LAW OF BIOT AND SAVART. 445 



This result seems at first to disagree with experiment, for the 

 action of the current on the pole is applied to the pole itself. This 

 contradiction arises from the fact that in practice the current is 

 necessarily closed. If, for simplicity, we suppose that the general 

 circuit is in a plane passing through the point P, the actions d$ 

 and d<$ of two corresponding elements ds and ds' situate at the 

 angle dQ, are in opposite directions, and inversely as the distances 

 r and r'. The portion which closes the circuit being supposed to be 

 very distant, the difference of the two forces is sensibly equal to the 

 action of the element ds ; but as rd<f> = r'd$, the point of application 

 of the partial resultant is the pole P. This is also the case for the 

 general resultant. The action of the whole circuit is sensibly equal 

 to that of the rectilinear part. 



If the intensity is expressed by means of the electromagnetic unit 

 (460), the action of the unlimited current on the pole m, placed at 



the distance a, is expressed by m , and the elementary formula 



a 



becomes 



mlds sin a 



(i) d$ = - 



or, noting that is the magnetic action F of the mass m at the 

 point occupied by the element of current, 



(2) d<j> 



dA denoting the surface of the parallelogram constructed on the 

 element and on the force F. 



The action exerted on the current Ids, situate in a magnetic field, 

 only depends on the intensity of the field at this point, whatever be 

 the system from which the force proceeds (458) : 



The action exerted on an element of current placed in a magnetic 

 field is equal to the product of the intensity of the current by the area of 

 the parallelogram constructed on the element of current, and on the 

 intensity of the field. This force is perpendicular to the plane of the 

 parallelogram, and directed to the left of the observer placed in the 

 current who is looking in the direction of the field. 



The plane of the parallelogram to which the magnetic force is 

 perpendicular, was called by Ampere the directive plane. 



