
Dia and Paramagentic propertis of materials are of no consequence whatsoever
for products of electrical engineering (or anything else!)  
Normal diamagnetic materials: c_{dia}
» – (10^{–5}  10^{–7})
Superconductors (= ideal diamagnets): c_{SC} = – 1 Paramagnetic
materials: c_{para}
» +10^{–3} 



Only their common denominator of being essentially "nonmagnetic" is
of interest (for a submarine, e.g., you want a nonmagnetic steel)  


For research tools, however, these forms of magnitc behavious can be highly interesting ("paramagentic
resonance")  

 


Diamagnetism can be understood in a semiclassical (Bohr) model of the atoms as
the response of the current ascribed to "circling" electrons to a changing magnetic field via classical induction
(µ dH/dt).  



The net effect is a precession of the circling electron, i.e. the normal vector of its orbit
plane circles around on the green cone. Þ 



The "Lenz rule" ascertains that inductive effects oppose their source; diamagnetism
thus weakens the magnetic field, c_{dia} < 0 must apply. 


  


Running through the equations gives a result that predicts a very small effect.
Þ A proper quantum mechanical treatment does not change this very much. 

c_{dia} = –

e^{2} · z · <r>
^{2} 6 m*_{e} 
· r_{atom} 
» – (10^{–5}  10^{–7}) 


 
 


The formal treatment of paramagnetic materuials is mathematically completely identical
to the case of orientation polarization  
W(j) = – µ_{0} · m
· H = – µ_{0} · m · H · cos j 
 Energy of magetic dipole in magnetic field 
N[W(j)] = c · exp –(W/kT)
= c · exp  
m · µ_{0} · H · cos j
kT 
= N(j) 
 (Boltzmann) Distribution of dipoles on energy states 
M  = 
N · m · L(b) 
  
  
 
b  = 
µ_{0} · m · H
kT_{ }   


Resulting Magnetization with Langevin function L(b) and argument
b 



The range of realistc b values (given by largest H
technically possible) is even smaller than in the case of orientation polarization. This allows tp approximate L(b) by b/3; we obtain: 


c_{para}  = 
N · m^{2} · m_{0}
3kT_{ } 

 


Insertig numbers we find that c_{para} is indeed
a number just slightly larger than 0.  
 
 
