28 : 2/ Magnetic Measurements 527 



determined by the magnetic induction B. In most materials, B and H 

 are proportional to one another, that is 



B = tJi 



where ^ is a constant called the permeability. In ferromagnetic sub- 

 stances, the permeability jx, measured in electromagnetic units (emu), is 

 very large compared to one. Moreover, for ferromagnetic substances, 

 /x is not a true constant but depends on H. For low field strengths, /x is 

 around 10 3 for some iron alloys. 



Nonferromagnetic substances all have values of \x very close to one. 

 If \x is greater than one, the substance is paramagnetic ; if less than one, 

 it is diamagnetic. In both cases, the values are very close to one. (In a 

 vacuum, the permeability is unity.) For the diamagnetic substance, 

 water, for example 



[i = 0.99999928 emu 



Writing all these nines is rather annoying; a more convenient quantity 

 is the susceptibility k defined by 



K = /x — 1 



For water, the susceptibility is 



k = -7.2 x 10" 7 emu 



Paramagnetic substances have a positive susceptibility. In such a 

 substance, the individual molecules act like small bar magnets, tending 

 to line up with the magnetic field and to reinforce it. This property is 

 found only in molecules with net permanent dipole moments which are 

 due to the electron orbital motion or the inherent spin of the electron. 

 (Both of these are discussed in Chapter 27.) In filled shells or subshells 

 of electrons, there is no net magnetic moment; pairs of electrons will 

 always be present with their spins in opposite directions and with their 

 orbital moments cancelling. If, however, there are unpaired electrons 

 present, as in most iron compounds, cupric compounds, and so on, then 

 there will be a net magnetic dipole moment. Certain substances, 

 notably the molecule 2 , although possessing an even number of 

 electrons, have two electrons whose spins are unpaired. These so-called 

 "antibinding electrons" make molecules of oxygen paramagnetic. 



Diamagnetic substances have pairs of electrons whose magnetic 

 moments cancel. There are no net dipoles to align with the magnetic 

 field and thus reinforce it. One may think of the pair of electrons as 

 being analogous to two parallel current loops with the current flowing 

 in opposite directions. The magnetic field will tend to alter both 



