TOPIC 2 – INTRO TO ELECTROMAGNETICS
2.2 EM Properties
2.2.1. Electric Permittivity
An electric property of a material.
Symbol is  and has physical units of Coul2 / N-m2
Engineering units are Farad/meter
As a fundamental constant, the permittivity of free space called
0 (vacuum) is 8.845(10-12) F/m.
The permittivity of a material is given relative to that of free
space as  = r * 0 where r is the relative permittivity or
dielectric constant.
TOPIC 2 – INTRO TO ELECTROMAGNETICS
2.2 EM Properties
2.2.1. Electric Permittivity
Remember that the capacitance of a parallel plate capacitor is
given by C = ( *A)/d.
So the relative permittivity or dielectric constant of a material is
an indicator of how well the material acts as a capacitor with
respect to free space.
 Typical dielectric constants are:
Glass
Mica
Rubber
Wood
Water
4–7
4.5 – 7.5
2.3 – 4.0
2.5 – 7.7
81
TOPIC 2 – INTRO TO ELECTROMAGNETICS
2.2 EM Properties
2.2.2. Magnetic Permeability
A magnetic property of a material.
Symbol is  and has physical units of Tesla-m/Ampere.
Engineering units are Henrys/meter (H/m).
As a fundamental constant, the permittivity of free space called
0 (vacuum) is 1.25(10-6) H/m.
The permeability of a material is given relative to that of free
space as  = r * 0 where r is the relative permeability.
TOPIC 2 – INTRO TO ELECTROMAGNETICS
2.2 EM Properties
2.2.2. Magnetic Permeability
So the relative permeability of a material is an indicator of how
well the material acts as a magnet with respect to free space.
 Typical relative permeabilities are:
Low
carbon steel
Silicon
Iron
Magnetic
alloys
150 – 5000
300 – 50,000
11,000 – 450,000
TOPIC 2 – INTRO TO ELECTROMAGNETICS
2.2 EM Properties
2.2.3. Characteristic Impedance
An electric property of a material.
Symbol is  and has physical and engineering units of Ohms.
As a fundamental constant, the characteristic impedance of
free space called 0 (vacuum) is 377 Ohms.
The characteristic impedance is calculated as:
0
= (0 0 ).5
The characteristic impedance of a material is given relative to
that of free space as  = 0 /n where n is the index of
refraction.
TOPIC 2 – INTRO TO ELECTROMAGNETICS
2.3 ElectroMagnetic Fields
2.3.1. EM Waves
Consists of:
 An electric intensity vector, E, with units of volts per meter
 A magnetic intensity vector, H, with units of amps per meter
These two vectors can generally be assumed to be
pertindicular to each other.
These two vectors can generally be assumed to be
pertindicular to the direction of propagation, Z.
The relationship between these two intensity vectors is:
E = 0 * H
TOPIC 2 – INTRO TO ELECTROMAGNETICS
2.3 ElectroMagnetic Fields
TOPIC 2 – INTRO TO ELECTROMAGNETICS
2.3 ElectroMagnetic Fields
2.3.2.Frequency and Wavelength
Both the E and the H intensity vary with time:
 The frequency  is the number of complete cycles completed
per second.
 The period, T, is the number of seconds it takes to complete
one complete cycle: T = 1/ 
 The angular frequency, , is defined as:  = 2*  *  in
units of radians per second.
The wavelength,  , is the unit of length required for the wave
to complete one cycle.
TOPIC 2 – INTRO TO ELECTROMAGNETICS
2.3 ElectroMagnetic Fields
2.3.3.Speed of Light
The speed of light (velocity of light in free space) is a
fundamental constant: c = 2.997925(108) m/s.
The frequency  and wavelength  are related as follows:
c=*.
A vacuum (free space) has three properties previously defined:
0 , 0 0.
The speed of light is also defined as:
c = (0 * 0 ) .5
In materials other than free space, the velocity of light becomes:
V light = c/n where n is the index of refraction.
TOPIC 2 – INTRO TO ELECTROMAGNETICS
2.3 ElectroMagnetic Fields
2.3.3.Speed of Light
Typical values of index of refraction in various materials are:
Material
n
air
1.0003
water
1.33
glass
1.46 – 1.58
lucite
1.51
sodium chloride
1.53
diamond
2.42
Also  = 0 /n for a given material.
TOPIC 2 – INTRO TO ELECTROMAGNETICS
2.3 ElectroMagnetic Fields
2.3.4 .Field Intensity and Field Density
In a given material or medium, EM field densities may be
defined as such:
Current Density:
J =  *E, units of amps/m2
Electric Field Density: D =  *E, units of coul/ m2
Magnetic Field Density B =  *H, units of weber/m2
Where is conductivity in units of mhos
and 1 weber/m2 = 1 tesla
= 104 gauss
= 109 gamma
TOPIC 2 – INTRO TO ELECTROMAGNETICS
2.3 ElectroMagnetic Fields
2.3.5. Maxwell’s Equations
This set of equations:
 Provides the relationship between electric field
intensities and magnetic field density.
 Provides the relationship between magnetic field
intensities and electric field density.
 Provides solutions for all materials and media.
Reveals the time-varying dependencies of all EM
wave characteristics.
TOPIC 2 – INTRO TO ELECTROMAGNETICS
2.3 ElectroMagnetic Fields
2.3.5. Maxwell’s Equations
TOPIC 2 – INTRO TO ELECTROMAGNETICS
2.3 ElectroMagnetic Fields
2.3.5. Maxwell’s Equations
q
Gauss’ Law for Electrostatics
 E  dA  0
Gauss’ Law for Magnetism
 B  dA  0
Faraday’s Law of Induction
d

B
E

dl



dt
Ampere’s Law
 B  dl  0 I
TOPIC 2 – INTRO TO ELECTROMAGNETICS
2.4 EM Wave Effects
2.4.1. EM Wave Effects - Mechanisms
A variety of effects take place as EM waves interact with media
and materials:
Amplification (Good) But doesn’t usually happen in nature.
Attenuation (Bad) – From atmospherics and obstructions.
Reflection/refraction (also Bad) – From the ground,
atmosphere or obstructions.
 Scattering (Bad) – From foliage, atmosphere or obstructions.
 Diffraction (Bad) – From edges or corners.
 Doppler (Bad) – From moving receivers/transmitters.
 Interference/fading – the net result.
TOPIC 2 – INTRO TO ELECTROMAGNETICS
2.4 EM Wave Effects
2.4.2. EM Wave Effects – Attenuation
TOPIC 2 – INTRO TO ELECTROMAGNETICS
2.4 EM Wave Effects
2.4.2. EM Wave Effects – Attenuation
TOPIC 2 – INTRO TO ELECTROMAGNETICS
2.4 EM Wave Effects
2.4.3. EM Wave Effects – Reflection/refraction
TOPIC 2 – INTRO TO ELECTROMAGNETICS
2.4 EM Wave Effects
2.4.4. EM Wave Effects – Diffraction
TOPIC 2 – INTRO TO ELECTROMAGNETICS
2.4 EM Wave Effects
2.4.4. EM Wave Effects – Diffraction
TOPIC 2 – INTRO TO ELECTROMAGNETICS
2.4 EM Wave Effects
2.4.5. EM Wave Effects – Interference
TOPIC 2 – INTRO TO ELECTROMAGNETICS
2.4 EM Wave Effects
2.4.6. EM Wave Effects – Fading/Loss of Signal (LOS)
TOPIC 2 – INTRO TO ELECTROMAGNETICS
2.4 EM Wave Effects
2.4.6. EM Wave Effects – Fading/LOS