Doubts about the strong and weak versions of Newton’s third law

Question

I was going through some assertion and reason questions.

(a) Both A and R are true, and R is the correct explanation of A.
(b) Both A and R are true, but R is not the correct explanation of A.
(c) A is true but R is false.
(d) A is false but R is true.
(e) Both A and R are false.

Statement A:

For a system of two charges $q_1$ and $q_1$ at a separation $r$, the Coulomb force of $q_1$ on $q_2$ and that of $q_2$ on $q_1$ are equal and opposite, and these may or may not act along the line that joins $q_1$ and $q_2$.

Statement B:

According to Newton's third law, action and reaction forces are equal and opposite but these may or may not act along the line joining the two particles

The answer key says (d).

My doubts:

According to the strong version Newton's third law, the forces must act along the line joining the two particles. So by “Newton's third law,” do we mean the weak version of Newton's third law? If so, why? If someone could provide a translated version of Newton's paper it would be helpful.

Does the Coulomb force follow the strong Newton's third law or the weak Newton's third law?

Does the Coulomb force ignore the fact that Newtonian mechanics cannot be used for small particles like electrons and protons, and rather we have to use quantum mechanics? (I don't know much about quantum mechanics.)

And lastly, what is the answer?

Answer 1

So by “Newton's third law,” do we mean the weak version of Newton's third law?

Yes.

If so, why?

Why is Newton's third law known as *weak law of action and reaction*?

Does the Coulomb force ignore the fact that Newtonian mechanics cannot be used for small particles like electrons and protons, and rather we have to use quantum mechanics.?

What is the range of the validity of Coulomb's law?

Does the Coulomb force follow the strong Newton's third law or the weak Newton's third law?

Electrostatic forces obey the strong form of Newton's third law. Hence statement A is false.

Statement R is true, since by “Newton's third law,” we mean the weak form of Newton's third law.

So the answer is d.

Answer 2

"Actioni contrariam semper et æqualem esse reactionem: sive corporum duorum actiones in se mutuo semper esse æquales et in partes contrarias dirigi."

"To every action there is always opposed an equal reaction; or the mutual actions of two bodies upon each other are always equal, and directed to contrary parts." (Mott's translation)

The relevant phrase in Newton's statement is "in partes contrarias dirigi" which translates (unequivocally, I think) as "directed towards contrary parts". "Parts" is used here for the first time in the statement of the law, and it's not clear to me whether Newton meant parts of the interacting bodies (in which case the strong statement seems to be implied) or "parts" meaning places (as in the expression "foreign parts"). The latter would allow the weak interpretation.

Perhaps we should remember that Newton would not have met any clear-cut cases of non-central forces, so he had no obvious motivation for wanting his law to include them (that is to require the weak interpretation). But then Newton could see beyond the obvious...

I conclude that Newton's words are open to interpretation as a statement of the strong law or of the weak law. For most purposes it doesn't matter which, but to answer this question it obviously does. The opening phrase of statement B, "According to Newton's third law", is unsafe. We need to insert "(weak form)" to make the statement clearly true.