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

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                                instant during the removal of the system 

F = [integral]Pdt 

Hence the part of the electromotive force which depends on 
the motion of magnets or currents in the field or their alteration 
of intensity is 

P = - dF/dt  Q = - dG/dt  R = - dH/dt (29) 

Electromagnetic Momentum of a Circuit 

(58) Let s be the length of the circuit, then if we integrate 

[integral](F dx/ds + G dy/ds + H dz/ds) ds (30) 

round the circuit we shall get the total electromagnetic momentum 
of the circuit, or the number of lines of magnetic force which pass through it the variations of which measure the total electromotive 
force in the circuit. This Electromagnetic momentum is the same thing to which 
Prof Faraday has applied the name of the Electronic State 

If the circuit be the boundary of the elementary area dy dz 
then its electromagnetic momentum is (dH/dy - dG/dz)dy dz 
and this is the number of lines of magnetic force which pass 
through the area dy dz. 

Magnetic Force ([alpha] [beta] [gamma]) 

(59) Let [alpha], [beta], [gamma] represent the force acting on a unit magnetic pole placed 
at the given point resolved in the direction of x, y and z. 

Coefficient of Magnetic Induction ([mu]) 

(60) Let [mu] be the ratio of the magnetic induction in a given medium 
So that in air under an equal magnetizing force, then the number 
of lines of force in unit of area perpendicular to x will be [mu][alpha] 
([mu] is a quantity depending on the nature of the medium, its temperature 
the amount of magnetization already produced and in crystalline 
bodies varying with the direction) 

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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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