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 soapbubbles 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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