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
Review of Electrostatics
1
Gradient
We dene the gradient operation on a eld F = F (x, y, z) by;
F = x F + y F + z F
x
y
z
This operation forms a vector as may be shown by its transformation properties under rotation and reection. We write the following us
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
Solutions to Laplaces Equation in Cylindrical
Coordinates and General Numerical solutions
Lecture 8
1
Introduction
We obtained general solutions for Laplaces equation by separtaion of variables in Cartesian
and spherical coordinate systems. The last syste
Solution to Laplaces Equation in Spherical
Coordinates
Lecture 7
1
Introduction
First 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) c
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, the eld will induce charge which moves in a conductor
so that the eld inte
Introduction and Vectors
Lecture 2
1
Vector Identities
The vector operations presented in lecture 1 can be combined or used to operate on combined
scalar and vector elds. There are several identities, presented below without proof, which
are extremely use
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
First do this in Cartesian coordinates. The equation takes the form;
2V + 2V + 2V = 0
x2
Fields and Energy
Lecture 4
1
Total energy of a charge distribution
Assume a set of positive charges placed at various positions in space. An energy is required
to assemble this distribution and it can be calculated by moving each charge from far away
to
Lecture 3
The Electric Field
1
Fields
A eld can be dened as a mathematical construction which connects a space-time geometry
to a physical process. It is obtained by assigning one or more functions to each point of a
spatial coordinate system. Generally,
Dielectric Problems and Electric Susceptability
Lecture 10
1
A Dielectric Filled Parallel Plate Capacitor
Suppose an innite, parallel plate capacitor with a dielectric of dielectric constant inserted
between the plates. The eld is perpendicular to the pla
Boundary value problems
Lecture 5
1
Introduction
We found that the electric potential is a solution of the partial dierential equation;
2 V = /0
This is Poissons equation where is the charge density and V the electric potential. If there
are a set of vari
Examples of magnetic eld calculations and
applications
Lecture 12
1
Example of a magnetic moment calculation
Consider the vector potential and magnetic eld due to a magnetic moment created by a
rotating surface charge, , on a cylinder. The geometry is sho
PHYSICS 6303 Test 1
24 Sep 2008
Instructor: K. Innanen
Name:
Instructions: Time: 1:30min. No calculators or electronic devices are needed. Good luck!
1.
Consider a vector F expressed rst over one set of Cartesian coordinates, ei , and
then another, ei , w
PHYSICS 6303 Midterm exam
27 Oct 2008
Instructor: K. Innanen
Name:
Instructions: Time: 1:30min. Vectors are lower case and in bold. Some formulas are found
at the back. The symbol BC is short for Boundary Conditions. No calculators or electronic
devices a
Introduction and Vectors
Lecture 1
1
Introduction
This is a course in classical Electromagnetism, and is the foundation for more advanced
courses in modern physics. All physics in the modern era, from quantum mechanics to astrophysics and from atoms to qu