MAGNETIC METHODS 



203 



The field H' due to the magnetic moment M is shown by the broken lines 

 of Figure 95, It is apparent that inside the sphere and in certain regions 

 outside, the induced field //' opposes 

 the earth's field (solid lines). The 

 demagnetizing field H' is proportional 

 to the moment of the magnetic dipole 

 to which it is due, and this in turn 

 is proportional to the intensity of mag- 

 netization. Hence, H' = —NI, where A^ 

 is a constant. The "demagnetizing 

 factor" A^ depends on the geometrical 

 form of the magnetized body. It may 

 be shown that for a sphere N — A/Zir. 

 Therefore, if the total intensity of the 

 earth's field is denoted by T, the efifec- 

 tive field inside the sphere may be 

 written: T — A/ZttI. 



The intensity of magnetization is 

 proportional to the effective field in- 

 side the sphere ; that is. 



Fig. 95. — Diagram illustrating de- 

 magnetization effect: Tiie field H' due 

 to a uniformly magnetized sphere op- 

 poses the earth's field. 



/ = .(r-4/3./) or/ = j^Ar_ (gj) 



where k is the susceptibility of the paramagnetic material constituting the 

 sphere. 



Equation 91 corresponds to the case that the susceptibility of the 

 medium in which the sphere is imbedded is zero. If the susceptibility ko 

 of the surrounding medium is not zero, the last equation becomes 



{k-ko)T 



1 = 



and 



M 



I + 4/37r {k - ko) 

 _4/3 7rR^ (k-ko) T 



1 + 4/37r (k - ko) 

 On introducing a new variable c defined by the equation 



_ 4/3 ttR^ (k-ko) 

 ^ l + 4/37r(yfe-)^o) 

 the expression for the magnetic moment M becomes 



M = cT 



(92) 



(93) 



(94) 



The potential AV at an external point P due to the uniformly magnetized 

 sphere is ,^ ^ 



^p. = M£2i« (95) 



where M is the magnetic moment of the sphere, r is the distance between 

 the center of the sphere and the point P, and 6 is the angle formed by r 



