HW1 - ECE 134 Introductory Field Theory Fall 2007 Reading...

ECE 134 Introductory Field Theory Fall 2007
1
Reading Assignment:
Cheng: Review Chapters 1-2, study sections 3.1–3.6
Schey: review material as needed
Cartoon Guide: Chapters 12-13
Homework #1 Due: Monday 8 October 2007
1) We have already seen in our limited study that the equations of electromagnetics
often involve a vector R 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 r and the source point by r
′
, then
R r r
′
= − . In rectangular coordinates it is easy to see that
2 2 2 ( ) ( ) ( ) R x x y y z z ′ ′ ′ = − + − + − (1.1)
Find R when the source and observation points are described in a) cylindrical
coordinates, or b) spherical coordinates.
2) In class we used the following identity in our derivation of the electrostatic potential
2
ˆ
1 R
R R
⎛ ⎞
∇ = −
⎜ ⎟
⎝ ⎠
(1.2)
where R is given by (1.1), and
ˆ
R is the unit vector in the direction of R . Prove the
result (1.2) by carrying out the gradient operation on