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

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                                72 Energy may e stored up in the field in a different way, namely 
by the action of electromotive force in producing electric 
displacement. The work done by a variable electromotive 
force, P, in producing a variable displacement, f, is got 
by integrating [integral]Pdf 
from P=0 to the given value of P. 
Since P=kf eq<sup>n<\sup> (E) this quantity becomes 
[integral] kfdf = [half]kf<sup>2<\sup> = [half]Pf 
Hence the intrinsic energy of any part of the field, as existing 
in the form of electric displacement is 
<s>[capital sigma] k/2(f<sup>2<\sup> + g<sup>2<\sup> + h<sup>2<\sup>)[delta]V<s> 
[half][capital sigma](Pf + Qg + Rh)dV 
The total energy existing in the field is therefore 
E = [capital sigma]{1/8[pi]([alpha][mu][alpha] + [beta][mu][beta] + [gamma][mu][gamma]) + [half](Pf + Qg + Rh)}dV (I) 
The first term of this expression depends on the magnetization 
of the field and is explained on our theory by actual motion 
of some kind. The second term depends on the electric 
polarization of the field and is explained on our theory 
by strain of some kind in an elastic medium. 
(73) I have on a former occasion* attempted to describe a particu[lar] 
kind f motion and a particular kind of strain so arranged 
as to account for the phenomena. In the present paper I avoid 
any hypothesis of this kind, and in using such words as electric 
momentum and electric elasticity in reference to the known 

*On Physical Lines of Force. Philosophical Magazine 1861-2 
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James Clerk Maxwell
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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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