Can Newton's 3rd Law be considered as a direct consequence of the coulomb's law of electric interactions? [closed]

Question

Let me explain my thought. Lets consider Coulomb's definition of electric force between two charges as the fundamental law. Under this consideration, forces between charges already follow What Newton's 3rd Law states.

It is well known that all contact forces obey Newton's Law. All contact forces are nothing but electrostatic interactions.

• Thus can it be stated that the truth of Coulomb's Law directly implies Newton's 3rd Law (at least for contact forces)?

Now, clearly Newton's 3rd Law (without considering it as a consequence of Coulomb's Law) is not obeyed in magnetic interactions between relatively moving charges.

• Thus is it safe to assume that Newton's 3rd Law is invalid for all non-contact forces and is valid only for contact forces?

If that is so, then it would clearly mean that Coulomb's law is the true form of Newton's 3rd Law.

P.S. I am aware that the 3rd Law can be proved by combining the 2nd Law with the law of conservation of momentum. But if that's so, then what is the proof of the law of conservation of momentum? Going in reverse, COM can be proved using the 2nd and 3rd laws. Then a proof for the 3rd law is required beforehand.

Answer 1

Coulumb's law states the ratio of the product of the charges of two particles to the distance between the particles squared is proportional to the total force of the charge exerted by both of the particles (Newton's third law holds they are equal and opposite). The constant of proportionality would be k, or the universal electrostatic constant approximately equal to $8.99 * 10^9 \frac{N·m^2}{C^2}. $ Thus, the formula is $F_e = \frac{kq_1q_2}{r^2}$.

Coulumb's law is similar to Newton's Law of Universal Gravitation, which states the ratio of the product of the gravitational forces of two particles to the distance between the particles squared is proportional to the total force of the charge exerted by both of the particles (Newton's third law holds they are equal and opposite). The constant of proportionality would be G, or the universal gravitational constant approximately equal to $6.67 *10^-11 \frac{N*m^2}{kg^2}. $ Thus, the formula is $F_g = \frac{GF_1F_2}{r^2}$.

As you can see, Newton's Law of Universal Gravitation and Coulumb's law have many similarities. I believe Coulumb's law can be based on Newton's Law of Universal Gravitation.

Yes, Coulumb's law (As well as Newton's Law of Universal Gravitation) do imply Newton's third law of motion. As you can see, it was an integral part of determining that the forces exerted by the particles are equal and opposite.

Conservation of momentum can be proven using elastic collisions in the following paper: http://www.lectures4you.de/pdf/chris_prot/collision.pdf

The proof of Newton's third law is derived in the following paper: https://www.lhup.edu/~dsimanek/cutting/3rdlaw.htm

Hope this helped, Kaien Yang