778 



ELECTRICAL METHODS 



[Chap. 10 



Miiller^^ has measured the field outside a rectangle 200 meters in length 

 and 150 meters in width and found a decrease approximately proportional 

 to the third power of distance. This is also true for the space outside a 

 circular loop (see below) and is in accordance with the well-known fact 

 that a closed loop is equivalent to a magnetic doublet with the moment 

 IS (S = area). 



For a circular loop of the radius R, the (axial) component Z and the 

 (radial) component Yr are given by 



^-'ihm 



-3 



^ _ Ittz r 45 



+ !5 



32 



©■ 



(kJ 



45 /z^ . 15 z* 



d. TH ~^ A. 



4 R 



4 R 



+ 



15 2 



> (10-50a) 



+ 



525 

 64 



(0 



525 2^ 105 

 16 R^ 8 



(;)'-]■, 



where / is in abamperes. The radial component becomes zero both in the 

 axis (r = 0) and in the plane of the loop (z = 0). In the center (r = 0, 

 z = 0), the vertical component 



Zo = -^^ (/in abamps.) 



or 



id 

 5R 



(/ in amps.). (10-506) 



The variation of Z inside and outside a circular loop is shown in Fig. 

 10-100. For outside points, the vertical component is 



^-'^b-m-m -■■■]■ '--' 



For large distances the series terms approach zero and the vertical com- 

 ponent is Zo = /R 7r/r = m/r , that is, the vertical component is propor- 

 tional to the magnetic moment m of the loop and inversel}^ proportional 

 to the cube of distance. 



(c) Reception equipment. Reception equipment in electromagnetic pros- 

 pecting varies from the simplest to the most complex, depending on what 

 information about the field is sought. If only the strike and dip of the 

 ellipse of polarization is desired, a simple coil with amplifier and phones 

 is sufficient. For intensity measurements without reference to phase, a 

 vacuum-tube voltmeter is used in the output stage of the amplifier. In- 



89 Muller, op. ciL, 30(1/2), 185 (1931). 



