PARALLEL CURRENTS. 



The action of a rectilinear and linear current of intensity I on a 

 point P, a distance r (444 and 449), is equal to 2 - , and is per- 

 pendicular to the plane which passes through this point and the 

 current. 



If the section of the conductor is circular, and the current is dis- 

 tributed in homogeneous concentric layers, the force F, by symmetry, 

 is the same for all points of a circumference which has the axis for a 

 centre. The value of the work of the current on an external mass 

 equal to unity, which is on the circumference of radius r^ is 2vrrF. 

 As this work, moreover, is equal to 4?rl (452), we have 



2l 



4?rl = F . 2-n-r, or F = ', 



the force is therefore inversely as the distance of the point from the 

 axis of the current. 



It follows from this, that the action on an internal point only 

 depends on the quantity of electricity which traverses the central 

 core, the radius r of which is equal to the distance of this point from 

 the axis. If the current is homogeneous and of density o- for unit 

 surface, the radius of the cylinder being #, the external action is 



2! a* 



(1) F e = = 27TO--, 



and the internal action 



(2) F f -^.nup-2l^; 



the action of the current which traverses the hollow cylinder TT (a 2 - r^) 

 is null in the cavity of the tube formed by the conductor. 



Let us draw a plane through the axis, and consider in this plane 

 a rectangle of height equal to unity, the base of which measured from 

 the axis is equal to b. The expression for the flow of force which 

 the current emits in the rectangle of base (b - a) is 



2! 



f'*-,K., 



Ja r a 



Let us now suppose that a current I' in the opposite direction 

 traverses a second wire of radius a' t the axis of which is at the 

 distance b. The flow of force from this second current in the 



