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

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                                (61) Expressing the <s>result of the<\s> electric momentum of small circuits 
perpendicular to the three axes in this notation we obtain 
the following 

Equations of Magnetic Force

[mu][alpha] = dH/dy - dG/dz 
[mu][beta] = dF/dz - dH/dx 
[mu][gamma] = dG/dx - dF/dy (B) 

Equations of Currents 

(62) It is known from experiment that the motion of a magnetic pole 
in the electromagnetic field in a closed circuit cannot generate 
work unless the circuit which the pole describes passes round 
an eectric current. Hence, except in the space occupied 
by the electric currents 

[alpha]dx + [beta]dy + [gamma]dz = d[phi] (39) 

a complete differential of [phi], the magnetic potential 

The quantity [phi] may be susceptible of an indefinite number of distinct 
values according to the number of times that the exploring point 
passes round electric currents in its course, the difference between 
successive values of [phi] corresponding to a passage completely 
round a current of strength C being 4[pi]C

Hence if there is no electric current 

d[gamma]/dy - d[beta]/dz = 0 

but if there is a current p' 

d[gamma]/dy - d[beta]/dz = 4[pi]p' 

Similarly d[alpha]/dz - d[gamma]/dx = 4[pi]q' 
d[beta]/dx - d[alpha]/dy = 4[pi]r' (C) <s>(10)<\s> 

We may call these the Equations of Currents 

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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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