30-01-2013, 12:40 PM
Electromagnetic Field Theory
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CLASSICAL ELECTRODYNAMICS
Classical electrodynamics deals with electric and magnetic fields and interactions
caused by macroscopic distributions of electric charges and currents. This means
that the concepts of localised electric charges and currents assume the validity of
certain mathematical limiting processes in which it is considered possible for the
charge and current distributions to be localised in infinitesimally small volumes of
space. Clearly, this is in contradiction to electromagnetism on a truly microscopic
scale, where charges and currents have to be treated as spatially extended objects
and quantum corrections must be included. However, the limiting processes used
will yield results which are correct on small as well as large macroscopic scales.
It took the genius of JAMES CLERK MAXWELL to consistently unify electricity
and magnetism into a super-theory, electromagnetism or classical electrodynamics
(CED), and to realise that optics is a subfield of this super-theory. Early in
the 20th century, HENDRIK ANTOON LORENTZ took the electrodynamics theory
further to the microscopic scale and also laid the foundation for the special theory
of relativity, formulated by ALBERT EINSTEIN in 1905. In the 1930s PAUL
ADRIEN MAURICE DIRAC expanded electrodynamics to a more symmetric form,
including magnetic as well as electric charges. With his relativistic quantum mechanics,
he also paved the way for the development of quantum electrodynamics
(QED) for which RICHARD PETER FEYNMAN, JULIAN SCHWINGER, and SINITIRO
TOMONAGA in 1965 received their Nobel prizes in physics. Around the
same time, physicists such as SHELDON GLASHOW, ABDUS SALAM, and STEVEN
WEINBERG were able to unify electrodynamics the weak interaction theory to yet
another super-theory, electroweak theory, an achievement which rendered them
the Nobel prize in physics 1979. The modern theory of strong interactions, quantum
chromodynamics (QCD), is influenced by QED.
Electrostatics
The theory which describes physical phenomena related to the interaction between
stationary electric charges or charge distributions in a finite space which
has stationary boundaries is called electrostatics. For a long time, electrostatics,
under the name electricity, was considered an independent physical theory of its
own, alongside other physical theories such as magnetism, mechanics, optics and
thermodynamics.1
Coulomb’s law
It has been found experimentally that in classical electrostatics the interaction
between stationary, electrically charged bodies can be described in terms of a
mechanical force. Let us consider the simple case described by figure 1.1 on
page 3. Let F denote the force acting on an electrically charged particle with
charge q located at x, due to the presence of a charge q′ located at x′.
Magnetostatics
While electrostatics deals with static electric charges, magnetostatics deals with
stationary electric currents, i.e., electric charges moving with constant speeds, and
the interaction between these currents. Here we shall discuss this theory in some
detail.