78 EXPLORATION GEOPHYSICS 



mass/density (F = W/d). That is, to get volume, mass is divided by 

 density. 



The seeming paradox referred to hinges on the equation in which it 

 was shown that k = k'd. This signifies that, to obtain a volume magnetic 

 susceptibility, a mass susceptibility is multiplied by the density. In like 

 manner mass susceptibility equals volume susceptibility divided by density, 

 as expressed in ¥ = k/d. 



Relation between Permeability and Susceptibility, — The situation 

 shown in Figure 12(b) brings out the way in which magnetic permeability 

 fi and magnetic susceptibility ^ of a substance are related. When such a 

 magnet, with cross-section A, is placed in a magnetic field H, it acquires a 

 certain pole strength m by induction. The ratio of the pole strength and 

 the cross-sectioned area is called the surface density of magnetization, or 

 m/A, which expresses the number of magnetic poles per square centimeter. 



The matter can be thought of in terms of magnetic force lines. The total 

 flux (or lines of force) in the bar is the sum of the lines originally present, 

 in the field H, and those arising from the m poles induced by the field H. 

 It has been developed that a unit magnetic pole gives out 47r lines of force, 



lit 

 so that the poles contribute 47r — lines. In equation form : 



1 



■f = H + 4.^ (16) 



wherein > -^ is total flux per unit area. 



As defined -t- = B ov flux density and -j- = / or intensity of mag- 

 netization. It can be written that 



B = H + AirI (17) 



If each side of this equation is divided by H, then 



-=1+4.-. 



-D J 



As shown in the earlier discussion-7^ = fx and -77- = k. Therefore : 



M ri 



permeability — ^1= I + Airk ( 18) 



susceptibility = ^ = — (19) 



Permeability describes the number of lines of force through a unit 

 cross-section of a substance in relation to the number of lines of force 

 through the same cross-section of air. Susceptibility describes how strong 



