o/Example 27.
This analogy is close enough so that we can recycle much of our
knowledge about electrostatics.
For example, we saw in example 9, p. 544, and problem 37,
p. 570, that charge tends to collect on the most highly curved
portions of a conductor, and therefore becomes especially dense
near a corner or knife-edge. This gives us a way of making es-
pecially intense magnetic fields. Most people would imagine that
a very intense field could be made simply by using a very large
and bulky permanent magnet, but this doesn’t actually work very
well, because magnetic dipole fields fall off as 1/r^3 , so that at a
point near the surface, nearly all the field is contributed by atoms
near the surface. Our analogy with electrostatics suggests that
we should instead construct a permanent magnet with a sharp
edge.
Figure o shows the cross-sectional shapes of two magnet poles
used in the historic Stern-Gerlach experiment (sec. 14.1, p. 957).
The external magnetic field is represented using field lines. The
field lines enter and exit the surfaces perpendicularly, and they
are particularly dense near the corner of the upper pole, indicat-
ing a strong field. The spreading of the field lines indicates that
the field is strongly nonuniform, becoming much weaker toward
the bottom of the gap between the poles. This strong nonunifor-
mity was crucial for the experiment, in which the magnets were
used as part of a dipole spectrometer. See example 7 and figure
p on p. 589 for an explanation of an electric version of such a
spectrometer.
This chapter is summarized on page 1085. Notation and terminology
are tabulated on pages 1066-1067.744 Chapter 11 Electromagnetism