James Clerk Maxwell and Modern PhysicsGlazebrook, Richard
History
James Clerk Maxwell and Modern Physics
Glazebrook, Richard
Maxwell, James Clerk, 1831-1879; Physics -- History
Now let us go back to the variable period when the current is flowing
in the wires; and to make ideas precise, let the two conductors be two
equal large flat plates placed with their faces parallel, and at some
small distance apart. In this case, when the plates are charged, and
the current has ceased, the electric displacement and the force are
confined almost entirely to the space between the plates. During the
variable period the total flow at any instant across each section of
the wire is the same, but in the ordinary sense of the word there is no
flow of electricity across the insulating medium between the plates.
In this space, however, the electric displacement is continuously
changing, rising from zero initially to its final steady value when the
current ceases. It is a fundamental part of Maxwell’s theory that this
variation of electric displacement is equivalent in all respects to a
current. The current at any point in a dielectric is measured by the
rate of change of displacement at that point.
Moreover, it is also an essential point that if we consider any section
of the dielectric between the two plates, the rate of change of the
total displacement across this section is at each moment equal to the
total flow of current across each section of the conducting wire.
Currents of electricity, therefore, including displacement
currents, always flow in closed circuits, and obey the laws of an
incompressible fluid in that the total flow across each section of the
circuit--conducting or dielectric--is at any moment the same.
It should be clearly remembered that this fundamental hypothesis of
Maxwell’s theory is an assumption only to be justified by experiment.
Von Helmholtz, in his paper on “The Equations of Motion of Electricity
for Bodies at Rest,” formed his equations in an entirely different
manner from Maxwell, and arrived at results of a more general
character, which do not require us to suppose that currents flow always
in closed circuits, but permit of the condensation of electricity at
points in the circuit where the conductors end and the non-conducting
part of the circuit begins. We leave for the present the question which
of the two theories, if either, represents the facts.
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