Does the third law of motion fail in magnetism?

[gfdbro]

Could you please also tell me where (else) the third law fails?

 

[Dale]

It doesn't fail in EM. The fields themselves carry and conserve momentum:
http://farside.ph.utexas.edu/teaching/em/lectures/node90.html
http://farside.ph.utexas.edu/teaching/em/lectures/node91.html

 

[rcgldr]

For non-contact attractive or repulsive forces, the equal and opposing pair of forces is the force (electrical, magnetic, or gravitational) each object exerts on the other.

 

[gfdbro]

@dalespam: Ummm... i think when they were talking of magnetism they meant charges and magnetism and not electromagnetic waves.

 

[Dale]

It doesn't matter. Momentum is conserved in general with Maxwell's equations whether you are talking about waves or other solutions.

 

[TurtleMeister]

For non-contact attractive or repulsive forces, the equal and opposing pair of forces is the force (electrical, magnetic, or gravitational) each object exerts on the other.

So two forces are involved? What if the field strengths are not equal? For example, two magnets, one with double the attractive force of the other one. We know for a fact that the third law will still hold true in this case. But how? If the field strengths of each magnet is different, then how do the two forces become equal?

 

[LukeD]

Momentum is conserved in E&M, but the transfer of momentum between particles has a speed of light delay. During this delay time, the momentum is carried by light, which is emitted by one particle and absorbed by the other.

So momentum is always conserved instantaneously if we consider that the exchange of momentum goes
particle 1 -> E&M field -> particle 2

 

[kanato]

So two forces are involved? What if the field strengths are not equal? For example, two magnets, one with double the attractive force of the other one. We know for a fact that the third law will still hold true in this case. But how? If the field strengths of each magnet is different, then how do the two forces become equal?

It's the same way that the two forces are equal if you have gravity from one large object and gravity from one small object. The magnetic field strength is proportionate to the current in the source object, and the force created by a magnetic field is proportionate to the current in the object the force acts on. So both forces go as the product of currents in the two source objects.

 

[Dale]

So momentum is always conserved instantaneously if we consider that the exchange of momentum goes
particle 1 -> E&M field -> particle 2

Exactly, that is why it is so important to understand that the fields themselves carry momentum.

 

[rcgldr]

It's the same way that the two forces are equal if you have gravity from one large object and gravity from one small object.

Even if the "small" object didn't generate any gravity itself (or you simply ignored the relatively insignifcant contribution to the total field and force from the "small" object), the gravitational effect from the large object produces equal and opposing attractive forces between the two objects.

 

[TurtleMeister]

It's the same way that the two forces are equal if you have gravity from one large object and gravity from one small object.

Even if the "small" object didn't generate any gravity itself (or you simply ignored the relatively insignifcant contribution to the total field and force from the "small" object), the gravitational effect from the large object produces equal and opposing attractive forces between the two objects.

Not according to http://en.wikipedia.org/wiki/Equivalence_principle#Active.2C_passive.2C_and_inertial_masses" Wikipedia entry. Scroll down to the section that starts with "Furthermore by Newton's third law of motion". Notice that if $M^{act}_0 <> M^{pass}_0$ or if $M^{act}_1 <> M^{pass}_1$ then $F_1 <> F_0$. Therefore, if the small object did not generate any gravity then there would be a third law violation. This has puzzled me for a long time and I have posted about it before. Why would two magnets with equal inertial mass but different magnetic field strengths obey the third law of motion while two objects with the same inertial mass but different gravitational mass would violate the third law of motion? What makes gravity unique in this respect?

 

[pallidin]

...two objects with the same inertial mass but different gravitational mass...

Out of curiousity, can you give a real world example of that statement?

 

[rcgldr]

Not according to http://en.wikipedia.org/wiki/Equivalence_principle#Active.2C_passive.2C_and_inertial_masses" Wikipedia entry. Scroll down to the section that starts with "Furthermore by Newton's third law of motion".

That section seems to conlfict with the earlier statement in that wiki entry:

All test particles at the alike spacetime point in a given gravitational field will undergo the same acceleration, independent of their properties, including their rest mass.

The principle does not apply to physical bodies, which experience tidal forces, or heavy point masses, whose presence changes the gravitational field around them.

Which is trying to make the point that the gravity field of the relatively huge object is the dominant field, and the behavior for the rate of acceleration of the relatively tiny objects in the huge objects gravitational field.

Continuing with the huge and tiny object analogy in two body system, since momentum is conserved, the attactive force should be causing both bodies to accelerate towards each other, with the rate of acceleration of each object being equal to the attractive_force / object_mass.

Perhaps trying to separate gravitational force into components based on the fields of the two objects involved is just complicating matters. The total force is related to the product of the masses, or in the case of an electrical force, the produce of the charges, it doesn't really matter how the mass or charge is distributed when considering the total force. It's either an attractive or repulsive (like charges) force, and the force on each object of a pair of objects is equal and opposing.

 

[TurtleMeister]

...two objects with the same inertial mass but different gravitational mass...

Out of curiousity, can you give a real world example of that statement?

No, of course not. It was a thought experiment to demonstrate how the methodology of the Wikipedia entry is in conflict with other real world observations that do not involve gravity.

That section seems to conlfict with the earlier statement in that wiki entry:

All test particles at the alike spacetime point in a given gravitational field will undergo the same acceleration, independent of their properties, including their rest mass.

The principle does not apply to physical bodies, which experience tidal forces, or heavy point masses, whose presence changes the gravitational field around them.

Which is trying to make the point that the gravity field of the relatively huge object is the dominant field, and the behavior for the rate of acceleration of the relatively tiny objects in the huge objects gravitational field.

I don't see the conflict. It's simply a statement of the equivalence principle. And the section that I linked to attempts to use Newton's laws to show that a violation of this principle would also produce a violation of the third law of motion.

Perhaps trying to separate gravitational force into components based on the fields of the two objects involved is just complicating matters. The total force is related to the product of the masses, or in the case of an electrical force, the produce of the charges, it doesn't really matter how the mass or charge is distributed when considering the total force. It's either an attractive or repulsive (like charges) force, and the force on each object of a pair of objects is equal and opposing.

Yes. that is the way I see it also. But in the case of gravity, it is not the same. Or at least, that is what the equations in the Wikipedia link seem to suggest. For example, in all other cases of force pairs (that do not involve gravity), it makes no difference which object is the source of the force. The forces seem to combine as one force that is equal and opposite for each object. But using the methodology of the Wikipedia page for the case of gravity, the force of each object acts separately on the other object and not itself. That is what puzzles me.