### 4.2.3 Summary to: Dia- and Paramagnetism

Dia- and Paramagentic propertis of materials are of no consequence whatsoever for products of electrical engineering (or anything else!)
 Normal diamagnetic materials: cdia » – (10–5 - 10–7) Superconductors (= ideal diamagnets): cSC = – 1 Paramagnetic materials: cpara » +10–3
Only their common denominator of being essentially "non-magnetic" is of interest (for a submarine, e.g., you want a non-magnetic 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, cdia < 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.
cdia  =  –  e2 · z · <r> 2
6 m*e
· ratom  » – (10–5 - 10–7)

The formal treatment of paramagnetic materuials is mathematically completely identical to the case of orientation polarization
W(j) =  –   µ0 · m · H  =  –   µ0 · m · H · cos j
Energy of magetic dipole in magnetic field
N[W(j)]  =  c · exp –(W/kT)  =  c · exp   m · µ0 · H · cos j
kT
= N(j)
(Boltzmann) Distribution of dipoles on energy states
M  =  N · m · L(b)

b  =  µ0 · 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:

cpara  =  N · m2 · m0
3kT

Insertig numbers we find that cpara is indeed a number just slightly larger than 0.