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

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                                <s>Electrical Quantity (e) 

Let e represent the quantity of free electricity in unit of volume 
(either positive or negative) then the equation of continuity is 

e + df/dx + dg/dy + dh/dz = 0 (5) <\s>

Electromotive force (P Q R) 

(56) Let P, Q, R represent the components of the Electromotive Force 
at any point. 

Then P represents the difference of potential per unit of length 
in a conductor placed in the direction of <u>x<\u> at the given point. 
We may suppose an indefinitely  short wire placed parallel to x 
at the given point and touched, during the action of the force P by 
two small conductors which are then insulated and removed from 
the influence of the electromotive force. The value of P might then 
be ascertained by measuring the charges of the conductors. 

Thus if l be the length of the wire the difference of potential of its 
ends will be Pl and if C be the capacity of each of the small conductors 
the charge on each will be [half]CPl. Since the capacities of moderately 
large conductors, measured on the electromagnetic system are exceedingly 
small, ordinary electromotive forces arising from electromagnetic 
actions could hardly be measured in this way. In practice such 
measurements are always made with long conductors forming closed 
or nearly closed circuits. 

Electromagnetic Momentum (F G H) 

(57) Let F G H represent the components of Electromagnetic Momentum 
at any point of the field, due to any system of magnets or 

Then F is the total impulse of the electromotive force that 
would be generated by the removal of these magnets or currents 
from the field, that is if P be the electromotive force at any 

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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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