If V is constant between x <= c. and x = c^ and zero elsewhere, 



../■_ 



y dx' 



vy 



J {co^ + {x - x') ] 



[oT^ + {x- x'f] 



Let (u denote an angle about the a?-axis measured from the a;y-plane, so that x, oT, w constitute 

 cylindrical coordinates. Then y = oTcos oj and 



= -;^ (cos d. - cos d„) cos (U 



[132c] 



where d^ and i?, are the angles between the positive a;-axis and lines drawn to {x, y, z) fror 

 the ends of the line of dipoles; see Figure 219. 



Figure 219 — A line of transverse 

 point dipoles. See Section 132. 



If the dipoles extend over the entire a!-axis, c ->-«=, C2 -> + o°, ^j = 0, 6„ = n, and 



2v 2vy 

 ,j!, = — - cos w = . [132d] 



as for a uniform line dipole; see Sections 15 and 37. 



If the dipoles extend only over the positive a;-axis, 0^ = n but 6^=0 where d is 

 measured from the a;-axis to a radius drawn from the origin, and 



(jj = —- (1 + cos d) cos w = ^3 ( 1 "*" — I cos &) 



[132e] 



331 



