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

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                                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

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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