The Electric Field
Lecture 3
1
Introduction
Static electricity has been known for centuries. The ancient Greeks reported that amber
rubbed with fur attracted small pits of papyrus, and of course lightning was present even
before humans could observe it. I
Boundary value problems
Lecture 5
1
Introduction
We have found that the electric potential is a solution of the partial dierential equation;
2 V = /0
The above is Poissons equation where is the charge density and V the electric potential. If there are a s
Poissons and Laplaces equations
Lecture 4
1
Including the Electric Potential in Gauss Law
Gauss law in dierential form is E = /. Insert
the above expression for the electric eld in terms of the
electric potential. This results in;
V = /0
This is a partia
Introduction and Vectors
Lecture 1
1
Introduction
This is a course on classical Electromagnetism. It is the foundation for more advanced
courses in modern physics. All physics of the modern era, from quantum mechanics to
quarks, can trace their theoretica
Introduction and Vectors
Lecture 2
1
Vector Identities
The vector operations obtained in lecture 1 can be combined or used to operate on combined scalar and vector
elds. There are several identities involving these operations that can be extremely useful.
Solution to Laplaces Equation In Cartesian
Coordinates
Lecture 6
1
Introduction
We wish to solve the 2nd order, linear partial dierential equation;
2 V (x, y, z) = 0
We rst do this in Cartesian coordinates. Thus the equation takes the form;
2V + 2V + 2V =
Examples of Dielectric Problems and the Electric
Susceptability
Lecture 10
1
A Dielectric Filled Parallel Plate Capacitor
Suppose an innite, parallel plate capacitor lled with a dielectric of dielectric constant .
The eld will be perpendicular to the plat
The Electric Field in Matter
Lecture 9
1
Introduction
With the exception of conductors, we have developed the physics of static electric elds in
vacuum. With respect to conductors, a eld will induce charge to move in a conductor so
that the eld internal t
The magnetic eld in materials
Lecture 13
1
Macroscopic Equations
Previously we assumed that J was known or could determined. In
the presence of matter this is not true or irrevelent on the atomic
scale, because all atoms have currents due to the movement
Solution to Laplaces Equation in Cylindrical
Coordinates
Lecture 8
1
Introduction
We have obtained general solutions for Laplaces equation by separtaion of variables in Cartesian and spherical coordinate systems. The last system we study is cylindrical co
The magnetic circuits and elds in materials
Lecture 14
1
Linear current above a magnetic block
In this example, assume a current density J above an innite slab of linear magnetic material, with permeability, , Figure 1. The eld created by J polarizes the
Examples of magnetic eld calculations and
applications
Lecture 12
1
Example of a magnetic moment calculation
We consider the vector potential and magnetic eld due to the magnetic moment created
by a rotating surface charge, , on a cylinder. The geometry i
Currents and the Magnetic Field
Lecture 11
1
Introduction
Magnetic forces have been observed at least as long as the electrical force. However it was
not until the experiments of Oersted in 1819 that a connection was found between moving
electric charge a
Solution to Laplaces Equation in Spherical
Coordinates
Lecture 7
1
Introduction
We rst look at the potential of a charge distribution . It is given by;
V =
d
(r )
|r r |
Now we suppose r > r and look at the term;
1
= (1/r)
|r r |
1
1 + (r /r)2 2 (r /r)