Magnetism

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Magnetism
Soft Gamma Repeater 1806-20, is the most powerful
known magnetic object in the universe. Only 10 of
these unusual objects have been discovered. With
a magnetic-field strength of 100 billion T.
0.00005 T

• Physics 355

National Magnet Lab (FL) 45 T
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From whence does magnetism come?
1. No answer from classical physics...
2. What is the role of conduction electrons?
3. What is the effect of localized electrons?
4. How do we make powerful permanent magnets?
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Why is magnetism a quantum effect?
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Orbital Angular Momentum
All known magnetic properties originate from the
attributes of charged particles.
Magnetic dipole moment
The right-hand rule determines the direction of
the magnetic moment of a current-carrying loop.
The direction of the electron's angular momentum
vector L can be obtained using the right hand
rule for angular momentum.
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Zeeman Effect
The Effect of Magnetisation on the Nature of
Light Emitted by a Substance P. ZeemanNature,
vol. 5511 February 1897, pg. 347
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Zeeman Effect
Pieter Zeeman 1865-1943
When considering atomic spectra, the atomic
energy levels, the transitions between these
levels, and the associated spectral lines are
produced with no magnetic fields influencing the
atom. If there are magnetic fields present, the
energy levels are split into a larger number of
levels and the spectral lines are also split.
This splitting is called the Zeeman Effect.
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The total Hamiltonian of an atom in a magnetic
field is                                       
                       where H0 is the
unperturbed Hamiltonian of the atom, and the sums
over a are sums over the electrons in the atom.
The term              is the spin-orbit
interaction for each electron (indexed by a) in
the atom. If there is only one electron, the sum
contains just a single term. The magnetic
potential energy                                
                is the energy due to the magnetic
moment µ of the a-th electron. It can be written
as a sum of the contributions of the orbital
angular momentum L and the spin angular momentum
S, with each multiplied by the appropriate Landé
g-factor, gL or gS. By projecting the vector
quantities onto the z-axis, the Hamiltonian may
be written as                                   
                                                  
where the approximation results from taking the
g-factors to be gL 1 and gS ? 2. The summation
over the electrons was omitted for readability.
Here, Jz Lz Sz is the total angular momentum,
and the spin-orbit (LS) coupling term has been
combined with H0 and written as Hat.
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Zeeman Effect
?
MJ ½
2
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MJ ?½
The probability that an ion is in a state with Jz
MJ is proportional to
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Spin Quantization
Otto Stern 1888-1969
Walther Gerlach 1889-1979
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Magnetic Susceptibility
H magnetic field intensity (external) M
magnetization, dipole moment per unit volume
(internal)
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Magnetic Classifications

• Paramagnetic
• Diamagnetic
• Ferromagnetic

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Example

• Suppose a long cylindrical specimen with a
  uniform magnetization M parallel to its axis is
  placed in a uniform applied magnetic field BA,
  applied along the axis of the cylinder. Suppose
  the specimen has a magnetic susceptibility ?.
• Find the magnitude of the magnetization M, the
  magnetic induction B and the magnetic field
  intensity H.

M
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Example - Answers

• If the material is paramagnetic, then the
  magnetization is in the same direction as the
  applied field and it produces a field ?0M in the
  same direction as the applied field.

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Example - Answers

• If the material is diamagnetic, then the
  susceptibility is negative. The results are the
  same as before, except that B lt BA.