ELECTRICAL METHODS 



607 



The application of Equation 11 in inductive prospecting will be indi- 

 cated in the following section. 



General Characteristics of Induced Fields. — Certain general ideas 

 relative to the type of magnetic field to be expected when currents are 

 induced in conducting masses 

 buried in the earth may be ob- 

 tained from a consideration of 

 the interaction between the two /^ 

 coils P and 5 shown in Figure 

 380. t 



An alternating current Ip = Ipm 

 cos wt is sent through the pri- 

 mary circuit P. This current 

 induces an E.M.F. in the secon- g 

 dary circuit whose magnitude is 

 given by Equation 11 ; that is, 





E = -M -jr = wMIpm sin wt 



where M is the mutual induct- 

 ance between the two circuits. 



The electromotive force E 

 causes a current /« to flow in the 

 secondary circuit. If the capacity 

 of the secondary circuit is small, 

 Rs denotes the resistance and Lg 

 current is : 



Fig. 380. — A, sketch illustrating resultant mag- 

 netic fields H and //, due to the primary and 

 secondary coils P and S. B, curve H,„ shows the 

 general shape of the vertical component of the mag- 

 netic field due to the induced current in the 

 secondary coil and curve H^, shows the general 

 shape of the horizontal component. (After Peters 

 and Bardeen, Bulletin of the Univ. of Wisconsin, 

 Engineering Experiment Station Series No. 71.) 



the impedance is Rs" + wLJ^, where 

 the inductance of this circuit, and the 



/.= 



wMIpm sin (wt — /3) 

 y/Rs^ + w^L? 



where 



, „ wLs _.wLs 

 tan j8 = —^— or jS = tan ^ 



Rs, 



R. 



The expression for /« can be put into a more conventional form by mak- 

 ing use of the trigonometric relation 



tan" 



R. 



-^--tan- 



R. 



wL. 



or 



i8 = 



t L. J. Peters and J. Bardeen, "The Solution of Some Theoretical Problems which .\rise in 

 Electrical Methods of Geophysical Exploration" (Bulletin of the Univ. of Wisconsin, Engineering 

 Experiment Station Series No. 71). 



