University of Waterloo
Department of Electrical and Computer Engineering
E&CE 126: ELECTRICITY AND MAGNETISM
Final Examination W03
April 14, 2003
Time Allowed: 3 hours Instructor: M.M.A. Salama
Instructions:
1- Answer all Nine questions.
2- The exam. is a
1/14
ECE 126 Midterm Exam, Fall 2008
(Monday Nov. 3, 2008)
University of Waterloo
Department of Electrical and Computer Engineering
ECE 126: Introduction to Electrostatics, Magnetism and Electronics
Mid-Term Exam - Fall 2008
Time Allowed: 2 Hours
Date: No
Units: In SI units, resistance is measured in Ohms, which is just a special name for
Volts/Amperes. In cgs units, the voltage is measured in esu/cm, and the current in esu/sec,
so the resistance is measured in sec/cm, a rather odd unit. From this, we can
13.3
The Biot-Savart law
Using the last result we derived the vector potential of wire we can work out another
very important result. By taking the curl of that vector potential, we derive the magnetic
eld of a wire:
I
B =
c
I
=
c along
d
l
along wire r
5.4
5.4.1
Some conductor examples
Example 1: Randomly shaped conductor
A chunk of conductor with a hollowed out core has charge placed on it until its potential
(relative to innity) is 0 . What is the potential inside the core?
=?
Surface potential0
Answe
4.2
Divergence in Cartesian coordinates
So far, weve only dened the divergence as a particular limit. We now want to develop a
concrete calculation showing its value. To do so, consider an innitesimal cube with sides
x, y, and z, centered on the coordinat
6.4
Dielectrics
The capacitors weve discussed here are somewhat articial: the space between their plates
is taken to be empty. In the real world, the normal situation is that this space is lled with
something air, plastic, paper, compressed leprechauns, w
10.4
Amperes law
Weve talked about the force that a magnetic eld exerts on charges and current; but, we
have not yet said anything about where this eld comes from. I will now give, without any
proof or motivation, a few key results that allow us to determ
2.3
Flux
The notion of ux is an important one in physics. It refers to the ow of some vectorial
quantity through an area. The simplest example to picture is the ow of uid. Imagine that
uid is owing with velocity = v. Now imagine that we dip a square wire
3.5
Energy of a charge distribution
If we can use innity as a reference point, then we can write down a formula for the energy
of a charge distribution that is sometimes quite handy. From an earlier lecture, we worked
out the formula
U=
1
2
i
j=i
qi qj
.
1.2
History of electromagnetism
Circa B.C. 500: Greeks discover that rubbed amber attracts small pieces of stu. (Note the
Greek word for amber: o, or electron.) They also discover that certain iron rich
rocks from the region of M (Magnesia) attract other