#   μ ```Magnetic Materials
I.
A.
Review

Magnetic Moment - μ 
I
Direction is determined by the ______________ _____________ ____________
B.
Spinning Electrons

L
The magnetic moment for a spinning electron is called the Bohr magnetron:
μ B  9.27 10 24 J/T
II.
Orbiting Electrons And Magnetic Moments
In the early part of the 20th century, Neils Bohr proposed a model of the atom in
which electrons traveled in circular orbits around the nucleus due to the Coulomb
force. Using the Bohr model as shown below, we have

v
R
Electron
Nucleus
I  dq 
dt
μ
From Physics I, we know that the magnitude of the angular momentum of the
electron is given by:
L
Thus, we have
μ
According to Bohr's model, the electron is only allowed to exist in orbits where
the magnitude of its angular momentum is given by
Ln  n h
2π
where h is Plank's constant and is equal to 6.63x10-34 Js
n is a positive integer
Substituting Bohr's angular momentum hypothesis into our previous equation, we
have


 n h 
e
μ
nμB



2 m  2 π 





Note: It is an interesting fact that Bohr's model correctly predicted the magnetic moment
due to orbital angular momentum and spin angular momentum. When Bohr
proposed the model, the concept of electron spin had not been invented.
Furthermore, Bohr realized that according to classical physics his model should
not be stable since an accelerating charge should emit energy and spiral into the
nucleus. In modern physics, we learn that the electron does not travel in circular
orbits. In fact, the entire concept of a particle trajectory is invalid at the atomic
level!
III.
Groups Of Electrons And Magnetism
We now consider a string of electrons. For an atom, electrons begin filling the
various energy levels (shells). For a complete shell, the magnetic moment due to
spin and orbital angular momentum vectors for the individual electrons add to
zero. However, the outer (valence) electrons may produce a net magnetic moment
since the shell isn't filled!!
Consider the following string of electrons shown below
μ Total 
From our picture, we see that if an atom has an odd number of outer electrons
then it will have some magnetism due to spin.
IV.
Ferromagnetism
In some materials like iron and nickel, the atom's magnetic moment is sufficiently
strong to cause the individual atoms to interact so as to form larger regions of
magnetism called domains. Each domain acts as a single larger magnet.
A.
Initially - No External Magnetic Field
B.
Apply An External Magnetic Field

B ext
Domains _______________ when an external magnetic field is applied. Thus,
the magnetic field _________________________ .
C.
Remove External Magnetic Field
The domains ___________________ _____________________ even after
the magnetic field is removed.
D.
Heat Or Bang The Magnet
The domains are _________ ___________________ _________________.
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