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 [equation] (8) 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 [formula] 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
 Author
 James Clerk Maxwell
 Reference
 PT/72/7
 Series
 PT
 Date
 1864
 IIIF

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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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