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

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                                <s>Hence the total counter current in each element 
1/[rho] (T<sub><s>0<\s>[infinity]<\sub> - T<sub><s>[infinity]<\s>0<\sub>) + [mu][pi]/[rho]<sup>2<\sup> Pr<sup>2<\sup> 
Integrating over the section of the wire from r = 0 to r = r 
1/[rho] (T<sub><s>0<\s>[infinity]<\sub> - T<sub><s>[infinity]<\s>0<\sub>)[pi]r<sup>2<\sup> + [mu][pi]/[rho]<sup>2<\sup> P[pi]r<sup>4<\sup>/2 
or since P/[rho] = p and if C be the total current c = [pi]r<sup>2<\sup>p 
the second term becomes [half][mu][pi]/[rho] C r<sup>2<\sup> 
Now if p instead of being variable from the centre to the 
circumference of the wire had been uniform at every instant 
throughout the section the second term would have been 
3/4 [mu][pi]/[rho] Cr<sup>2<\sup> 
Now the counter current is L/R C 
Hence the correction to be applied on account of the 
current being variable is 
- 1/4 per unit of length <\s>

                            
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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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