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

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                                The instantaneous discharge is therefore [psi]/ak or the quantity which 
would be discharged by <s>an air<\s> a condenser of air of the equivalent 
thickness a, and it is <s>independent of<\s> unaffected by the want of perfect insulation. 

(88) Now let us suppose the connexion between the surfaces 
broken and the condenser left to itself and let us consider 
the gradual dissipation of the internal charges. Let [psi]' be the 
difference of potential of the extreme surfaces at any time t, then 
[psi]' = a<sub>1<\sub>k<sub>1<\sub>f<sub>1<\sub> + a<sub>2<\sub>k<sub>2<\sub>f<sub>2<\sub> + &c (56) 
but a<sub>1<\sub>k<sub>1<\sub>f<sub>1<\sub> = <s>- a<sub>1<\sub>k<sub>1<\sub>e<sub>1<\sub><\s> = - r<sub>1<\sub> df<sub>1<\sub>/dt 
a<sub>2<\sub>k<sub>2<\sub>f<sub>2<\sub> = - r<sub>2<\sub> df<sub>2<\sub>/dt. 
Hence <s>a<sub>1<\sub>k<sub>1<\sub>f<sub>1<\sub><\s> f<sub>1<\sub> = A<sub>1<\sub> e<sup>-<s>a<sub>1<\sub>k<sub>1<\sub>/r<sub>1<\sub> t<\sup> f<sub>2<\sub> = A<sub>2<\sub> e<sup>-<s>a<sub>2<\sub>k<sub>2<\sub>/r<sub>2<\sub> t<\sup> &c 
and by referring to the values of e'<sub>1<\sub> e<sub>2<\sub> &c we find 
A<sub>1<\sub> = [psi]/r r<sub>1<\sub>/a<sub>1<\sub>k<sub>1<\sub> - [psi]/ak 
A<sub>2<\sub> = [psi]/r r<sub>2<\sub>/a<sub>2<\sub>k<sub>2<\sub> - [psi]/ak
&c

so that we find for the difference of extreme potentials at any time 
<s>[eqation]<\s>
[equation]
(89) It appears 
from this result that if all the layers are made 
of the same substance [psi]' will be zero always. I f they are of 
different substances, the order in which they are placed is 
indifferent, and the effect will be the same whether each 
substance consists of one layer or is divided into any 
number of thin layers and arranged in any order among 
thin layers of the other substances. Any substance, therefore 
the parts of which are not mathematically homogeneous, though they may 
be apparently so, may exhibit phenomena of absorption. 
                            
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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

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