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

```                                Electromagnetic Relations of two Conducting Circuits.
(28.) In the case of two conducting circuits A and B we shall assume
that the electromagnetic momentum belonging to A is
Lx + My
and that belonging to B, Mx + Ny
where L M N correspond to the same quantities in the dynamical
illustration except that they are supposed to be capable of variation
<s>according<\s> when the conductors A or B are moved.
Then the equation of the current x in A will be
[xi] = Rx + d/dt(Lx + My)  (4)
and that of y in B [eta] = Sy + d/dt(Mx + Ny) (5)
where [xi] and [eta] are the electromotive forces x and y the currents
and R & S the resistances in A and B respectively.

Induction of one Current by another

(29) Case 1<sup>st<\sup> Let there be no electromotive force on B except that which arises
from the action of A, and let the current of A increase from 0 to the
value x then Sy + d/dt(Mx + Ny) = 0
whence Y =[integral]ydt = - M/S x <s>(6)<\s>
that is a quantity of electricity Y being the total induced current
will flow through B when x rises from 0 to x. This is induction
by variation of the current in the primary conductor. When M
is positive, the induced current due to increase of the primary
current is negative.

Induction by motion of conductor

(30) Case 2<sup>nd<\sup> Let x remain constant and let M change from M to M'
then Y = - M1 -M / S x <s>(7)<\s>
so that if M is increased, which it will be by the primary and
secondary circuits approaching each other, there will be a
negative induced current, the total quantity of electricity passed
through B being Y.

This is induction by the relative motion of the primary and secondary conductors.
```
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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