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

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                                If these surfaces are so drawn that when a unit pole passes 
from any one to the next in order, unity of work is done 
then the work done in any motion of a magnetic pole 
will be measured by the strength of the pole multiplied by 
the number of surfaces which it has passed through in the 
positive direction. 

(52) If there are circuits carrying electric currents in the field, then there will 
still be equipotential surfaces in the parts of the field external 
to the conductors carrying the currents, but the work done 
on a unit pole in passing from one to another will depend 
on the number of times which the path of the pole <s>passes<\s> 
[ci]rculates round any of these currents. Hence the <s>value of the<\s> potential 
in each surface will have a series of values in arithmetical 
progression, differing by the work done in passing completely 
round one of the currents <s>of<\s> in the field. 

The equipotential surfaces will not be continuous closed surfaces 
but some of them will be limited sheets, terminating in the 
electric circuit as their common edge or boundary. The 
number of these will be equal to the amount of work done 
on a unit pole in going round the current, and this 
by the ordinary measurement = 4[pi][gamma] where [gamma] is the value 
of the current. 

These surfaces, therefore, are connected with the electric current 
as soap-bubbles are connected with a ring in M Plateaus 
experiments. Every current [gamma] has 4[pi][gamma]surfaces attached 
to it. These surfaces have the current for their common 
edge and meet it at equal angles. The form of the surfaces 
in other parts depends on the presence of other currents and magnets 
as well as on the shape of the circuit to which they belong. 
                            
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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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