Biomedical Engineering Reference
In-Depth Information
time-varyingphenomena.IntheiroriginalformMaxwell'sequations
were 20 in number and the variables were potentials, not the E
and H fields of Eqs. (1.1a-d). Maxwell understood these equations
as having an underlying wave basis, and he succeeded in deriving
second-order wave equations showing the EM phenomenon was
a plane-wave propagating in free space at the speed of light. The
relativistic Lienard-Wiechert potentials are taken directly between
charge points and give the time-varying EM fields for point charges
in arbitrary motionrelative to oneanother.
In 1903-1904 Abraham and Lorentz attempted to solve the
problem behind what is referred to as the self-field problem, the
backreactionofitsfieldonanelectron'sownmotion.Theymodelled
the electron as a spherical surface of current density that moved
at relativistic speeds, finding that CEM resulted in a '4/3 problem'
where force on the electron contradicts Newton'slaw
F
=
ma
:
q
3
c
3
a
4
3
m
e
a
2
3
F
e
=
−
+
'structure terms'
Many tried to modify the classical equations. At that time CEM
was seen to be failing. Yaghjian recently reviewed the problem,
finding inconsistencies with
both
quantum theory as well as CEM
as the radius of the electron approaches zero. He found the generic
solution of a charged surface of finite radius moving at relativistic
speeds was correct within the macroscopic domain. The self-field
problem of CEM theory remained unsolved until recently, when its
modern variant succeeded in solving the hydrogen atom. The main
reasonforthissuccessistheexaminationof
mutual
effectsbetween
pairs
ofparticlesratherthanlookingateffectsduetosingleparticles.
Einstein by 1915 proposed the equations of both special
relativity (SR) and general relativity (GR). His 1905 paper on
SR assumed (1) physics is unchanged across inertial frames and
(2) the speed of light
c
is unchanged across inertial frames
regardless of whether the light is emitted by a body at rest or
by a body in uniform motion. From these postulates he derived
the Lorentz transformations and the Fitzgerald-Lorentz time and
space dilations. Einstein also showed any ether was superfluous
to his deductions. SR was the culmination of efforts to understand
why Maxwell's equations were invariant to the Lorentz coordinate
transformation. As we have noted relativity is applied as if all
