# J. C. Maxwell’s, ‘Dynamical theory of the electromagnetic field’ ```                                of the current due to induction, is sometimes called the
counter current.

(36) If an additional resistance v is suddenly thrown into
the circuit, as by breaking contact, so as to force the current to
pass through a thin wire of resistance v, then the original
current is u =[xi]/R and the final current is b = [xi]/R + v.
The current of induction is then [half][xi] 2R + v / R(R + v) and continues for a time 2 L / R + v. This current is greater than that which the battery
can maintain in the two wires R and r and may be sufficient
to ignite the thin wire v.

When contact is broken by separating the <s>parts<\s> wires in air
this additional resistance is given by the interposed air and
since the electromotive force across the new resistance may be
estimated equal to [half][xi} v / R a spark will be force across

If the elctromotive force is of th form E sin pt as in the
case of a coil revolving in a magnetic field then

x = E/[rho] sin (pt - [alpha])

where [rho]<sup>2<\sup> = R<sup>2<\sup> + L<sup>2<\sup>p<sup>2<\sup> and tan [alpha] = L p/R

```
images

## 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