# J. C. Maxwell’s, ‘Dynamical theory of the electromagnetic field’ ```                                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
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## Cite as

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