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

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                                Part III General Equations of the Electromagnetic Field 

(53) Let us assume three rectangular directions in space as the 
axes of x and z and let all quantities having direction 
be reduced to these directions so as to be expressed by their 
components in these three directions. 

Electrical Currents (p q r) 

(54) An electrical current consists in the transmission of electricity 
from one part of a body to another. Let the quantity of electricity 
transmitted in unit of time across unit of area perpendicular 
to the <s>direction<\s> axis of x be called p, then p is the component 
of the current at that place in the direction of x 

We shall use the letters p q r to denote the components 
of the current per unit of area in the <s>coordinate<\s> directions of x, y , z. 

Electrical Displacements (f g h) 

(55) Electrical Displacement consists in the <s>[text?] polarization which<\s> 
opposite electrification of the sides of a molecule or particle of a 
body which may or may not be accompanied with transmission 
through the body. Let the quantity of electricity which would appear 
on the faces dy dz of an element dx dy dz cut from the body be 
f <s>dx<\s> dy dz then f is the component of electric displacement 
parallel to x. We shall use f, g, h to denote the electric 
displacements parallel to x y z respectively. 

The variations of the electrical displacement must be added 
to the currents p q r to get the total motion of electricity 
which we may call p' q' r',  so that 

p' = p + df/dt
q' = q + dg/dt 
r' = r + dh/dt 

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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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