606 EXPLORATION GEOPHYSICS 



associated with one circuit due to unit current in the other. That is, 



yr _ magnetic flux in secondary circuit _ magnetic flux in primary circuit 



current in primary circuit current in secondary circuit 



or 



M = ^ (9) 



where ^ denotes the magnetic flux in one circuit due to a current / in 

 the other. 



M is a constant for any two circuits and depends on the geometrical 

 configurations and orientations of the circuits and the magnetic properties 

 of the media surrounding them. 



The approximate value of the mutual inductance between two parallel 

 coaxial circles, one of which has a radius h small compared to the radius 

 a of the other, is readily calculated. The field at the center P of the 

 smaller coil due to the current / in the larger coil is given by Equation 

 8. That is, 



„ _ 2irla^ 

 (a^ + x^y' 



where x = OP. Because b is assumed to be small compared to a, the field 

 H is approximately constant over the entire cross section of the smaller 

 coil. Therefore, the magnetic flux through the smaller coil is 



where /x is the magnetic permeability of the medium surrounding the 

 coils. But from Equation 9, the mutual inductance is equal to the mag- 

 netic flux of induction divided by the current. Hence, 



^^ (a^ + x^y^ '^^^^ 



If the coils have A'"! turns and N2 turns respectively, the last equation be- 

 comes 



M = -fff^N^N, (10a) 



The mutual inductance M is an important quantity in the analysis of 

 inductive processes because the magnitude of the induced E.M.F. in a 

 secondary circuit due to an alternating current in the primary circuit 

 is directly proportional to M. That is, 



dt 

 or 



E = -M§ (11) 



