Magnetic Fields in Matter

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Chapter 6
Magnetic Fields in Matter
Department of Physics , ROCMA
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• Magnetization

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• Magnetization

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• Magnetization

Torques and Forces on Magnetic Dipoles
rotation
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• Magnetization

paramagnetism
random
External B field
Diamagnetism
Ferromagnetism
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• Magnetization

Force on magnetic dipole Case of uniform field
(Bconstant)
0
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• Magnetization

Case of nonuniform field (B ? constant)
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• Magnetization

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• Magnetization

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• Magnetization

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• Magnetization

Effect of magnetic field on atomic orbits
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• Magnetization

only electric force
add magnetic field
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• Magnetization

when B is turn on,the electron speeds up.
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• Magnetization

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• Bound Currents

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• Bound Currents

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• Bound Currents

0
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• Bound Currents

--Using Biot-Savart law
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• Bound Currents

Exp 1 Find the magnetic field at the center of a
uniformly magnetized sphere.
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• Bound Currents

Exp 1
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• Bound Currents

Exp 1
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• Bound Currents

Exp 1
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• Bound Currents

Find the magnetic field of point P.
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• Bound Currents

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• Physical Interpretation of Bound Currents

When the magnetization is uniform
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• Physical Interpretation of Bound Currents

When the magnetization is nonuniform
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• The Auxiliary Field H

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• The Auxiliary Field H

Exp 2 A long copper rod of radius R carries a
uniformly distributed (free)
current I. Find H inside and outside the rod.

• The Auxiliary Field H

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• The Auxiliary Field H

Exp 2
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• A Deceptive Parallel

Ampere law in vacuum
Ampere law in magnetic materials
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• Boundary condition

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• Boundary condition

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• Linear and Nonlinear Media

???
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• Linear and Nonlinear Media

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• Linear and Nonlinear Media

For linear isotropic homogeneous media
Electric
Magnetic
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• Linear and Nonlinear Media

Exp 3 An infinite solenoid (n turns per unit
length, current I) is filled with linear
material of susceptibility ? m. Find the
magnetic field inside the solenoid.
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• Ferromagnetism

Ferromagnetic Materials Fe, Co, Ni, Gd, Dy
domain
domain wall
The domains range from about 10-12 to 10-8 m3 in
volume and contain 1017 to 1021 atoms.
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• Ferromagnetism

Ferromagnetic domains. (photo courtesy of R. W.
DeBlois)
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• Ferromagnetism

Hysteresis loop
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• Ferromagnetism

Hysteresis loop
hard
soft
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• In diamagnetic materials (bismuth?) spin moments
  tend to be dominant and produce fields that
  oppose the external field. Thus, the internal
  magnetic field is reduced slightly compared to
  the external field.
• If diople moments dominate slightly, then the
  internal field is increase slightly over the
  external field and the material is paramagnetic
  (tungsten ?).
• Large diople moments are produced in certain
  regions or domains for the ferromagnetic
  materials (iron). A random domain alignment
  exists for virgin ferromagnetic material. When an
  external field is applied and then removed, a net
  alignment occurs given permanent magnetization
  and hysteresis effect . Alloys of some of the
  ferromagnetic materials are also ferromagnetic
  (alnico????)
• In ferrimagnetic materials, adjacent atoms
  develop unequal, but oppositely directed moments,
  allowing a rather larger response to external
  fields. From the point of view of engineering
  applications, the ferrites are very important
  ferrimagnetic materials. Ferries possess a very
  high resistance, and hence give very little eddy
  current loss at higher frequencies when used as
  transformer cores.
• The magnetic tape used for audio and video
  recording is a superparamagnetic material and is
  composed of an array of small ferromagnetic
  particles.

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• The Auxiliary Field H