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

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                                On Lines of Magnetic Force 

(49) Let any surface be drawn, cutting the lines of magnetic 
force, and on this surface let any system of lines be drawn 
at small intervals, so as to lie side by side without cutting 
each other. Next, let any line be drawn on the surface 
cutting all these lines, and let <s>another<\s> a second line be drawn 
near it, its distance from the first being such that the value 
of M for each of the small spaces enclosed between these two lines 
and the lines of the first system is equal to unity. 

In this way let a second system of lines be drawn so that 
the value of M for every reticulation formed by the intersection 
of the two systems of lines is unity. 

Finally from every point of intersection of these reticulations 
let a line <s>of magnetic force<\s> be drawn through the field, always 
coinciding in direction with the direction of magnetic force. 

(50) In this way the whole field will be filled with lines of 
magnetic force at regular intervals, and the properties of 
the electromagnetic field will be completely expressed by them. 
For 1<sup>st<\sup> If any closed curve be drawn in the field, the value 
of M for that curve will be expressed by the <u>number<\u>  of lines 
of force which <u>pass through<\u> that closed curve. 
2<sup>nd<\sup> If this curve be a conducting circuit and be moved through 
the field an electromotive force will act in it, represented by 
the <s>number<\s> rate of decrease <s>in unit of time<\s> of the number of lines passing through the 

3<sup>rd<\sup> If a current be maintained in the circuit, <s>it<\s> the conductor will be 
acted on by forces tending to move it so as to increase the 
number of lines passing through it, and the amount of 
work done by these forces is equal to the current in the 
circuit multiplied by the number of additional lines. 
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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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