ELECTRICAL METHODS 593 



between two surface electrodes, with the surface conductor and power 

 supply arranged as shown in Figure 367. Assume, as before, that the 

 earth is homogeneous and non-magnetic. Under these conditions, the 

 subsurface distribution of a very low frequency alternating current will 

 be substantially the same as that of a direct current. The E.M.F. induced 

 in a vertical coil or loop whose plane includes the line joining the ener- 

 gizing stake electrodes can be calculated readily, provided the area of the 

 loop is small relative to the separation of the electrodes so that the mag- 

 netic field H may be considered as constant over the area embraced by 

 the coil. Let A denote the area of the loop and let N denote the number 

 of turns of wire in the loop. 



Neglecting the field due to the surface or return conductor, the field 

 at a point x on the line joining the two electrodes is given by Equation 

 4. That is. 



\ ;t: L — X / 



This field is perpendicular to the line joining the electrodes. Hence, the 

 magnetic flux cutting the loop is normal to the loop and is given by the 

 relation 



<}> = ^NHA=,.NIA Q +j^) 



where /a is the effective magnetic permeability of the subsurface. If, as 

 is frequently the case, /a may be set equal to unity, the expression for <j) 

 becomes : 



The induced E.M.F. is given by Equation 5. That is, 





\ X L — X ) dt 



This equation gives the induced E.M.F. in electromagnetic units when / 

 is expressed in electromagnetic units, A in square centimeters, x in centi- 

 meters, and L in centimeters. 



In practical units, the last relation becomes 



3.05 



E = - 



108 



^^(^+r^)f (^) 



where E is given in volts, / in amperes, A in square feet, x in feet and 

 L in feet. 



Numerical Illustration. — A low frequency alternating current is applied to the 

 ground by means of two stake electrodes separated by a distance of 100 feet. Suppose 



