ELECTROMAGNETIC RADIATION IN A MOVING CONDUCTING MEDIUM: FIRST-ORDER THEORY,
CASE INST OF TECH CLEVELAND OHIO
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The primary objective of the investigation was to examine the electromagnetic radiation resulting from sources of arbitrary time dependence in a homogeneous, isotropic, conducting medium of infinite extent. The material is assumed to be moving at a uniform velocity with respect to the rest frame of the source distribution. To avoid excessive difficulties in the ensuing development, only the non-relativistic approximation situation was considered. Because no solution to this problem could be found in the literature, it was considered worthwhile to find the modification of the character of the radiation due to the presence of conductivity. It is determined first that the electromagnetic field intensities referred to the laboratory system are expressible in terms of a pair of scalar and vector potential functions satisfying symmetric hyperbolic partial differential equations of the second order with respect to time and space coordinates. This is made possible by invoking a generalized Helmholtz theorem, and specifying a new type of Lorentz condition. Ordinarily, one would proceed to solve for the time-dependent Greens function associated with the potential equations by using both time and space Fourier transformations. Instead of following this classical approach, however, the author introduced an alternative method which is based on the fact that there exists a relation between the fundamental solution of a radiation problem and that of a corresponding Cauchy initial-value problem.
- Electricity and Magnetism
- Quantum Theory and Relativity