Electromagnetic Relations of two Conducting Circuits. (28.) In the case of two conducting circuits A and B we shall assume that the electromagnetic momentum belonging to A is Lx + My and that belonging to B, Mx + Ny where L M N correspond to the same quantities in the dynamical illustration except that they are supposed to be capable of variation <s>according<\s> when the conductors A or B are moved. Then the equation of the current x in A will be [xi] = Rx + d/dt(Lx + My) (4) and that of y in B [eta] = Sy + d/dt(Mx + Ny) (5) where [xi] and [eta] are the electromotive forces x and y the currents and R & S the resistances in A and B respectively. Induction of one Current by another (29) Case 1<sup>st<\sup> Let there be no electromotive force on B except that which arises from the action of A, and let the current of A increase from 0 to the value x then Sy + d/dt(Mx + Ny) = 0 whence Y =[integral]ydt =  M/S x <s>(6)<\s> that is a quantity of electricity Y being the total induced current will flow through B when x rises from 0 to x. This is induction by variation of the current in the primary conductor. When M is positive, the induced current due to increase of the primary current is negative. Induction by motion of conductor (30) Case 2<sup>nd<\sup> Let x remain constant and let M change from M to M' then Y =  M1 M / S x <s>(7)<\s> so that if M is increased, which it will be by the primary and secondary circuits approaching each other, there will be a negative induced current, the total quantity of electricity passed through B being Y. This is induction by the relative motion of the primary and secondary conductors.
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Manuscript details
 Author
 James Clerk Maxwell
 Reference
 PT/72/7
 Series
 PT
 Date
 1864
 IIIF

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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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