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Swartz 06/5/23
ECE 303 –
Electromagnetic Fields and Waves
– Fall 2008
Lecture 5:
ECE 3030
Electromagnetic Fields and Waves
Instructor:
Dr. Wesley E. Swartz
Fall 2008 Lecture 5
2008/6/8
Electrical Conduction
More on Electric Field Boundary Conditions
Electrical Conduction in Materials
The Concept of Perfect Conductors
Electroquasitatics Problems with Perfect Metals
Method of Images
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V
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Swartz 06/5/23
ECE 303 –
Electromagnetic Fields and Waves
– Fall 2008
Lecture 5:
Demo and Homework Problems
•
Demo problems:
–
Some trig
–
Position vectors
–
Taylor’s Series
–
Boundary Conditions
–
Misc.
–
Problem 3.5: Charged disk.
–
Problem 4.3: Charge images
•
Homework:
–
Problem 3.13
–
Problem 3.16
–
Problem 4.5
4
Swartz 06/5/23
ECE 303 –
Electromagnetic Fields and Waves
– Fall 2008
Lecture 5:
Electric Field Boundary Conditions
•
There are two boundary conditions for the
electric field at a material interface:
–
The
discontinuity
of the
normal component
of
the Efield at an interface is related to the
surface charge density at the interface
–
The
parallel component
of the Efield at an
interface is always
continuous
at the interface
σ
⊥
1
E
⊥
2
E
()
ε
=
−
⊥
⊥
1
2
o
E
E
0
E
E
1
2
=
−
1
E
2
E
**For formal proofs see the Appendix at the end of these lecture notes**
We have seen this before!
5
Swartz 06/5/23
ECE 303 –
Electromagnetic Fields and Waves
– Fall 2008
Lecture 5:
Electrical Conductivity
•
When Efield is present inside a material,
–
it forces the charges inside the material to move causing an electric
current.
–
The current density
(units:
Amps/m
2
) is related to the Efield by
the relation:
where
σ
is the material conductivity (units:
1/(
Ω
m) or S/m
)
r
E
r
J
=
J
Material
S/m
Rubber
Water
Alcohol
Gold
Aluminum
Copper
Silver
10
15
2X10
4
3X10
4X10
7
3X10
7
5X10
7
6X10
7
6
Swartz 06/5/23
ECE 303 –
Electromagnetic Fields and Waves
– Fall 2008
Lecture 5:
Perfect Conductors (1)
•
A perfect conductor has infinite conductivity (i.e.
σ
=
∞
).
–
Of course, no real metal has infinite conductivity. However, some
metals like Silver, Copper, and Gold have high enough conductivity
that they may be considered “perfect conductors” or “perfect
metals” for simplicity in many calculations
•
A perfect conductor cannot have any Efield inside it.
•
The current density and Efield are related by:
•
An infinite conductivity implies that for any nonzero E
field one would get an infinite current density – and this is
physically impossible.
–
The only way such a catastrophe is avoided is to never have an E
field inside a perfect conductor.
–
(More on this later …)
r
E
r
J
=
7
Swartz 06/5/23
ECE 303 –
Electromagnetic Fields and Waves
– Fall 2008
Lecture 5:
Perfect Conductors (2)
•
Perfect conductors are always “equipotentials”
–
(i.e. the electric potential inside a perfect conductor has the same
value everywhere)
•
The potential difference between any two points is given
as:
–
If the Efield is zero inside a perfect conductor then the potential
difference at any two points must be the same.
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 Electromagnet

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