124 COEFFICIENTS OF INDUCTION. 



The geometrical mean distances R^ and R ? relative to the circle, 

 of radius _>, and to the square of the side 2 (y + s) which circumscribes 

 the insulating layer of the wire, gives the ratio 



Rir y 3 36 y 



The excess of the coefficient of self-induction of the circular wire 

 over that of the square wire for unit length is then, from formula (10), 



(14) 2/.^=2 /. -^ + 0-1380606 



&* L 2 J 



761. MUTUAL ACTION OF Two CIRCLES. The formulae given 

 in the preceding chapter for expressing the magnetic field of a 

 circular current will enable us to calculate the coefficient of mutual 

 induction of two circles. We shall assume that the medium is not 

 magnetic, and shall, in the first place, neglect the thickness of the 

 wires. If one of the circles S has a smaller diameter in respect of 

 the distances of the centres, we might take as mean value of the 

 force that which the second circle would exert for unit current on 

 the centre of the first. In the opposite case we should take into 

 account the variations of the force. 



Consider two circular currents S and S' parallel and in the same 

 direction, of radii a and a having the same axis, at a distance x, and 

 take the centre of the first as origin of the co-ordinates. The flow 

 of force which the first circuit sends for unit current in the surface 

 of the second that is to say, the coefficient of mutual induction is 

 then 



The expression of the mean force F m is defined, as we have seen, 

 by that of the component X, which gives 



.SST. 34**->a". 3-5 



The various expressions of X, which we have calculated for coils 

 in particular cases, will give directly the coefficient of mutual 

 induction of these coils, and of a circle with the same axis. 



762. MUTUAL INDUCTION OF Two COILS. Knowing thus the 

 mean action F of a cofl on a circle of radius 7, we can calculate the 



