Nice example. Person A pulls on one end of the broomstick. The boomstick exerts an equal and opposite force on Person A. This is one pair of NTN 3 forces. Another pair is between Person B and the other end of the broomstick. In this case no one would say that Person A and Person B forms a NTN 3 pair (even though, as you stated, they "interact" indirectly).
If we replace the broomstick with gravitational fields and the people with the Sun and a planet, all of a sudden we say (in most general physics texts) that the NTN pair is the Sun and the planet. I would seem that my word "fuzzy" hardly begins to cover this inconsistency. Also, we talk of the field producing a force on the object, but I have not seen a claim in a basic text that the object exerts a force on the field.
I feel that some of the suggestions posed so far, like not using NTN 3 for fields, sweep the issue under the rug. Perhaps I'm just making a mountain out of a molehill here, but all of this is part of introductory physics courses and it seems that there must be a better way to handle the terminology.
Bob at PC
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Two people pulling a broomstick in opposite directions do interact with
each other, indirectly. But the sun-earth interaction involves two
fields. Sun creates one field and earth creates another field. A field
created by an object acts on other objects only; not on its own source.
The field created by sun at earth location is much larger than the
field created by earth at sun location. But forces are identical due
to differences between masses. I tend to agree with Bob's observation
about fuzziness.
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Ludwik Kowalski, a retired physicist
5 Horizon Road, apt. 2702, Fort Lee, NJ, 07024, USA
Also an amateur journalist at http://csam.montclair.edu/~kowalski/cf/