the system donotall have the sameq/m, then thegof the system
as a whole need not be 2. For example, a collection of positive and
negative charges could easily have zero net charge butm 6 = 0, giving
g= 0.
Particles such as the electron, the neutron, and the proton may
be pointlike, or they may be composites of other particles. The elec-
ton and proton, which are charged, have the expectedgfactors of
exactly 2 when we measure theLandmthat they have due to their
motion through space. But we also find that electrons, neutrons,
and protons all come equipped with a built-in angular momentum,
present even when they are at rest. This intrinsic angular momen-
tum, called spin, is fixed in magnitude but can vary in direction,
like that of a gyroscope. Thus if we measure theLandmof these
particles when they areat rest, they have fixedgfactors, which are
as follows:
electron 2.002319304361
neutron 0
proton 5.58569471
The electron’s intrinsicgfactor is extremely close to 2, and if
we ignore the small discrepancy for now, we are led to imagine
that the electron is either a pointlike particle or a composite of
smaller particles, each of which has the same charge-to-mass ratio.
The neutron does have a nonvanishing dipole moment, so its zero
g factor suggests that it is a composite of other particles whose
charges cancel. The proton’sgfactor is quite different from 2, so we
infer that it, too, is composite. The current theory is that protons
and neutrons are clusters of particles called quarks. Quarks come in
different types, and the different types have different values ofq/m.
It is remarkable that we can infer these facts about the internal
structures of neutrons and protons without having to do any exper-
iments that directly probe their interior structure. We don’t need
a super-powerful microscope, nor do we need a particle accelerator
that can supply enough energy to shake up their internal structure,
like shaking a gift-wrapped box to tell what’s inside. Merely by
measuring the external, aggregate properties of the “box,” we can
get clues about the structure inside. This is closely analogous to the
Tolman-Stewart experiment (example 11, p. 592), in which the sub-
atomic structure of metals was probed by measuring inertial effects
in an electric circuit. A more famous and important experiment
using these ideas, by Stern and Gerlach, is described in sec. 14.1,
p. 957.11.2.5 The Biot-Savart law (optional)
In section 11.2.3 we developed a method for finding the field due
to a given current distribution by tiling a plane with square dipoles.
This method has several disadvantages:696 Chapter 11 Electromagnetism