# J. C. Maxwell’s, ‘Dynamical theory of the electromagnetic field’ ```                                Part V Theory of Condensers

Capacity of a Condenser

(3) The simplest form of condenser consists of a uniform layer of
insulating matter bounded by two conducting surfaces, and its
capacity is measured by the quantity of electricity in either surface
when the difference of potentials is unity
Let S be the area of either surface, a the thickness of the dielectric
and k its coefficient of electric elasticity then on one side of the
condenser the potential is [psi]<sub>1<\sub> and on the other side [psi]<sub>1<\sub> + 1
and within its substance d[psi]/dx = 1/a = kf (48)
Since d[psi]/dx and therefore f is zero outside the condenser, the quantity
of electricity on its first surface = - Sf and on the second + Sf.
The capacity of the condenser is therefore Sf = S/ak in electromagnetic measure

Specific Capacity of Electric Induction

If the dielectric of the condenser be air then its capacity
in electrostatic measure is S/4[pi]a (neglecting corrections arising
from the conditions to be fulfilled at the edges. If the dielectric
have a capacity whose ratio to that of air is D then the capacity
of the condenser will be DS/4[pi]a

Hense D = k<sub>0<\sub>/k* where k<sub>0<\sub> is the value of k in air which is
taken for unity. *49

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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