Figure 218 — Streamlines due to a point dipole at b near a sphere. See Section 131. 



132. LINE OF TRANSVERSE DIPOLES 



Suppose that point dipoles are distributed continuously along a line with their axes 

 lying perpendicularly to the line but in a common plane. Let the a;-axis be taken along the 

 line and the y-axis in the direction of the dipole axes, and let the dipole strength per unit 

 length be v. Then the potential due to the dipoles on an element t/a;' located at a; = x% as 

 found by writing in Equation [119s] ii= vdx% x^ = x% y^ = 2j = 0, Z = n = and m = I, is 



vydx' 



[2^:^ + {x-x'f\' 



9 7 1/2 



[132a, b] 



The total potential at {x, y, z) is then ^d(fi which can be evaluated when i/ is known as a 

 function of x. 



330 



