776 



ELECTRICAL METHODS 



[Chap. 10 



The electromagnetic fields of cables or loops are readily calculated. For 

 a long cable the field some distance away is practically vertical if the 

 observation points are located at the same elevation. Since the magnetic 

 intensity of a current element ds at a point P having the polar coordinates 

 R and a is equal to Ids sin a/R , the normal field is 



Zo = — - (sin aa ± sin ai), 

 lOr 



(10-49a) 



where r is the distance normal to the line, and the current 7 is in amperes 

 (see Fig. 10-99a). The minus sign apphes if P is below Ei . If P, Ei , 



f, (a) 



(c) 



Fig. 10-99. Horizontal cables and loops. 



and J&2 are all at the same elevation, the horizontal components are zero. 

 If P is halfway between Ei and E2 , oci = 02 and 



Zo = 



I 



5r ^/p-^ri' 



(10-496) 



where 21 is the distance between Ei and E2 . 



If the point P is not at the same elevation with the cable and if a line 

 connecting the center of the search coil and the line E1-E2 makes an angle 

 (pi with the vertical (Fig. 10-996), a horizontal component is produced in 



