MAGNETIC METHODS 



191 



are approximately the same as those produced by surface distributions of 

 magnetic charge located on the upper and lower faces of the stratum. 



Before deriving the anomalies produced by two-dimensional geologic 

 bodies, it will be convenient to describe: (a) the magnetic fields produced 

 by linear distributions of charge and (b) the general expressions for the 

 magnetic potential and magnetic field produced by surface distributions 

 of charge. 



Fig. 83. — Sketch illustrating geomet- 

 ric relations between a linear distribu- 

 tion of magnetic charge in the direction 

 X and an external point P. 



Magnetic Fields Produced by Linear Distributions of Charge. — The 



magnetic field of force in the direction R due to element dx (Figure 82) is : 



dF = 



dx 



i?2 



where m equals the pole strength per unit length. The force dF is the 

 vector sum of the components of dF^ in the direction normal to .r and dF^. 

 in the direction parallel to x. 



But 



dFr = ^dx 



Hence, the component in the direction r due to the whole line is 



dx 



i mr , ^ i mr , ^ i 

 \^dx = 2\-^dx = 2mr I 





/ 



Let 



then 



X -= r tan Q 

 dx — r sec-^ dQ 



x^ + r^ 



r^ sec" 



F.= 



L m r 



7r/2 



cos ede = 



2in 



(78) 



