Physics 315
Electrodynamics
General Information
Physics 315, Electrodynamics, is
required for the physics major, and may be counted toward the completion
of a physics minor. It is best to have completed Math 223, Calculus III
prior to taking Physics 315, but they may be taken concurrently with the
instructor's permission. We begin with a crash course in the mathematics
of vector fields (review for those who have had Calc III), emphasizing
theorems that will illuminate the topics to follow.
There are four known fundamental forces at work in nature, the strong
and weak nuclear forces, electromagnetic forces, and gravity.
Nearly every force that we experience in everyday life is of the electromagnetic
persuasion. Friction, "normal" forces, forces that bind molecules and solids,
and forces that deflect billiard balls are just a few examples. Electrostatic
forces between charged particles are stronger than gravitational forces
by about forty orders of magnitude. Gravity is such a weak force that it
is only noticeable in the proximity of enormous masses (like the earth).
And while the strong nuclear force (which binds atomic nuclei) is stronger
than the electromagnetic force, it only acts at tiny distances on the order
of 10-15 meters. It is no exaggeration then, to say that we
live in a relentlessly electromagnetic world.
There are four major sections of course content:
I: ELECTROSTATICS
Considerable attention is paid to the special case of electric fields created
by stationary distributions of charged particles. This may initially
be surprising, since the only physical principle involved is Coulomb's Law,
one of the simplest fundamental ideas encountered in introductory physics.
We develop rather sophisticated mathematical techniques for finding fields
and forces in and around charged particles, conductors, and dielectric
media.
II: MAGNETOSTATICS
In this section, we learn how to determine the magnetic fields produced
by steady currents in circuits of various geometries, and the forces these
fields exert on moving charged particles. We go on to describe fields in
magnetic media.
III: ELECTRODYNAMICS
By the time we get to the "title" of
the course, the semester is more than half gone. Here, we discuss induction
of electric fields by time-varying magnetic fields and develop Maxwell's
equations, which describe the intimate relationships between electric and
magnetic fields in a most elegant and compact fashion. Maxwell's four equations,
plus one describing the force exerted by E-M fields on charged particles,
constitute the entirety of the classical theory of electromagnetism, and
represent the crowning achievement in nineteenth century theoretical physics.
James Clerk Maxwell, Eighteen sixty something
IV: ELECTROMAGNETIC WAVES AND RADIATION Maxwell's equations predict the existence of self-propagating waves of
undulating electric and magnetic fields. In a vacuum, these waves are expected
to move at the known speed of light. Maxwell's theory most elegantly answered
the longstanding question, "What wiggles?" with regard to light, and indicated
that other kinds of "rays", eg infrared, radio, x-ray, and ultraviolet
were different than visible light only in their frequency. We will go on
to discuss how accelerated charged particles produce these electromagnetic
waves and transfer energy to remote particles.
V: RELATIVISTIC ELECTRODYNAMICS
It is unlikely that we will have time to get this far, but if we do, we
will review the special theory of relativity as it pertains to mechanics,
which is introduced in Physics
224. Then we will express electromagnetism in the relativistic framework
of the field tensor and see how magnetism is the natural consequence of
an electrostatic field in a moving reference frame.
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This page was created by Mark
Gealy, e-mail: gealy@.cord.edu