Indeed, JD's questions have raised lots of interesting issues.
"I'm not sure I'm comfortable with the electron/proton example as a
violation of the third law." I of course agree totally with the fact that
the right way (and the only feasible way) to calculate magnetic forces is
to first calculate the field made by other (moving) charges and then
calculate the cross-product force. But the fact remains that you end up
with two forces that are not F and -F, which calls for some discussion.
How do you feel about the Coulomb force law? Surely there too one should
first calculate the field made by other charges and then calculate the
force (for one thing, retardation effects require this approach). Yet in
the intro course one rarely requires this of students, and it's probably
common to say "See? Here's an example of Newton's 3rd law." But then what
do you say when the two magnetic forces don't match?
In this context I'll mention that at Carnegie Mellon with very strong
students, at a time when we introduced magnetic field and force late in the
course as is traditional, when we came to magnetism the students said, "Oh!
I never really got the field concept before! I now realize that I was
always falling back on Coulomb's force law and not thinking in terms of
charges make a field, and field affects charges. It's only now with a
different example of a field that I really understand the field concept, in
particular because there's no practical way to calculate the magnetic
forces that two moving charges exert on each other except by first
calculating the field and then the force, due to the two sets of cross
products." This led us to move magnetic field much earlier in the E&M
semester than has been traditional, in order to make the field concept more
salient and more solid.
Here's an alternative view of Newton's 3rd law, which is the approach Ruth
and I have taken. Don't claim that Newton's 3rd law is general. Rather,
show by the symmetry of m_1*m_2 and q_1*q_2 that the gravitational and
electric force laws show the property of "reciprocity", that F is paired
with -F. Mention that later we'll encounter magnetic forces that do not
have this property. The reciprocity of electric forces provides a kind of
microscopic underpinning for the forces between the big truck and the small
car having the same magnitude, because the interatomic forces between
bumpers must have the same magnitude.
When discussing magnetic force, have the students calculate the forces in
the vx-vy case to see the lack of "reciprocity" and draw their attention to
the primacy of momentum conservation, and the conclusion that there must be
momentum in the fields, and that the field momentum must change in such a
way as to cancel the change in the momentum of the two particles (whose
verification is beyond the scope of the course).
There is a somewhat related issue with energy conservation, which we point
out in the mechanics course. Consider two distant equal-mass stars at rest,
or distant electron and positron at rest. Taking the two objects as the
system, the increasing kinetic energy of the system plus the decreasing
potential energy of the system is zero, which lets you calculate the speeds
for any separation distance. We say that the energy of system (the two
objects) plus the energy of the surroundings (nothing) doesn't change.
Now choose just one of the objects as the system. Work is done on the
system by the force exerted by the other object, and this work increases
the kinetic energy of the object. Energy conservation says that the energy
of the system (the chosen object) plus the energy of the surroundings (the
other object) doesn't change. But in fact the energy of the other object
(the supposed surroundings) does NOT decrease, it too increases. This
suggests that there is energy in the fields made by the objects. And even
though at this stage we have no idea what "field energy" is, if we believe
in energy conservation as primal, then we can actually calculate the change
in the field energy: If the kinetic energy of object 1 increased by an
amount K, and by symmetry the energy of object 2 increases by an amount K,
then the field energy must decrease by -2K. (Shades of dealing with dark
matter or dark matter, where we calculate something about things about
whose nature we're completely ignorant.)
We then comment that dealing with the two-object system using the concept
of potential energy does give the right answer, but that clearly there will
be times when one must be aware of field energy.
I don't claim that the approach I've outlined is the only appropriate
scheme in the intro course, but I did want to point out that there is at
least one other way of talking about Newton's 3rd law.