Tl6 COEFFICIENTS OF INDUCTION. 



rectangle of base (b - a) is 2! (Ib Id). If the second current is only 

 the return of the first we have I = I', and the flow of force comprised 

 between the two conductors, for a height equal to unity, is 



/ b b\ P 



2 I (/._ + / ) =2 I/ 



\ a a J aa 



The expression 



& 



(3) l***,y 



represents the induction relative to a current equal to unity ; that is, 

 the coefficient of self-induction of two parallel wires for unit length. 

 The value thus obtained is, however, in any case only approximate ; 

 we have to take account of the action which each wire exerts in the 

 space it occupies. 



757. Let us suppose that the cylindrical conductor has any given 



section S, and that the density o- of the current is constant. The 



magnetic action which the filament of intensity ov/S, corresponding 



to the element ^S, exerts on a point P at a distance r, is equal to 



, and is perpendicular to the plane rd. 



If, at the point P, there is a linear current parallel to the first, and 

 of unit strength, the action which the filament o-^S would exert on 

 unit length of the second, is directed along the straight line V, and 

 is equal to - . The potential of this action, to within a constant, 

 is - 2<rdStr. 



This expression integrated with respect to the surface S would 

 give for the potential V of the total action of the current ov/S on 

 unit length of the other 



V= - 



Putting 



(4) S/.R 



we may write 



V= -2o-S/.R = -2l/.R . 



