# J. C. Maxwell’s, ‘Dynamical theory of the electromagnetic field’ ```                                Electromotive Force in a Circuit

[6?]3 Let [xi] be the electromotive force acting round the circuit A
then [xi] = [integral](P dx/ds + Q dy/ds + R dz/ds)ds (32)
where ds is the element of length and the integration is
performed round the circuit
Let the forces in the field be those due to the circuits A & B, then
the electromagnetic momentum of A is
[integral] (F dx/ds + G dy/ds + H dz/ds) ds = Lu + Mv (33)
where u and v are the currents in A & B
and [xi] = -d/dt(Lu + Mv) (34)

Hence if there is no moton of the circuit A

P = -dF/dt - d[psi]/dx
Q = -dG/dt - d[psi]/dy
R = -dH/dt - d[psi]/dz (35)

where [psi] is a function of x y z & t which is indeterminate as
far as regards the solution of the above equations because the
terms depending on it will disappear on integrating
round the circuit. The quantity [psi] can always however
be determined in any particular case when we know
the actual conditions of the question. The physical interpretation
of [psi] is that it represents the <u>electric potential<\u> at each
point of space.

```
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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