J. C. Maxwell’s, ‘Dynamical theory of the electromagnetic field’

```                                Relation between Electric <s>Condu<\s> Resistance and Transparency

(106) If the medium, instead of being a perfect insulator is a
conductor whose resistance per unit of volume is [rho] then
there will be not only electric displacements but true currents
of conduction in which electrical energy is transformed into
heat and the undulation is thereby weakened. To determine
the coefficient of absorption let us investigate the propagation
along the axis of x of the transverse disturbance G
By the former equations
d<sup>2<\sup>G/ dx<sup>2<\sup> = - 4[pi][mu](H')
= —4[pi][mu](df/dt + q) by (A)
d<sup>2<\sup>G/dx<sup>2<\sup> = + 4[pi][mu](1/k d<sup>2<\sup>G/dt<sup>2<\sup> - 1/[rho] dG/dt) by (E) & (F) (95)
If G is of the form G = e<sup>-px<\sup> cos (qx + nt> (96) we find that
p = 2[pi][mu]/[rho] n/q = 2[pi][mu]/[rho] V/i (97)
where V is the velocity of light in air and i is the index of refraction
The proportion of incident light transmitted through the thickness x
is e<sup>-2px (98)
Let R be the resistance in <s>absolute<\s> electromagnetic measure of a
plate of the substance whose thickness is x, breadth b and length l
then R = l[rho]/bx
2px = 4[pi][mu] V/2 l/bR (99)

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Manuscript details

Author
James Clerk Maxwell
Reference
PT/72/7
Series
PT
Date
1864
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Cite as

J. C. Maxwell’s, ‘Dynamical theory of the electromagnetic field’, 1864. From The Royal Society, PT/72/7

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