Clerk Maxwell's electromagnetic theoryLorentz, H. A. (Hendrik Antoon)
Science
Clerk Maxwell's electromagnetic theory
Lorentz, H. A. (Hendrik Antoon)
Electromagnetic theory; Maxwell, James Clerk, 1831-1879
We are also concerned with a stress-energy-tensor, similar to the
electromagnetic one, when we consider a system of material particles,
whether unconnected like the molecules of a gas, or held together by
internal forces as in an elastic body or a fluid. The question naturally
arises: are these stress-energy-tensors, the electromagnetic and, let me
say, the material one, wholly independent or can one be reduced to the
other? One has often tried to do so and, more particularly, to imagine
electromagnetic phenomena as produced by some invisible mechanism moving
according to the laws of dynamics.
This was a favourite idea of Maxwell's and one of his most brilliant
chapters is devoted to the dynamical theory of electromagnetism. It is
the more important because it shows that such a theory can be developed
on very general lines, it not being necessary to make definite
assumptions regarding the underlying mechanism. Maxwell showed that in
the case of linear circuits carrying electric currents we can account
for the ponderomotive forces and for the phenomena of self and mutual
induction by Lagrange's or Hamilton's equations of motion, provided that
we introduce, besides the coordinates which determine the positions of
the material circuits, a certain number of new coordinates, one for each
circuit, the velocities belonging to these coordinates for the several
circuits being proportional to the current intensities. In fact, the new
or "internal" coordinate for each circuit represents the total quantity
of electricity that has traversed some section since a fixed instant
that is chosen as the origin of time. When the internal coordinates are
given this meaning, the magnetic energy becomes the kinetic energy of
the system, whereas the electric energy has to be identified with the
potential energy and is comparable to the energy of deformation of an
elastic body.
While he was applying the laws of dynamics in this very general way,
Maxwell was led to discuss certain phenomena that might perhaps be
expected to exist and some of which have been actually observed in our
days though Maxwell was not able to detect them with the means at his
disposal.
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