Page 263 - Engineering Electromagnetics, 8th Edition

CHAPTER 8 Magnetic Forces, Materials, and Inductance 245

Let us first consider atoms in which the small magnetic fields produced by the
motion of the electrons in their orbits and those produced by the electron spin combine
to produce a net field of zero. Note that we are considering here the fields produced
by the electron motion itself in the absence of any external magnetic field; we might
also describe this material as one in which the permanent magnetic moment m 0 of
each atom is zero. Such a material is termed diamagnetic.Itwould seem, therefore,
that an external magnetic field would produce no torque on the atom, no realignment
of the dipole fields, and consequently an internal magnetic field that is the same as the
applied field. With an error that only amounts to about one part in a hundred thousand,
this is correct.
Let us select an orbiting electron whose moment m is in the same direction as
the applied field B 0 (Figure 8.8). The magnetic field produces an outward force on
the orbiting electron. Since the orbital radius is quantized and cannot change, the
inward Coulomb force of attraction is also unchanged. The force unbalance created
by the outward magnetic force must therefore be compensated for by a reduced orbital
velocity. Hence, the orbital moment decreases, and a smaller internal field results.
If we had selected an atom for which m and B 0 were opposed, the magnetic force
would be inward, the velocity would increase, the orbital moment would increase, and
greater cancellation of B 0 would occur. Again a smaller internal field would result.
Metallic bismuth shows a greater diamagnetic effect than most other diamag-
netic materials, among which are hydrogen, helium, the other “inert” gases, sodium
chloride, copper, gold, silicon, germanium, graphite, and sulfur. We should also re-
alize that the diamagnetic effect is present in all materials, because it arises from an
interaction of the external magnetic field with every orbiting electron; however, it is
overshadowed by other effects in the materials we shall consider next.
Now consider an atom in which the effects of the electron spin and orbital motion
do not quite cancel. The atom as a whole has a small magnetic moment, but the random
orientation of the atoms in a larger sample produces an average magnetic moment
of zero. The material shows no magnetic effects in the absence of an external field.

Figure 8.8 An orbiting electron is shown having
a magnetic moment m in the same direction as an
applied field B 0 .