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School of Electrical and Computer Engineering, Cornell University
ECE 303: Electromagnetic Fields and Waves
Fall 2005
Homework 2
Due on Sep. 09, 2005 by 5:00 PM
Reading Assignments:
i) Review the lecture notes.
ii) Relevant sections of the online
Haus and Melcher
book for this week are 4.04.6. Note that the book
contains more material than you are responsible for in this course. Determine relevance by what is
covered in the lectures and the recitations. The book is meant for those of you who are looking for more
depth and details.
Spherically or Cylindrically Symmetric Solutions of Laplace’s Equation
Spherical Coordinate System
Cylindrical Coordinate System
()
B
r
A
r
+
=
φ
( ) ( )
B
r
A
r
+
=
ln
Problem 2.1: (Electric dipole)
Consider two equal and opposite charges sitting on the zaxis at locations
2
d
z
±
=
, as shown in the
figure below.
a) Find the potential
()
r
r
at a location
r
r
far away from the dipole (where
d
r
>>
r
).
b) Find the electric field
()
r
E
r
r
from your result in part (a).
r
r
z
d
x
q
+
q
−
θ
1
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View Full Document Problem 2.2: (Electric dipole near a perfect metal ground plane – electric
quadrupole)
Consider the dipole of Problem 2.1 placed near a semiinfinite perfect metal ground plane, as show in the
figure below.
a) Using the method of images draw the image charges corresponding to the dipole and indicate the
location and orientation and magnitude of these image charges in a sketch.
b) Find the potential
()
r
r
φ
outside the perfect metal for all
r
r
in the xz plane (i.e. for the angle
in the
spherical coordinates equal to zero).
Hints:
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This note was uploaded on 09/20/2007 for the course ECE 3030 taught by Professor Rana during the Fall '06 term at Cornell University (Engineering School).
 Fall '06
 RANA
 Electromagnet, Electric charge, metal spherical shell, perfect metal, Cylindrically Symmetric Solutions, Melcher

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