Is Newton's Third Law Always Obeyed?

[Fusina]

Hello

I am Fusina, I wish to ask you Three questions which bother my mind.

Its all about Newton's third Law.



Is Newtons third law always obeyed?
Is there an example of two moving particles, who's velocities are such that their mutual magnetic force doesn't obey Newton's 3rd law?

I tried answering this by thinking of two particles moving along the x and y axes respectively, but i can't explain.

Also, i don't know the reason why in practice, the mutual magnetic force of two moving electons is not the same (i heard it has something to do with the momentum lost to the medium of interaction)

 

[jostpuur]

It is not true always. Magnetic forces are the classical example of a situation, where Newton's third law gets violated.

A conservation of momentum is a kind of law that doesn't get violated ever. The Newton's third law is true if you can assume that the objects are interacting so directly, that their combined momentum is conserved.

When you have charged particles interacting, they are in fact interacting with the electromagnetic field. Both the particles and electromagnetic field contain energy and momentum. So in this case the particles' total momentum is not conserved, but instead it is the total momentum of both particles and the field, that is conserved. This is why Newton's third law doesn't apply with magnetic forces anymore.

That's the idea. If you want it more precise, you need to get into mathematics of it.

 

[alvaros]

jostpuur wrote:

It is not true always. Magnetic forces are the classical example of a situation, where Newton's third law gets violated.

Could you give a link where this is further explained ?
Thanks.

 

[meopemuk]

Is Newtons third law always obeyed?
Is there an example of two moving particles, who's velocities are such that their mutual magnetic force doesn't obey Newton's 3rd law?

This is a very good question. Yes, the Biot-Savart magnetic interaction law formally violates the Newton's third law. This situation is a subject of ongoing debate in research literature. See, for example,

E. Breitenberger, "Magnetic interactions between charged particles", Am. J. Phys. 36 (1968), 505

When you have charged particles interacting, they are in fact interacting with the electromagnetic field. Both the particles and electromagnetic field contain energy and momentum. So in this case the particles' total momentum is not conserved, but instead it is the total momentum of both particles and the field, that is conserved. This is why Newton's third law doesn't apply with magnetic forces anymore.

This is the standard explanation. However, the idea of momentum and energy contained in the electromagnetic field leads to even more paradoxes. For example, the total energy of the field around a point charge is infinite.

There are experiments which can be interpreted as an evidence that magnetic interactions between charges are not described by the Biot-Savart law:

P. Graneau, N. Graneau, "Electrodynamic force law controversy"
Phys. Rev. E 63, 058601 (2001)

Eugene.

 

[alvaros]

jostpuur:

This is why Newton's third law doesn't apply with magnetic forces anymore.

If there is no link, could you tell an experiment ( real or imaginary ) that shows this fact.
meopemuk:

For example, the total energy of the field around a point charge is infinite.

? Could you explain this further ?

 

[meopemuk]

For example, the total energy of the field around a point charge is infinite.

? Could you explain this further ?

This is a well-known fact. The field energy is given by the space integral of \mathbf{E}^2. In the vicinity of the point charge, the electric field \mathbf{E} becomes infinite, and the integral diverges.

Eugene.

 

[jostpuur]

alvaros, I don't know any site at the moment. I could try to search web, but I probably won't find anything that you couldn't find yourself. The Lorentz force and Biot-Savart law got confirmed by experiment more than 100 years ago (I don't know in fact very accurately when, but something like that anyway). If you know these laws, you can verify yourself by calculating some examples, that Newton's third law can get violated.

One way to go around the problem of infinite energies in classical fashion is to not use point charges, but instead replace them with small balls of finite but large charge density. When you solve the electric field for them, and its energy, you can see that it approaches infinity when the radius of the ball is taken to zero. But the problem is solved to some extent simply by not letting the radius go zero, and instead giving it some small but nonzero value.

 

[meopemuk]

The Lorentz force and Biot-Savart law got confirmed by experiment more than 100 years ago (I don't know in fact very accurately when, but something like that anyway).

It is true that Lorentz and Biot-Savart force laws are integral parts of Maxwell's electrodynamics, as presented in all textbooks. However, it is not true that these laws were confirmed by experiment beyond any doubt. Over the years alternative expressions for the magnetic force were proposed. They include the Ampere force law and Darwin potentials. It appears that it is very difficult to distinguish these different force laws in usual experiments by measuring interactions of closed current loops. All these force laws give the same total force when integrated along the closed loop.

There are experimental groups, which continue to investigate these questions. These are not "mainstream" activities, but they are not "crackpot" either. One recent example is:

N. Graneau, T. Phipps Jr., D. Roscoe, "An experimental confirmation of longitudinal electrodynamic forces" Eur. Phys. J. D 15 (2001), 87.

Eugene.

 

[alvaros]

Right now I am confused, I've never thougth about Newton 3rd-law and magnetic forces. I must study the issue.
Anyway

For example, the total energy of the field around a point charge is infinite.

There are no "point charges" and I don't know how this fact could be related to the OP question.
Thanks to all.

 

[meopemuk]

There are no "point charges"

What about the charge of the electron?

Eugene.