true.
How is electromagnetic inertia practically eliminated? First, by the
use of two massive copper wires, and secondly by symmetrically
revolving them around each other. Now L depends on the geometry of the
circuit, that is, on the relative form and position of the different
parts of the circuit, which is invariable for the same circuit, and is
represented by a coefficient, [lambda]. It depends also on the
magnetic qualities of the conductors employed and of the space
embraced by the circuit. This specific magnetic capacity is a variable
quantity, and is indicated by [mu] for the conductor and by [mu]_{0}
for air. It depends also on the rate at which currents rise and fall,
and this is indicated by the differential coefficient dC / dt. It
depends finally on the number of lines of force due to its own current
which cut the conductor in the proper direction; this is indicated by
[beta]. Combining these together we can represent the electromagnetic
inertia of a metallic telephone circuit as
L = [lambda] ([mu] + [mu]_{0}) dC/dt x [beta]
Now, [lambda] = 2 log (d squared/a squared) Hence the smaller we make the distance,
_d_, between the wires, and the greater we make their diameter, _a_,
the smaller becomes [lambda]. It is customary to call the value of
[mu] for air, and copper, 1, but this is purely artificial and
certainly not true. It must be very much less than one in every
medium, excepting the magnetic metals, so much so that in copper it
may be neglected altogether, while in the air it does not matter what
it is, for by the method of twisting one conductor round the other,
the magnetization of the air space by the one current of the circuit
rotating in one direction is exactly neutralized by that of the other
element of the circuit rotating in the opposite direction.
Now, [beta], in two parallel conductors conveying currents of the same
sense, that is flowing in the same direction, is retarding, Fig. 2,
and is therefore a positive quantity, but when the currents flow in
opposite directions, as in a metallic loop, Fig. 3, they tend to
assist each other and are of a negative character. Hence in a metallic
telephone circuit we may neglect L _in toto_ as I have done.
[Illustration: Fig 2.]
[Illustration: Fig. 3.]
I have never yet succeeded in tracing any evidence of electromagnetic
inertia in long single copper wires, while in iron wires the value of
L may certainly be taken at 0.005 henry per mile
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