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ECE 134
Introductory Field Theory
Fall 2010
1
Reading Assignment:
Cheng: Review Chapters 12, study sections 3.1–3.6
Schey: review material as needed
Cartoon Guide: Chapters 1213
Homework #1
Due:
Monday 4 October 2010
1)
We have already seen in our limited study that the equations of electromagnetics
often involve a vector
that describes the separation between the
source location
and the
observation
point
at which we want to determine the fields.
If we describe
the observation point by the position vector
and the source point by
, then
.
In rectangular coordinates it is easy to see that
(1.1)
Find
when the source and observation points are described in a) cylindrical
coordinates, or b) spherical coordinates
2)
We will use the following identity in the derivation of the electrostatic potential
(1.2)
where
is given by (1.1), and
is the unit vector in the direction of
.
Prove the
result (1.2) by carrying out the gradient operation on
.
Note that (1.2) is nothing
more than the vector equivalent of the more familiar expression
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 Fall '08
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