EXTERNAL POTENTIAL OF A LONG COIL. 135 



768. CIRCULAR CURRENT. From equation (14) of (367) the 

 potential on the axis of a circular current of radius a, and intensity 

 equal to unity, is for x>a 



2. 4 ...(2+2) 



The potential at the point P beyond the axis is then 



.4. . 



The components of the action are then, taking into account 

 equations (27), 



(31) 



When the point P is very near the plane of the current, but at a 

 greater distance from the centre of the circle than the radius a, we 

 may put = - - 8, the angle 8 being very small. Neglecting then 

 terms of the order of S 3 , we get 



769. EXTERNAL POTENTIAL OF A LONG COIL. Let us consider 

 a cylindrical coil C (Fig. 141) of radius a, of length ^, and formed of 

 a single layer of wires comprising n l turns for unit length. The 

 potential at an external point P is the same as that of the two bases 

 A and B on which are the magnetic layers of densities respectively 

 equal to +n l and - n l ; that is to say, from equation (26), 



