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

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                                Now if work is done when a body is moved it must arise from 
ordinary mechanical force acting on the body while it is moved 
Hence this part of the expression shows that there is a 
mechanical force urging every part of the conductors themselves in that 
direction in which L M and N will be most increased 

The existence of the electromagnetic force between conductors 
carrying currents is therefore a direct consequence of the joint and 
independent action of each current on the electromagnetic field. 
If A and B are allowed to approach a distance s so as to increase 
M from M to M' while the currents are x and y, then the 
work done will be (M' - M) xy and the force in the direction 
s will be dM/dS xy (12) 
and this will be an attraction if x and y are of the same sign 
and if M is increased as A & B approach. 

(35) It appears therefore that if we admit that the unresisted part 
of electromotive force goes on as long as it acts a 
self=persistent state of the current which we may call (from 
mechanical analogy) its electromagnetic momentum 
and that this momentum depends on circumstances external to the 
conductor, then both induction of currents and electromagnetic 
attractions may be proved by mechanical reasoning. 

What I have called electromagnetic momentum is the same quantity 
which is called by Faraday* the Electrotonic State of the circuit 
every change of which involves the action of an electromotive force 
just as change of momentum involves the action of mechanical force. 
If therefore the phenomena described by Faraday in the Ninth Series 
of his Experimental Researches were the only known facts about electric 
currents, the laws of Ampere relating to the attraction of conductors 
carrying currents, as well as those of Faraday about the mutual induction 
of currents might be deduced by mechanical reasoning. 
* Exp. Re. Series I 60&c


                            
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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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