I. Poles and dipoles

  A. An electric dipole consists of a (+) charge and a (-) charge that are closely spaced.

  B. A magnetic dipole is a current loop, usually microscopic.

   1. When a magnetic dipole is placed in an external B-field, it feels a torque.

   2. For microscopic magnetic dipoles in a solid, there is a tendency for each dipole to align with the external field and reach    the state of lowest energy. How large is the typical dipole in a solid?

   3. The magnetization M is the result of this alignment and is the magnetic moment per unit volume.


   4. The result is that the external B-field has a "material-generated B-field" added to it because of this magnetization.

     Btotal = Bext + Bm

III. Magnetic Materials

 A. Diamagnetism

  1. Based on Lenz's law, the external B-field induces a change in the electron circulation which creates a magnetization that is    opposite in direction to the external field. This is almost always a weak effect.

 B. Paramagnetism

   1. There is a tendency for partial alignment of the microscopic dipoles with the external field and M adds to Bext.

    a. Curie Law of Paramagnetism: M is proportional to 1/T, where T is the Kelvin temperature.

  C. Ferromagnetism

    1.Strong cooperative interaction between atoms which can produce regions with permanent magnetism.

     a. Permanent magnets - iron, nickel, cobalt - have magnetic domains

IV. Induced B-fields

 A. Can an E-field be produced by a changing B-field?

 B. Can a B-field be produced by a changing E-field?

 C. What is a displacement current?