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

```                                <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
currents.

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

Author
James Clerk Maxwell
Reference
PT/72/7
Series
PT
Date
1864
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Cite as

J. C. Maxwell’s, ‘Dynamical theory of the electromagnetic field’, 1864. From The Royal Society, PT/72/7