ELECTRO-MAGNETISM. 



or E F,/-. 123, through which an elec- 

 tric current is passing, will be urged by 

 the straight current C D, situated in the 

 same plane with it, in the various direc- 

 tions indicated by the dotted arrows. 

 If these forces were all equal, or nearly 

 Fig. 123. 



so, which could only happen when C D 

 was at an infinite distance, or one in- 

 comparably greater than the diameter of 

 the circle, they would all be in equili- 

 brium. But, in all other cases, portions of 

 the circles nearest to the current will be 

 more powerfully acted upon than the 

 remoter parts, and the forces by which 

 they are impelled will therefore prevail, 

 and the whole circle will tend to ap- 

 proach or recede from C D, according 

 as the direction of the currents in that 

 part is similar or contrary to that of the 

 current C D. Thus it appears that the 

 approximative force is equal to the dif- 

 ference between the resultants of the 

 attractive and repulsive forces. 



(213.) If the circular conductor be 

 now made to revolve on an axis X Y, 

 fg. 124, parallel to C D, and if it be 



Fig. 124. 

 A 



E 



turned on this axis so that its plane is 

 inclined to that which passes through its 

 centre O, and the rectilinear current 

 C D, the directions of the forces at A 

 and B, being out of the plane of the 

 circle, may be decomposed each into a 

 force in that plane along the radius of 



rotation, and into one at right angles to 

 it. The latter of these forces will tend 

 to produce rotation, and to bring back 

 the circle into its position of stable equi- 

 librium E e in the plane common to it 

 and to the current C D. Hence the 

 directive force, or that which tends to 

 bring the circle into this position, by 

 turning it on its axis, is composed of 

 the sum of the resultant forces acting 

 upon the portions on each side of the 

 axis. As the two sets of forces con- 

 spire to produce the same rotation, it 

 matters not, as to the ultimate effect, 

 whether or not the axis pass through 

 the centre of the circle, provided it be 

 parallel to C D, and either within the 

 circle or beyond it, because, in the latter 

 case, where there is an opposition of 

 rotatory forces, the force acting on B 

 being greater than that which acts on A, 

 and also acting at a mechanical advan- 

 tage, will always prevail. 



(214.) Let us next suppose the axis X Y 

 of the circular conductor to be at right 

 angles to C D, as represented in Jig 125. 

 The position of equilibrium will, under 



these circumstances, be precisely the 

 same as the former : for any disturbance 

 from the situation of the circle in which 

 its plane includes the current C D, would 

 give rise, in the portions of the circle 

 nearest to it, to rotatory forces that tend 

 to bring it back to that plane, as may 

 be understood from what was explained 

 in 21 0. These forces will be aided by 

 those that act on the lateral portions of 

 the circle, in which an attraction exists 

 towards those portions of the straight 

 current where the directions correspond, 

 as far as regards the approach to, or 

 recession from the nearest points of the 

 two conductors. The only forces op- 

 posing these are the forces acting upon 

 the remoter parts of the circle, which are 

 of course too weak to change the nature 

 of the effect resulting from the former. 



