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
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