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

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                                different cases in which the rectangular section considered has always 
the same breadth, while the depth was 
A, B, C, A + B, B + C, A + B + C 
and n = 1 in each case 
Calling the results L(A) L(B) L(C) &c 
we calculate the coefficient of mutual induction M(AC) of the <s>extreme<\s> two 
coils thus 
2AC M(AC) = (A + B + C)<sup>2<\sup>L(A + B + C) - (A + B)<sup>2<\sup>L(A + B) - (B + C) <sup>2<\sup>L(B + C) + B<sup>2<\sup>L(B) 
Then if n<sub>l<\sub> is the number of windings in the coil A and n<sub>2<\sub> in the 
coil B the coefficient of self induction of the two coils together is 
L = n<sub>1<\sub><sup>2<\sup>L(A) + 2n<sub>1<\sub>n<sub>2<\sub>L(AC) + n<sub>2<\sub><sup>2<\sup>L(B) 

(114) These values of L are calculated on the supposition that the windings 
of the wire are evenly distributed so as to fill up exactly the whole 
section. This however is not the case, as the wire is generally circular 
and covered with insulating material. Hence the current in the 
wire is more concentrated than it would have been if it had been distributed 
uniformly over the section, and the currents in the neighbouring wires do 
not act on it exactly as <s>they<\s> such a uniform current would do 
The corrections arising from these considerations may be expressed 
as numerical quantities, by which we must multiply the length of the wire 
and they are the same whatever be the form of the coil 
Let the distance between each wire and the next, on the supposition 
that they are arranged in square order be D and let the diameter of the 
wire be d then the correction for diameter of wire is 
+ 2(log D/d + 4/3 log2 + [pi]/3 = 11/6) 
The correction for the eight nearest wires is 
+ 0.0236 
For the sixteen in the next row 
+ 0.00083 

                            
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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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