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

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                                (17) We know that when an electric current is established in a conducting 
circuit, the neighbouring part of the field is characterized by certain 
magnetic properties, and that if two circuits are in the field, the 
magnetic properties of the field due to the two currents are combined. 
Thus each part of the field is in connexion with both currents, 
and thus the two currents are put in connexion with each other 
in virtue of their connexion with the magnetization of the field. 
The first result of this connexion that I propose to examine 
is the induction of one current by another, and by the motion 
of conductors in the field. 

The second result, which is deduced from this, is the mechanical 
action between conductors carrying currents. The phenomenon 
of the induction of currents has been deduced from their mechanical 
action by Helmholtz* and Thomson+. I have followed the reverse order 
and deduced the mechanical action from the laws of induction. 

<s>(18)<\s> I have then <s>explain<\s> described experimental methods of determining 
the quantities L, M, N on which these phenomena depend. 

(18) I then apply the phenomena of induction and attraction of currents 
to the exploration of the electromagnetic field, and the laying down 
systems of lines of magnetic force which indicate its magnetic 
properties. By exploring the same field with a magnet, I show 
the distribution of its equipotential magnetic surfaces, cutting 
the lines of force at right angles. 

In order to bring these results within the power of 
symbolical calculation, I then express them in the form 
of the General Equations of the Electromagnetic Field. 

These equations express 
(A) the relation between electric displacement, true conduction and 
the total current, compounded of both. 
(B) The relation between the lines of magnetic force and the inductive coefficients 
of a circuit, as already deduced from the laws of induction. 
(C) The relation between the strength of a current and its magnetic 
effects, according to the electromagnetic system of measurement. 

*Conservation of Force. Physical Society of Berlin, 1847 & Taylors Scientific Memoirs 1853 p 114 
+Trans British Association 1848 Phil Mag. Dec 1851 
                            
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Manuscript details

Author
James Clerk Maxwell
Reference
PT/72/7
Series
PT
Date
1864
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J. C. Maxwell’s, ‘Dynamical theory of the electromagnetic field’, 1864. From The Royal Society, PT/72/7

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