Figure 27-9. 



w 



cosOdudv 



(25) 



= k<j | do, — 



kaQ, 



where O is the solid angle subtended by the lamina at the origin of coordinates. 

 If we measure u and v in units of h, we see that 



n 



J J (u 



dudv 



(u 2 + v 2 + l) 3/i 



(26) 



By dividing the lamina into narrow rectangular strips and computing 

 the solid angle subtended by each strip, we can find a sufficiently good approxi- 

 mation to O. The solid angle O' subtended by the strip shown in Figure 

 27-7 is given approximately by 



Q' = 



(y 3 *+l ) (x 2 2 +y 3 2 +l ) V 2 (y 3 2 +l ) ( Xl *+y s *+l ) 1 12 



(y 2 - yi ) (27) 



A map of the function 



— TT-rrz may be plotted from 



l)(x z + y 2 + I) 112 



[y 2 + l)(x* + y~ + 1) 

 values given in Table 27-VI. This map is shown in Figure 27-10. 



MAGNETIC EFFECTS In the problem of computing magnetic fields 



of magnetized bodies the quantity correspond- 

 ing to mass is called the magnetic moment of the body, and the magnetic 

 moment per unit of volume, the quantity corresponding to mass density, 

 is called the intensity of magnetization. In the attraction problem we use the 



597 



