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

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                                Equation of Work and Energy 

(31) To form the equation between work done and energy produced 
multiply (1) by x and (2) by y and add 

Here [xi] is the work done in unit of time by the electromotive 
force [xi] acting on the current x and maintaining it, and [eta]y is the 
work done by the electromotive force [eta]. Hence the left hand side 
of the equation represents the work done by the electromotive forces 
in unit of time. 

<u>Heat produced by the Current<\u> 

(32) On the other side of the equation we have first 
Rx<sup>2<\sup> + Sy<sup>2<\sup> = H (9) 
which represents the work done in overcoming the resistance 
of the circuits in unit of time. This is converted into Heat. 
The remaining terms represent work not converted into heat 
They may be written 


Intrinsic Energy of the Currents. 

(33) If L, M, N are constant, the whole work of the electromotive 
forces which is not spent against resistance will be devoted to 
the development of the currents The whole intrinsic energy 
of the currents is therefore 
[half] Lx<sup>2<\sup> + Mxy + [half]Ny<sup>2<\sup> = E (10) 
This energy exists in a form imperceptible to our senses 
probably as actual motion, the seat of this motion being not 
merely the conducting circuits but the space surrounding them 

Mechanical Action between conductors 
(34) The remaining terms 
[half]dL/dtx<sup>2<\sup> + dM/dtxy + [half]dN/dty<sup>2<\sup> = W (11)

are the work done in unit of time arising from the variations 
of L M & N, or what is the same thing alterations in the form 
and position of the conducting circuits A and B. 
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Manuscript details

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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