ACTION OF TWO PARALLEL CURRENTS. 465 



CHAPTER III. 

 PARTICULAR CASES. 



480. ACTION OF Two PARALLEL CURRENTS. According to 

 Ampere's formula, two elements of currents parallel to each other, 

 and perpendicular to the right line which joins their centres, will 

 attract or repel according as the currents are in the same, or in 

 opposite directions. 



This result is usually verified by bringing a rectilinear current, 

 which we may suppose unlimited, near a portion of a rectilinear 

 current movable parallel to itself. The experiment is really more 

 complicated, for each of the currents in question forms part of a 

 closed circuit. In whatever manner we may suppose the planes of 

 the two currents placed in reference to each other, bringing the two 

 rectilinear portions near each other will increase, for each of them, 

 the flow of force which it will receive from the other by its negative 

 surface, and will diminish the relative energy if the currents are in 

 the same direction ; the converse takes place when they are in 

 opposite directions. 



Let I be the intensity of the unlimited current, I' that of the finite 

 current, which is parallel to it, and b its length. If we vary the 

 distance a of the two currents (which we suppose in the same 

 direction) by da, the variation in the flow of force which enters the 

 circuit from the movable current is 



= -bda = -2lb ; 

 a a 



the force exerted upon the movable part of the circuit is expressed 



by I'- = 211'-, it is therefore inversely as the distance a. 

 da a 



481. ANGULAR CURRENTS. Two rectilinear currents placed 

 near each other tend to set parallel. This result is usually enunciated 



H H 



