Can the Newton's third law be violated in wires at right angles?

[hikaru1221]

So shift my example along so that it matches yours.It makes no difference and you can draw the circuits and how they are arranged in a whole variety of ways.It's the principle you should be looking at.

I still don't think they're the same. Anyway, from the file ehild gave us, I found that the 3rd law is valid in the case of 2 circuits exerting forces on each other (the Neumann force's formula is symmetrical). Though I haven't figured out how to prove the formula yet, I believe this is what you're trying to point out, am I correct? I guess I missed something in my analysis of the 2nd picture. So in short, here are your points:
_ The 2 circuits exert on each other forces that obey the 3rd law.
_ There is no way to find the element force, i.e. force between the sections on the circuits.

You were right at the first point (assume that the Neumann force's formula is right). Back to the 2nd point, which is the central issue of the problem (anyway I still care about the forces between the straight sections). From post #47:

"Take two long parallel pieces of straight wire each with connecting wires and a battery. Do you agree that the third law applies to this situation."

I found a website which contains a simulation of the experiment: http://www.magnet.fsu.edu/education/tutorials/java/parallelwires/index.html. In the simulation, they connect the straight red sections in one circuit, but I believe if we separate them into 2 circuits, there will be no problem. So if the 3rd law applies to the straight sections only, which means the effect of the rest of the circuit is not taken into account, then we still can calculate the force due to sections only, which violates your 2nd point.

 

[Dadface]

Hikaru ,lets extend this to two circuits X and Y and let them be of any shape,size and orientation.Let x be a current element(small section)of circuit X and let y be a current element of circuit Y.Now let's use Biot and Savarts law to calculate the forces on x and y.Now the value of B at x is due to the whole of circuit Y and similarly the value of B at y is due to the whole of circuit X.Because the whole of each circuit is involved we cannot pin down what the force at x would be due to y alone and what the force at y would be due to x alone.

 

[Physiana]

why would the forces be of different strength? I can't see it.

 

[hikaru1221]

why would the forces be of different strength? I can't see it.

Do you refer to the first picture? The magnitude might be the same if it's symmetrical, but the direction is not.

Hikaru ,lets extend this to two circuits X and Y and let them be of any shape,size and orientation.Let x be a current element(small section)of circuit X and let y be a current element of circuit Y.Now let's use Biot and Savarts law to calculate the forces on x and y.Now the value of B at x is due to the whole of circuit Y and similarly the value of B at y is due to the whole of circuit X.Because the whole of each circuit is involved we cannot pin down what the force at x would be due to y alone and what the force at y would be due to x alone.

For the 1st point, I have done proving it. So I'm totally convinced that the 3rd law still applies to the forces between 2 circuits regardless of their shapes, sizes and orientations.

Back to your reasoning above. I have just read the lecture notes at MIT OpenCourseWare. They say that \vec{F}=q\vec{v}\times\vec{B} is an empirical law so far, and from this, people deduce the force on a current element: \vec{dF}=I\vec{dl}\times\vec{B}.
Therefore, for 2 circuits: \vec{F}_{1-on-2} = \int _{L2} \int _{L1} I_1I_2\frac{\mu_o}{4\pi}\vec{dl_2}\times(\frac{\vec{dl_1}\times\vec{r}}{r^3}).
From that, people usually deduce the force that element 1 exerts on element 2: d\vec{F}_{1-on-2} = I_1I_2\frac{\mu_o}{4\pi}\vec{dl_2}\times(\frac{\vec{dl_1}\times\vec{r}}{r^3})
which is mis-derived. Have I got your point?

 

[Physiana]

why would the forces be of different strength? I can't see it.

Do you refer to the first picture? The magnitude might be the same if it's symmetrical, but the direction is not.

Then I don't understand why Newton's third law would be violated.

 

[hikaru1221]

Then I don't understand why Newton's third law would be violated.

Newton's 3rd law: \vec{F_{12}}=-\vec{F_{21}}
If the forces are perpendicular to each other, the law is violated.

 

[Dadface]

Do you refer to the first picture? The magnitude might be the same if it's symmetrical, but the direction is not.



For the 1st point, I have done proving it. So I'm totally convinced that the 3rd law still applies to the forces between 2 circuits regardless of their shapes, sizes and orientations.

Back to your reasoning above. I have just read the lecture notes at MIT OpenCourseWare. They say that \vec{F}=q\vec{v}\times\vec{B} is an empirical law so far, and from this, people deduce the force on a current element: \vec{dF}=I\vec{dl}\times\vec{B}.
Therefore, for 2 circuits: \vec{F}_{1-on-2} = \int _{L2} \int _{L1} I_1I_2\frac{\mu_o}{4\pi}\vec{dl_2}\times(\frac{\vec{dl_1}\times\vec{r}}{r^3}).
From that, people usually deduce the force that element 1 exerts on element 2: d\vec{F}_{1-on-2} = I_1I_2\frac{\mu_o}{4\pi}\vec{dl_2}\times(\frac{\vec{dl_1}\times\vec{r}}{r^3})
which is mis-derived. Have I got your point?

I'm not sure about the point you are making here.Are you in agreement with me now?

 

[hikaru1221]

I'm not sure about the point you are making here.Are you in agreement with me now?

Yes I just tried to explain your point. Is that correct?

 

[Dadface]

Yes I just tried to explain your point. Is that correct?

Yes.You may know that Biot and Savart found,experimentally, the equation for the force between parallel wires and it is this that that led to their general equation.By carrying out the full integrations we can calculate the total(resultant) force between circuits and this we can measure.We cannot make experimentally verifiable predictions about separate current elements because this would necessitate that we separate them from the rest of the circuits of which they are a part,thereby making them non current elements and because,by definition,the elements are infinitessimally small.A theory is only as good as the predictions it makes.

 

[hikaru1221]

How did they find the equation for the force between parallel wires experimentally? The wires, again, are just parts of the circuits, aren't they?

And if the equation \vec{F}=q\vec{v}\times\vec{B} is fundamental, I think the force is due to the interaction between the moving charge (or current) and the magnefic field, not between currents. If so, whether the forces obey the 3rd law or not, it doesn't matter.

 

[Dadface]

How did they find the equation for the force between parallel wires experimentally? The wires, again, are just parts of the circuits, aren't they?

And if the equation \vec{F}=q\vec{v}\times\vec{B} is fundamental, I think the force is due to the interaction between the moving charge (or current) and the magnefic field, not between currents. If so, whether the forces obey the 3rd law or not, it doesn't matter.

Good morning hikaru,
When I wrote that they found the force etc I jumped to a conclusion that may be incorrect.According to my source it was the value of B close to a parallel wire they found and I assumed that back in the day when this was done they found B by measuring the force
using some sort of current balance.Anyway,I don't think you are questioning the history of this but are picking up on the terminology I used.Yes, strictly speaking the force is due to the whole of each circuit but if the straight sections of wire are very long the contribution to the B fields from the other current elements are very small.In a previous post I mentioned that the "force between parallel wires" is used to define the ampere.I just did a quick search and according to WIKI(yes I know) the error involved is of the order of a few parts per ten to the power of seven.

 

[hikaru1221]

Good morning, Dadface. It's actually afternoon in my place
Thank you very much. I have one more question to ask: Is the force due to the interaction between the magnetic field and the current, not between currents?

 

[Dadface]

Good morning, Dadface. It's actually afternoon in my place
Thank you very much. I have one more question to ask: Is the force due to the interaction between the magnetic field and the current, not between currents?

Well the way we've been describing it here is that each current sets up a field which interacts with the opposite current.My wife has just told me that we have to go shopping.Heeelp

 

[hikaru1221]

Go shopping at 4a.m?

That led to some of my questions in the previous posts (and I forgot most of them :( ). Is it the total magnetic field, or only the magnetic field formed by the opposite current, that interacts with the current?

 

[ehild]

As Dadface is on shopping, I step in with a question: If you have two point charges, a and b, how do you calculate the force on b? Using the total electric field or only the one produced by a?

ehild

 

[hikaru1221]

The formula says \vec{F}_{1-on-2}=q_2\vec{E}_{1-at-2}. But can that prove that the charge only interacts with the field set by the other charges? I mean, can the charge "discriminate" its own field from the other's while the space is filled with the total field, and the electric energy is stored in the total field?

The picture in this link shows the magnetic field of 2 long straight currents: http://www.1stardrive.com/solar/mag9.gif
In this picture, the total magnetic field looks like pushing the currents out of the place of higher field density and pulling the currents into the place of lower density.
And the two pictures in the attached file shows the electric fields of 2 charges of opposite signs and of the same sign respectively. Again, the field lines from one charge are like pulling that charge, and the other field lines are like pushing it.
From that, I think of 2 ways to explain:
1 - That is the interaction between the fields of each current/charge. But if so, then where are the currents/charges in the interaction so that there can be forces on them?
2 - There might be some kind of pulling and pushing effect of the total field. This seems reasonable to me.

But in the gravitational field of 2 masses which looks exactly like the electric field of 2 charges of the same sign, the masses attract while the charges repel. And I'm stuck here.

 

[ehild]

When you say the the field exist as an entity remember that the idea of the field is our invention, as every ideas about the real world.

We do not see the real world. We see the image produced in our brain. We do not really investigate reality: we investigate the models of it which we invented.

Each model is built on its own principles and axioms, and these can not be used in an other model. If you use the same word, you have to explain what you mean on it.

The classical mechanics is based on force between material bodies and their motion, and the idea of mass is derived. In classical electrodynamics, charge is defined by the force the charges interact with each other. Electric field strength is defined as force on unit positive charge. The field is the space where there is force on charges. The principal quantities are charge and force.
In mechanics, gravitational interaction is defined as the force between masses, and the gravitational force field is defined by the force on unit mass. The principal quantities are force and mass here.

There is something in both cases that both produces the field and also "feels" the field. But the field is just an idea to make calculations easier.

Is such a thing among the principles of classical Mechanics that fields interact?

Neither do we speak about interaction of fields in Electrostatics. Force is exerted by charges, the force field is produced by some charge distribution.

The definition of the magnetic field is more complicated. It is produced by moving electric charges, and acts on moving electric charges, but magnetic charge does not exist. There exist magnetic momentum, and it is connected to angular momentum of charged particles. There is force acting on moving charges and torque on magnetic dipoles (magnets or current carrying loops).

When measuring the field strength, we have to use a probe, and assume that neither the probe changes the field nor the field changes the probe. But measurement is interaction, and both sides are involved.
The form of the electric field of two point charges are very different from the field of a single point charge, but you would measure the field of the single charge spherically symmetric, don't you?
If you say that the resultant field acts on the probe charge, it is the sum of the "own" field and the "external" field, but the own field is spherically symmetric and cancels at the place of the probe. You get the result that the force is the external field strength multiplied by the charge of the probe. The same, as if you said "the point charge does not interact by itself".

ehild

 

[hikaru1221]

When you say the the field exist as an entity remember that the idea of the field is our invention, as every ideas about the real world.

We do not see the real world. We see the image produced in our brain. We do not really investigate reality: we investigate the models of it which we invented.

It is like the nature doesn't show up in the equations, but it is in agreement with the equations, isn't it?

Each model is built on its own principles and axioms, and these can not be used in an other model. If you use the same word, you have to explain what you mean on it.

The classical mechanics is based on force between material bodies and their motion, and the idea of mass is derived. In classical electrodynamics, charge is defined by the force the charges interact with each other. Electric field strength is defined as force on unit positive charge. The field is the space where there is force on charges. The principal quantities are charge and force.
In mechanics, gravitational interaction is defined as the force between masses, and the gravitational force field is defined by the force on unit mass. The principal quantities are force and mass here.

There is something in both cases that both produces the field and also "feels" the field. But the field is just an idea to make calculations easier.

Is such a thing among the principles of classical Mechanics that fields interact?

No, Classical Mechanics doesn't mention that. But a model can be built based on the old model, right? (Oh, I don't mean to invent new theory or anything, I just ask for the right concept)

The electric field strength is first defined as force per charge unit \vec{E}=lim_{q\rightarrow 0}\frac{\vec{F}}{q}. This definition is based on the things we can "see" (force ~ the displacement of the spring, and charge ~ some characteristics of particle, which means it exists), so that we can do the experiment I think. But the meaning implied is that the electric field is independent from what we can see, i.e. force and the test charge. Moreover the electric field stores energy, which means it is matter. So the idea about the electric field is not just a method to calculate, I think it is a way to perceive. Isn't that an improvement in the idea from "classical mechanics", which is represented by force here, to electrostatics?

When measuring the field strength, we have to use a probe, and assume that neither the probe changes the field nor the field changes the probe. But measurement is interaction, and both sides are involved.
The form of the electric field of two point charges are very different from the field of a single point charge, but you would measure the field of the single charge spherically symmetric, don't you?
If you say that the resultant field acts on the probe charge, it is the sum of the "own" field and the "external" field, but the own field is spherically symmetric and cancels at the place of the probe. You get the result that the force is the external field strength multiplied by the charge of the probe. The same, as if you said "the point charge does not interact by itself".

ehild

So aren't considering the field as a whole and seperating the fields equivalent? I mean, they both lead to one force formula eventually.

Since the field is a kind of matter, i.e. it stores energy, if we consider the fields set by the charges are separate from each other, the total energy stored by the system should be the sum of the energy of all the fields (like the system of 2 moving masses has the energy of 0.5m_1v_1^2+0.5m_2v_2^2+m_1c^2+m_2c^2). But here, the energy density is proportional to E^2_{total}=E_1^2+E_2^2+2\vec{E_1}\vec{E_2} which doesn't equal to the sum of energy densities of the component fields.

 

[Dadface]

I agree with ehild,the field is an imaginary construct.The concept can be useful but it has its limitations.hikaru,this thread seems to be going off in a different direction so I suggest you start a new thread.
By the way,it is 8.49 AM here

 

[hikaru1221]

I agree with ehild,the field is an imaginary construct.The concept can be useful but it has its limitations.hikaru,this thread seems to be going off in a different direction so I suggest you start a new thread.
By the way,it is 8.49 AM here

Limitation? Like in quantum physics? But it's still useful now, right? Anyway I just tried to get the right concept, though it's not a very new model.
Yes, it seems a bit digressing. But I think if we solve the problem about the interaction, then we also solve the problem about the 3rd law, so no need to start a new topic.

 

[ehild]

It is like the nature doesn't show up in the equations, but it is in agreement with the equations, isn't it?

Who knows?

Moreover the electric field stores energy, which means it is matter.

Not in Classical Physics.

Since the field is a kind of matter, i.e. it stores energy, if we consider the fields set by the charges are separate from each other, the total energy stored by the system should be the sum of the energy of all the fields (like the system of 2 moving masses has the energy of 0.5m_1v_1^2+0.5m_2v_2^2+m_1c^2+m_2c^2). But here, the energy density is proportional to E^2_{total}=E_1^2+E_2^2+2\vec{E_1}\vec{E_2} which doesn't equal to the sum of energy densities of the component fields.

You see, this argument is entirely wrong. The electric fields of different sources add up as vectors, but it does not mean that their energies do the same.

Your equation for the energy of two moving free particles is also wrong. What do you mean on 1/2 mv^2? It is the kinetic energy in Classical Mechanics, but not in Relativity Theory. It states that the energy of a particle is mc^2. You can not mix models and theories.

So again: Newton's Classical Mechanics is built up on three axioms, (sometimes independence of the forces is called as the 4-th axiom) and Galilean relativity. It is valid for low speeds. It is valid in inertial frames of reference, which are defined that these axioms hold there :) Well, yes, it is said that Newton's axioms hold for a frame of reference fixed to very distant stars. But they fail in a car, for example. They are not true in a frame of reference fixed to the Earth, either. If you are in closed car so you can not know about the outside world, you would not think Newton's axioms valid. The same with the Earth. According to the observations, the Sun and the stars orbit around the Earth, just by themselves.

Electrodynamics is not Mechanics. You can use the concept of force, but with care. The third axiom of Classical Mechanics refers to the interaction of two bodies. The electric current is not a body. Two pieces of wire do not interact just by themselves without current flowing through them. Current cannot arrive from nowhere and leave to nowhere. Current can flow in a closed loop. Current carrying loops do interact, with force and torque.



ehild

 

[hikaru1221]

Not in Classical Physics.

I'm not sure about the border line between classical physics and modern physics. But even if it doesn't belong to classical physics, it's true and holds validity to problems of classical physics.

Your equation for the energy of two moving free particles is also wrong. What do you mean on 1/2 mv^2? It is the kinetic energy in Classical Mechanics, but not in Relativity Theory. It states that the energy of a particle is mc^2. You can not mix models and theories.

I'm sorry, I forgot to include the condition of low speed.

You see, this argument is entirely wrong. The electric fields of different sources add up as vectors, but it does not mean that their energies do the same.

Yes, their energies don't do the same. Only the E vector does. But does that contradict with my argument?
For 2 masses, we can add up their energies. For 2 fields, we can't. So why do we have to treat them as 2 separate fields, while we can consider it as only 1 field and the result about the force on the charge is still the same?

So again: Newton's Classical Mechanics is built up on three axioms, (sometimes independence of the forces is called as the 4-th axiom) and Galilean relativity. It is valid for low speeds. It is valid in inertial frames of reference, which are defined that these axioms hold there :) Well, yes, it is said that Newton's axioms hold for a frame of reference fixed to very distant stars. But they fail in a car, for example. They are not true in a frame of reference fixed to the Earth, either. If you are in closed car so you can not know about the outside world, you would not think Newton's axioms valid. The same with the Earth. According to the observations, the Sun and the stars orbit around the Earth, just by themselves.

Electrodynamics is not Mechanics. You can use the concept of force, but with care. The third axiom of Classical Mechanics refers to the interaction of two bodies. The electric current is not a body. Two pieces of wire do not interact just by themselves without current flowing through them. Current cannot arrive from nowhere and leave to nowhere. Current can flow in a closed loop. Current carrying loops do interact, with force and torque.

I think it's more like Electrodynamics "borrows" the concept "force" from Classical Mechanics. Because we can only see the final effect (e.g. the displacement of the spring which shows the existence of force in Classical Mechanics), so we use it to define electric field strength at the start. But as Classical Mechanics has its own object (i.e. bodies), Electrodynamics deals with fields. Electrodynamics only gives us the force on the charge, but what happens to the charge after that must be found in Classical Mechanics.

The Newton's 3rd law applies to bodies as you said. Field is not body. So if the force on the current is due to the field, it doesn't matter whether the 3rd law is violated or not, because it doesn't apply. This is what we have agreed so far (have we?). The remaining problem is how to treat the fields.

Current carrying loops do interact, with force and torque.

Do you mean that it is the currents/charges that interact, and the field is not involved?

 

[Hdeasy]

It's one of those funny coincidences, but just a few weeks ago I had an idea about how to exploit this N3 violation in wires at right angles. It's a bit like the setup in post 25. I had been looking at the problem about 2 years ago with some others but we couldn't see a way round. Now I think I do. The only thing stopping a system like this working seems to be the possibility that the field pressure balances any unbalanced force. That's what some of the few papers on it say. But could that be the case? magnetic pressure is proportional to the square of B. That should be the same on both sides of the wire. Any asymmetry would only be expected at the meeting of the 2 wires. So who could build one of these? You need very sensitive accelerometers or huge currents to get a measurable force.

 

[hikaru1221]

Thank you very much, Dadface and ehild
It's good to see there is still somebody interested in this thread.

It's one of those funny coincidences, but just a few weeks ago I had an idea about how to exploit this N3 violation in wires at right angles. It's a bit like the setup in post 25. I had been looking at the problem about 2 years ago with some others but we couldn't see a way round. Now I think I do. The only thing stopping a system like this working seems to be the possibility that the field pressure balances any unbalanced force. That's what some of the few papers on it say. But could that be the case? magnetic pressure is proportional to the square of B. That should be the same on both sides of the wire. Any asymmetry would only be expected at the meeting of the 2 wires. So who could build one of these? You need very sensitive accelerometers or huge currents to get a measurable force.

I saw you mentioned post 25. You really did read all the posts? Wow!

What is the unbalanced force? Do you mean the external force besides the magnetic force, such as friction? By the way, I have already proven to myself that theoretically the magnetic forces between the circuits obey the Newton's third law, so I think any setup like in post 25 (please note that the setup in post 25 is not symmetrical) won't work.