PROPERTIES OF CIRCULAR CURRENTS. 477 



considered as attractive, which is exerted between the two circuits, 

 and we have 



dh ' 



We thus obtain, all reductions being made, 



If the strengths of the currents in the two frames are respectively 

 I and I', the expression for the mutual action is 



where P is the sum of the terms in the brackets. 



493. PROPERTIES OF CIRCULAR CURRENTS. The potential of 

 a circular current is equal, within a constant, to that of a shell of the 

 same strength and the same contour. We have given above (368) 

 the expression of this potential for any given point. If the point is 

 on an axis at a distance x from the centre, it is sufficient in equation 

 (16) to make p = 0; replacing < by I, we get 



V=27Tl 



from which is deduced 



a 2 IS 



denoting by S the surface of the circle. For a point on the axis the 

 force is inversely as the cube of the distance to the contour. 



This force is a maximum at the centre of the circle ; we 

 have then 



IS I IL 



L being the length of the circumference. 



