Field of a Circular Current. 



357 



On account of the symmetry of the current round its 

 axis through 0, the lines of force and those of constant 

 vector potential are the same in all planes through the axis. 

 We may, then, confine our attention to the plane PON, 

 and suppose fig. 2 to be in this plane, the current being 



Fig. 2. 



in this figure represented in projection by the line BA. 

 Describe a series of circles having their centres on BA pro- 

 duced and cutting the circle described on BA as diameter 



. PA 



orthogonally. Along each of these circles, then, the ratio p^ 



is constant, P being any point on the circle. 



Consider first the lines of constant vector potential. For 



2 

 each of the circles let the value of the quantity ^ (K — E) — K 



be calculated. Denote this quantity by Q for any one circle ; 

 then 



so that if we wish to trace out the line of constant vector 

 potential for which G- has any given value, we can find the 

 point, P, in which it cuts any circle of the series by measuring 



