TWO CIRCLES WITH CURRENTS IN OPPOSITE DIRECTIONS. Ill 



the length of the wire is then a little less, so that this latter com- 

 bination is advantageous from all points of view. 



752. Two CIRCLES WITH CURRENTS IN OPPOSITE DIREC- 

 TIONS. Let us suppose in two parallel frames the current passed in 

 opposite directions. The components parallel to the axis of the 

 actions of the two frames are at each point in opposite directions, 

 and the components perpendicular to the axis remain in the same 

 direction in the interval of the frames. 



Let X0 and Y be the values of each of the partial components 

 in the plane of symmetry of the two currents. In two planes on 

 either side at the distance dx, and for the same distance from the 

 axis, we shall have 



and analogous expressions for the components V l and Y 2 . 

 Limiting ourselves to the first terms 



. 

 ~dx' 2 u^ u u 6 u^ u 



In these expressions x represents the distance of the middle 

 plane of the two circles. It will be seen that the component will be 

 independent of y, and the component Y independent of dx, if we 

 take 4* 2 = 3tf 2 . 



With this arrangement the field is symmetrical in respect of the 

 centre of the system of the two frames, and the action of the current 

 would be null on a needle exactly centred in this point. 



753. MEAN ACTIONS. Let us suppose a circle of radius y, 

 covered with a uniform magnetic layer of density equal to unity, 

 and situate in the field of a current or of a coil. If the circle has 

 the same axis as the currents in question, the action of the field 

 on this axis is parallel to the axis and equal to the integral of 

 ~X.2irydy taken between the limits and y. If the value of X has 

 an expression of the form 



