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ECEN5341/4341
Spring 2017
Lecture 2
January 20,2017
Radiation .
The power radiated from a charged q is given by
Where a is the acceleration and c is the velocity of light
For a short wire power radiated is given by
I  l 
2 2 l 
W
   40 I 0  
3 

2
0
2
q 2a 2
W
6 0c 3
2
η Is the impedance of free space
The difference between induced fields and radiation depends on the dimensions of
the device and the wave length.
At 60Hz the wavelength is given by
8
c 3x10
 
 5000km
f
60
The radiation resistance for short linear dipoles of length l <<λ is given by
The radiated power is given by
Electromagnetic Fields Near a Dipole
H
I 0 h  jkr  jk
1 

e
 2  sin 

4
r 
 r
Radiated field
Near H Field
I 0h  jkr  2
2 
Er 
e


 cos 
2
3 

4
jr 
 r
Induced E Field
E 
Radiated field
Near E Fields
I 0h  jkr  j
1
 
e



 sin 
3
2 

4
jr
r 
 r
h is the height of the dipole, k is the propagation constant k=2π/λ,  is the
angular frequency  is the wave impedance r is the distance from the radiating
element
Low Frequency Fields
• 1
B
dI
V    E  dl   
 dS   L
s t
dt
• 2. For a cylinder
E 
rB
2
4
Maxwell’s Equations
• 1
2. Another Form
 
d  
 
 B  0
Boundary Conditions

E p1  E p 2  0


 1 En   2 E2


H p1  H p 2  J
Results for Low Frequencies
• 1 Almost all the fields are static or induced.
• 2. At 60Hz fields with in a few km, the radiated
fields are orders of magnitude smaller than
the static or induced fields .
• 3. Heating from radiated fields is very small at
low frequencies but not at RF.
1
The penetration of DC Electric Fields from Air to Tissue
At DC the Parallel Components
The perpendicular Components
Tangential components
For Air
For tissue
So that for a wave from air to tissue
And θ2 is nearly 0 so that E1 is nearly perpendicular and E2 is nearly parallel to the
surface.
Low Frequency Field Penetration from
Air to Tissue
Boundary conditions for incident wave with the E field 
Where
s
is the surface charge density
For tissue at very low frequencies
 2  10 1
6
109 F
0 
36 m
At 60Hz this gives
So the E field inside the body is very small for reasonable external E fields!!
Low Frequency Field Penetration from
Air to Tissue
• For DC
• For 60 Hz
Eint eranal
 10 12
Eexternal
Eint eranal
 4 x10 8
Eexternal
This says that the high conductivity and dielectric constants
of tissue basically shield the body from external low
frequency electric fields.
However you need to be more careful if you look at skin
and the sensory nerves near the surface.
Low Frequency Magnetic Field Effects
• 1. Orientation of ferromagnetic particles
– Fe3O4 in birds , fish and possibly Humans
• 2. Orientation of diamagnetically or paramagnetically
anisotropic molecules and cellular elements
• 3. Generation of potential differences at right angles to a
stream of moving ions
• (Hall effect, also sometimes called a magnetohydrodynamic
effect) as a result of the magnetic force Fm =¼ qvB sin θ, where
q is the electric charge, v is the velocity of the charge, B is the
magnetic flux density, and sin θ is the sine of the angle θ
between the directions v and B. One well-documented result of
this mechanism is a ‘‘spike’’ in the electrocardiograms of
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vertebrates subjected to large dc H fields.
Low Frequency Magnetic Field Effects
• 4. Shifts in Energy of Atomic and Molecular
States, Zeeman shifts in electron energies and
hyperfine splitting of nuclear energy levels.
– This effects things like free radical lifetimes and
concentrations, metabolic processes in things like
hemoglobin and chlorophyll
• 5. Induction of E fields with resulting electrical
potential differences and currents within an
organism by rapid motion through a large static H
field. Some magnetic phosphine's are due to such
motion
12
Field Required to get 10mV/m vs frequency for air to muscle
• 1
External E and H field required to obtain an internal E field of 10 mV/m (conductivity and
dielectric permittivity
for skeletal muscle from Foster, K.R., Schepps, J.L., and Schwan, H.P. 1980. Biophys. J.,
29:271–281. H-field
13
calculation assumes a circular path of 0.1-m radius perpendicular to magnetic flux).
EM Waves at a Plane Boundary
Electric Fields and Dielectric Sphere
Transmission for E Parallel vs Frequency Skeletal Muscle
Er

 T 1
Ei
FIGURE 0.8
External E and H field required to obtain an internal E field of 10 mV=m (conductivity and
dielectric permittivity for skeletal muscle from Foster, K.R., Schepps, J.L., and Schwan, H.P.
1980. Biophys. J., 29:271–281. H-field calculation assumes a circular path of 0.1-m radius
perpendicular to magnetic flux).
16
Depth of Penetration
• 1. For a good conductor ,Skin Depth
• 2. A good conductor means a large ratio of
conduction current J =σ E to displacement
current
• or
17
More General Skin Depth
• 1. Most biological materials are not good
conductors (0.1 < p < 10) and we need a
more general expression.
18
Ratio of Transmitted to Reflected Power
For Perpendicular Incidence at Air Muscle
Interface.
1
19
Transmission and Reflection
• 1 The reflection coefficient
• 2. The Transmission coefficient
20
Some Values for Coefficients
for Muscle
21
The Wave Impedances η = E/H
• 1. Homogenous Medium
• 2. For Air or Vacuum
22
1-
Transmitted and Reflected Power
• 1 R mean the real part of η
• 2. η* Means complex conjugate of η
•
2,
1 2*  1* 2
P

=12
P1
22
23
Skin Depth for Plane Wave vs
Frequency for Muscle
Electromagnetic skin depth in muscle tissue
from plane wave expression (Equation 0.19,
Table 0.1).
24
Power Transmitted
Pr
P 12*  1* 2
2
=1-  1  

2
Pi
P1
22
25
Waves at an Angle
• 1
26
Generalize Snell’s Law
27
Transmission as Function of Angle
Electromagnetic skin depth in muscle tissue
from plane wave expression (Equation 0.19,
Table 0.1).
28
Frequency, Wave Length,
Energy in Electron Volts (eV)
• 1
29
Bond Strengths and Thermal Energy
30