electromagnetic
Field
Theory
10
Charge Distributions:
â˘Charges are sources of electric fieldsâŚ
â˘Two types: discrete and continuous types
ďSingle/group of point charges belong to first
category.
ďLine charge, Surface charge and Volume charge
belong to the second category
12. Electromagnetic
Field
Theory
12
Line Charge:
â˘Shape of the charge is in the form of a thin line, it has only the length
dimension, with no area or volume.
â˘The charge per unit length, uniform or otherwise, is usually indicated by
symbol, Îť (Lambda). Its units are Coulombs per meter or C/m.
â˘The charge within a differential length dl, called differential charge, dQ
becomes
dQ = Îťdl.
â˘The total charge within a length L can be obtained from the differential
charge using the relation
= Îť
L
Q dl
ď˛
13. Electromagnetic
Field
Theory
13
Surface Charge:
â˘Charge exists in the form of a thin sheet. This distribution has both length
and width dimensions but no thickness.
â˘The charge per unit area is usually indicated by symbol, Ď (Sigma). It can
be non uniform and its units are Coulombs per sq. meter or C/m2.
â˘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 = Ď da.
â˘The total charge with in an area A then is
= Ď
A
Q da
ď˛
14. Electromagnetic
Field
Theory
14
Volume Charge:
â˘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.
â˘The charge per unit volume is usually indicated by symbol, Ď (Rho). It may
be uniform or non-uniform and its dimensions are C/m3.
â˘The differential charge, dQ the charge within differential volume, dĎ,
which can also be considered as a point charge because of its negligible
dimensions, becomes
dQ = ĎdĎ.
â˘The total charge with in a volume V then is
= Ď
V
Q dď´
ď˛
15. Electromagnetic
Field
Theory
15
1.2.Steady Magnetic Fields:
â˘Force â Lorentz Force law
âAmpereâs Force law
â˘Field Intensity â Biot-Savart law
â˘Magnetic Flux â Ampereâs Circuital law
â˘Vector/Scalar Potentials
â˘Laplace Equation
â˘Boundary conditions
â˘Energy storage
â˘Magnetic materials: Dia, para and ferro
â˘Magnetization
â˘Inductance
16. Electromagnetic
Field
Theory
16
Current Distributions:
Currents are sources of magnetic fieldsâŚ
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
ď¨ ďŠ ď¨ ďŠ ď¨ ďŠ ď¨ ďŠ
1
n
i i
line surface volume
i
q dl da dď´
ď˝
ďĽ ď˛ ď˛ ď˛
v I K J
18. Electromagnetic
Field
Theory
18
2.1.Time varying Fields:
â˘Maxwellâs Equations::Div and Curl of fields
ďFaradayâs law
ďAmpereâs law
ďGaussâ law
ďNo name
â˘Continuity Equation
â˘Retarded Potentials
â˘Boundary conditions
â˘Energy storage + power flow: Poynting theorem
19. Electromagnetic
Field
Theory
19
2.2.EM Waves:
â˘Wave Equations
â˘EM Waves, TEM and non-TEM
â˘Uniform plane waves
ďDepth of penetration
ďSurface impedance
â˘Wave polarization
ďLinear polarization
ďNon linear polarization and its sense
â˘Reflection & Refraction: Snellâs laws
ďConductor surface
ďDielectric surface