# Homework Help: Newton's 3rd law is violated?

1. Jun 10, 2010

### hikaru1221

So here is the problem:
2 thin straight wires carrying steady currents are placed perpendicular as shown in the attached file. The magnetic field at all points of the red wire due to the blue one is downward through the screen, and thus, the net force F exerting on the red wire due to the blue wire is upward and parallel to the blue wire. Similarly, the force F' that the blue wire experiences due to the red one is parallel to the red wire. So F and F' don't equal, which violates the Newton's 3rd law!
Was I wrong at some point here?
Thank you.

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2. Jun 10, 2010

### atyy

Are the wires infinitely long?

3. Jun 10, 2010

### hikaru1221

^ No. Or you may consider them as parts of 2 infinitely long wires.

4. Jun 11, 2010

### hikaru1221

Anyone, please? Is it too easy? :uhh:

5. Jun 11, 2010

### Staff: Mentor

Newton's third law does not apply in general to electromagnetic forces.

However, in classical mechanics, the third law is equivalent to conservation of the total momentum of a system. In electrodynamics, the total momentum of a system is still conserved, provided that you take into account the momentum carried by the electromagnetic field.

Conservation of momentum is more general than Newton's third law.

6. Jun 11, 2010

### hikaru1221

Thank you.
For electrostatic field and gravitation, the law might be still valid I guess (e.g. the force between 2 charges show such symmetry). Is it a coincidence, or is there an explanation for that? Is there any other case, i.e fields carrying momentum, where the law is violated?

7. Jun 11, 2010

### Staff: Mentor

It is not a coincidence, in a purely electrostatic field the field does not carry any momentum, so all of the momentum is carried by matter and Newton's 3rd law results.

8. Jun 11, 2010

### hikaru1221

9. Jun 13, 2010

I don't think you've considered the geometry of the whole of each circuit .Remember that there is not a red and blue wire alone,there are connecting wires as well and the field at any point is due to the whole circuit and not just part of it.Newton's law is not necessarily violated here.

10. Jun 13, 2010

### hikaru1221

But you know, in the universe, there are many planets besides Earth and Sun, but the 3rd law can still be applied for the interaction between Earth and Sun only. The 3rd law doesn't require the system to be isolated.

11. Jun 13, 2010

But the force on each wire is due to the whole of each circuit.The effects of the connecting wires etc cannot be considered as negligible in this problem as it was presented.Consider a very long current carrying wire.In the centre of the wire we can assume,to a good first approximation,that the field pattern is circular and concentric to the wire.This assumption becomes less valid as we move towards each end of the wire because now the circuit becomes non linear.

12. Jun 13, 2010

### hikaru1221

Force on each wire = force of the other wire + force of the rest of the two circuits.
But the 3rd law states that: force on 1st wire due to 2nd wire = force on 2nd wire due to 1st one. Just like the example about Earth and Sun: Earth experiences forces due to many planets, but force on Earth due to Sun = force on Sun due to Earth. The 3rd law doesn't care whether the forces due to other planets are negligible or not.

13. Jun 13, 2010

I am assuming you considered the field shape and field direction around each wire and then applied the left hand rule or similar.If so fine but the field at the edge where the wires meet is not circular in the way described.In order to work out the force at each point on each wire you have to take into account the field at that point due to the other circuit.

14. Jun 13, 2010

### hikaru1221

I still don't get your point. The wires don't have to intersect each other. Even if they are, the force on the edge is too small comparing to the total force on the other points on the wires, so it wouldn't matter much.
And again, what's the point of considering the rest of the circuit, when the 3rd law only focuses on the interaction between the 2 wires?

15. Jun 14, 2010

### ehild

Would you say that Newton's 3rd law is violated in the problem in the figure with two boxes interacting through a string? Box 1 acts with a vertical force on box 2 while box 2 acts with a horizontal force on box 1.

ehild

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16. Jun 14, 2010

### hikaru1221

No. The forces are due to the string. The boxes don't interact with each other directly. I guess you mean the magnetic field is like the string, right? (so thank you for giving me a great analogy)
So is it like the forces are the result of the interaction between each wire/current and the magnetic field created by the other wire, or between each wire and the magnetic field formed by both, or between both magnetic fields formed by both wires?

Last edited: Jun 14, 2010
17. Jun 14, 2010

### ehild

Correct, I meant so that the electromagnetic field is something like a string between two objects. Well, it is very difficult... Using fields is an approximation already. And the magnetic field interacts with the electrons moving in the wire instead of the wire itself. And an electron does not interact with its own field. I think it would better to speak about interaction of the electrons moving in the wires, taking into account that this interaction is not instantaneous.
Anyway, Newton's 3rd law is one of the postulates of Classical Mechanics, in inertial frames of reference. Electromagnetism is beyond Classical Mechanics. You certainly will study Relativity Theory, and then you'll get a more accurate description of such phenomena. I know two little for that.

ehild

18. Jun 14, 2010

Hello again hikaru.Your circuit is not real,its imaginary.You could make it real by extending the length of each wire and taking each end of each wire to the poles of a battery.This is equivelent to adding connecting wires and now your wires are not straight along their whole length.When you consider the field set up by each wire you should consider the whole wire and not the straight bits only.In your thought experiment you ignored the contribution to the field from the non straight(connecting wire)bits even though these connecting wires carry the same current and are probably longer than the straight bits.There is not a "rest of the circuit" which is irrelevant as you imply, the connecting wires are an integral part of the whole circuit and the field contribution due to them increases as you approach the edges of the straight sections.

19. Jun 14, 2010

### hikaru1221

Thank you very much, ehild. So:
1 - Why is using fields an approximation?
2 - Why can't an electron interact with its own field? The field is like another entity and "touches" the electron, so why not? If I consider a charged sphere moving freely, it will emit electromagnetic wave and thus, lose energy gradually, which means there must be some force (though infinitesimal) decelerating it, is that correct?
3 - Since you mentioned electron, I guess you mean each magnetic field "acts on its own", which means each field due to each moving electron can be discriminated somehow. Or things are like there is only one magnetic field (summing up all the magnetic fields) besides currents?
Any reply would be appreciated very much.

Oh yes, there certainly are things besides the straight wires. But why do we have to consider the whole circuit, when we only care about the interaction between the 2 wires?
So how would you find the force that one wire (not the whole circuit) exerts on the other?

20. Jun 14, 2010

hikaru,you can use Biot and Savarts law to calculate the value of B and in many geometries,including the central portion of a long straight wire,you can ,to a good approximation,ignore the contribution from the connecting wires.In your circuit you are considering the field close to the junction where the straight wire and connecting wire meet and this is at a place where the contribution due to the connecting wire(which can be considered as an extension of the straight wire) is not negligible.We do "care about the interaction between the two wires" but the two wires are not made of the straight sections only.

Last edited: Jun 14, 2010
21. Jun 15, 2010

### hikaru1221

I'm sorry, I haven't got your point yet.
The two wires here are parts of 2 circuits, and those two wires are particularly made straight. Then I use the Biot-Savarts law to calculate B due to one wire at the other wire so that I can calculate the force that one wire exerts on the other, which is my main purpose and also where the problem comes from. So I don't understand why considering B value due to the rest, because that doesn't mean the effect of the rest is negligible, it's just that all I care is the force between the wires.

22. Jun 15, 2010

The magnitude and orientation of the force at any location on each wire depends,amongst other things,on the magnitude and orientation of B at that location due to the opposite wire.The value of B depends on the whole circuit and not just part of it.You have deliberately made two sections of wire straight but these sections make up less than fifty percent of the total circuit.How can you justify considering only a certain part of a circuit whilst ignoring the bulk of that circuit?As I have stated before there are many geometries where the effects of the rest of the circuit can be ignored but your circuit is not one of these for reasons I have already pointed out.
I think the main problem here is that yours is a thought experiment and you have possibly not considered what is needed to make it into a real experiment.Try sketching out your circuit diagram again but with each straight section of wire connected to its power supply.

23. Jun 15, 2010

### hikaru1221

The B value at one point is due to the whole circuit, I agree with that point. However, in order to find the force between the 2 wires only (there is force by the rest of the circuit which is NOT negligible), I calculate B due to one wire only and then deduce the force from that. So is that an incorrect way to calculate the force that one wire exerts on the other? If so, then how would you calculate it?

24. Jun 16, 2010

I'm not sure what you're asking here but I'll have a guess.It seems that you want to calculate the force between the two straight sections of wire only and ignore the effects of the rest of the circuit.To a good approximation you can do this if the geometry is such that the rest of the circuit is very remote from the two sections of straight wire you are considering.One example of this would be if the wires are parallel and very long.In fact this arrangement is used to define the ampere(the definition states that the wires are infinitely long)
It's all well and good ignoring the rest of the circuit in such arrangements but look again at the arrangement you presented and see if you can draw it in full with the rest of the circuit being very remote from the region you are considering.

25. Jun 16, 2010

### hikaru1221

Yes, that's what I'm trying to do, but I'm not ignoring the effect of the rest (I mean, it's not negligible); it's just that I only consider the force F between the 2 straight wires (or straight sections as you call). So the problem is the method: I calculate B due to one section, and then, use that B to calculate F. If the method is correct, then the 3rd law is violated.

Okay, here is a circuit which satisfies the conditions you make (see picture). The power supplies are far away from the straight wires. I make the connecting wires particularly in that shape so that the B field due to them is canceled. Is it a circuit that you want?

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