Chap. 10] ELECTRICAL METHODS 685 



B. Conditions for A.C. Fields 



The use of alternating current for potential investigation introduces two 

 limitations which may prove to be severe if experimental conditions are 

 unfavorable: (1) reduced depth penetration and (2) elliptical polarization. 



Contrary to direct current, the passage of alternating current is con- 

 trolled by the capacitive and inductive reactance as well as by the resist- 

 ance of the circuit. For a conductor of sufficient section the inductance 

 of the current fibers in the interior is greater than that at the surface. 

 Thus the current has a tendency to flow nearer the surface. For very 

 high frequencies the current is confined to the outermost "skin." 



Relations governing the depth penetration of A.C. such as used in equi- 

 potential-line methods (300 to 1000 cycles) may be derived from the laws 

 of electromagnetic wave propagation by introducing certain simplifications. 

 Since for the above frequencies the displacement current may be neglected, 

 the current density at a depth d from the surface of a conductor (where 

 the current density is iq) may be written 



2 id , 



-— -\/y/<' 

 td = «o-e ^ -sm 



{2ft-'^^y/^fa^, (10-23a) 



where the depth is in centimeters, / is frequency, y is permeability, c is 

 conductivity (in e.s.u.), c is light velocity, and t is time. The equation 

 states that an attenuation of amplitude and a phase shift between surface 

 and depth current occurs. The attenuation for the peak values of the 

 current is therefore 



/, = Zo.e ^^^ (10-236) 



where the permeability has been assumed to be equal to 1. Hence, the 

 depth at which the surface-current density has dropped to 1/e of its value, 

 with p as resistivity, is 



<i = iy^. (10-23C) 



Since the presence of good conductors at the surface or near the surface 

 reduces the depth of penetration, provision is made in some A.C. methods 

 to lower the frequency when greater penetration is desired. Fig. 10-34 

 shows the depth penetration of alternating currents of the frequencies 1, 

 25, 60, and 500, as a function of resistivity, in double logarithmic scale. 

 For any other frequency the penetration may be read off on the frequency 

 scale, which is half that of the depth scale, since the penetration is inversely 

 proportional to the square root of frequency. 



