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

View transcription
                                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. 


                            
Please login to transcribe

Manuscript details

Author
James Clerk Maxwell
Reference
PT/72/7
Series
PT
Date
1864
IIIF
Open IIIF manifest
(What's this?)
This is a link to the IIIF web URL for this item. You can drag and drop the IIIF image link into other compatible viewers

Cite as

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

Copy

Comments

Please login to comment