# Coloumbs law and Newtons third law

## Main Question or Discussion Point

Coloumbs law states that the force exerted by two charged particles on each other is given by f = kq1q2/d^2

Now say two charged particles (charge type irrelevant in question) x and y are d metres from each other then y exerts a force f on x. But since x is also exerting f on y then wont it experience another force f as a result of Newtons 3rd law? So the total force x experiences will be equal to 2f but Im seeing calculations in my textbook which uses only f when calculating accelerations for x so this is wrong.

My guess is that the force y is exerting on x itself is the third law as a result of x exerting f on y but then that implies that only x is exerting an electric force but how can that be when both particles are charged, shouldnt they both exert non 3rd law forces on each other independently(and feel 3rd law forces as a result consequently in addition to that)?

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But since x is also exerting f on y then wont it experience another force f as a result of Newtons 3rd law?
the evidence which supports this is that two charges will each experience acceleration when placed nearby each other....but I'd say that's exactly what the third law describes....mutal force

In any case, Coulombs law covers the observed forces.

The cause of the force here is the charge on each object.Draw a diagram with 2, lets say + charged balls. They will experience repulsion forces so you need to draw an arrow on each ball pointing away from each other. The force on each ball is the same but in opposite directions.
This is Newton's 3rd law. It does not say that there are extra forces (I have assumed the balls have no mass!!!)

If I understand coloumbs law correctly, two charged particles exert equal and opposite forces on each other. These two forces are independent electric forces, one isnt the third law pair of the other but an independent field force. But shouldnt we also take into account the third law forces?

Put simply, x creates an electric field which exerts an electric force f on y and by the third law, y exerts f too on x, this is a reaction force. But then y also has its own field which exerts f on x anyways, this is not a reaction force. Hence x experiences 2f?

jtbell
Mentor
If I understand coloumbs law correctly, two charged particles exert equal and opposite forces on each other. These two forces are independent electric forces, one isnt the third law pair of the other but an independent field force.
No, those two forces are a Third Law "action and reaction" pair.

No, those two forces are a Third Law "action and reaction" pair.
But doesnt that imply that only one charge is exerting the force on the other and the other charges exertion back is just a reaction force? But I thought that both charged particles will exert electric forces on each other independently because both create independent fields not that only one exerts a force and the other just a reaction...

jtbell
Mentor
The two forces have equal status. You cannot consider one of them to be "cause" and the other to be "effect." You should not take the words "action" and "reaction" in the context of the Third Law as indicating "cause" and "effect". They are simply a commonly-used terminology.

[added] When I teach Newton's Third Law in an introductory course, I avoid using the words "action" and "reaction" except to address confusions such as this.

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Coloumbs law states that the force exerted by two charged particles on each other is given by f = kq1q2/d^2

Now say two charged particles (charge type irrelevant in question) x and y are d metres from each other then y exerts a force f on x. But since x is also exerting f on y then wont it experience another force f as a result of Newtons 3rd law? So the total force x experiences will be equal to 2f but Im seeing calculations in my textbook which uses only f when calculating accelerations for x so this is wrong.

My guess is that the force y is exerting on x itself is the third law as a result of x exerting f on y but then that implies that only x is exerting an electric force but how can that be when both particles are charged, shouldnt they both exert non 3rd law forces on each other independently(and feel 3rd law forces as a result consequently in addition to that)?
Coulomb law is compatible with Newton 3rd law. Indeed Coulomb obtained it in analogy with Newton law for gravity.

If f_12 =f_21 = kq_1q_2/R^2 is the modulus of the force then f_12 = - f_21 and for the two body system the total force (F = f_12 - f_21) is zero

No man what you said want exactly right.Cause each charge would individually experiences an equal and opposite force.Its just that in the case of charges its quite neglligable.Well either that or they cancel out each other. The two forces have equal status. You cannot consider one of them to be "cause" and the other to be "effect." You should not take the words "action" and "reaction" in the context of the Third Law as indicating "cause" and "effect". They are simply a commonly-used terminology.

[added] When I teach Newton's Third Law in an introductory course, I avoid using the words "action" and "reaction" except to address confusions such as this.
Could you restate Newtons 3rd Law then? I do not think I understand the law when applied to non contact forces here then (for contact forces, the two are obviously action-reaction...).

jtbell
Mentor
Third Law: When object A exerts a force on object B, then object B also exerts a force of the same type on object A, with equal magnitude and opposite direction.

I'd better note that in electromagnetism, this works only for the electrostatic force (Coulomb's law). Magnetic forces do not obey the Third Law, in general. To "get around" this, we say that conservation of momentum (which in mechanics can be derived from the Third Law) is actually more general than the Third Law. We satisfy conservation of momentum in electromagnetism by endowing the electromagnetic field with momentum. The total momentum of particles plus fields is conserved. But for electrostatic forces (no magnetism) the field momentum doesn't come into the picture.

Third Law: When object A exerts a force on object B, then object B also exerts a force of the same type on object A, with equal magnitude and opposite direction.

I'd better note that in electromagnetism, this works only for the electrostatic force (Coulomb's law). Magnetic forces do not obey the Third Law, in general. To "get around" this, we say that conservation of momentum (which in mechanics can be derived from the Third Law) is actually more general than the Third Law. We satisfy conservation of momentum in electromagnetism by endowing the electromagnetic field with momentum. The total momentum of particles plus fields is conserved. But for electrostatic forces (no magnetism) the field momentum doesn't come into the picture.
Right so the fact that each charge exerts equal and opposite forces on each other is already a consequence of N3L. Thanks for clarifying and for the magnetic forces issue which Ill meet soon too.

D H
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