# Newton's 3rd law not applicable to megnetic forces?

1. Jan 6, 2008

### mdeng

I just read the following from http://www.physicstoday.org/vol-57/iss-10/p11.html [Broken]. Could anyone shed some details about the claim? Coming from a professor at MIT, it must be true.

Last edited by a moderator: May 3, 2017
2. Jan 7, 2008

### Staff: Mentor

The magnetic force acting on an object depends explicitly on the object's velocity:

$$\vec F_{mag} = q \vec v \times \vec B$$

Also, the magnetic forces exerted by two moving charges on each other are in general not equal in magnitude and opposite in direction. We account for this by assigning momentum to the electromagnetic field. The momentum per unit volume due to the electromagnetic field is

$$\vec g = \epsilon_0 \vec E \times \vec B$$

See for example

http://farside.ph.utexas.edu/teaching/em/lectures/node90.html
http://farside.ph.utexas.edu/teaching/em/lectures/node91.html

In classical mechanics (excluding electromagnetism), Newton's Third Law is equivalent to conservation of total momentum. When electromagnetic forces are involved, the total momentum of the particles is not conserved. However, the total momentum of the partlcles and the electromagnetic field is conserved.

3. Jan 7, 2008

### arildno

You can think of "momentum" as tiny balls that are "thrown" from one object to the other.
What one object loses, the other gains.

Or, that would be true if there was an INSTANTENOUS transmission of the tiny momentum ball.

This is true for the so-called "contact force interactions".

However, the electro-magnetic forces are NOT contact forces, and there is a non-zero timelag where the tiny ball of momentum lies in the electric field in between the two objects.

This, of course, is a pictorial description of the situation..

4. Jan 7, 2008

### mdeng

Jtbell, thanks for the pointers and your helpful summary.

It's interesting to see that the emitter of an electromagnetic wave is subject to a negative momentum change of value equal to that of the electromagnetic wave. What kind of electromagnetic radiation would be "unidirectional" to cause its emitter to move backwards? Ordinary electromagnetic radiation is outward toward all directions.

5. Jan 7, 2008

### mdeng

Thanks for the insights. I gather then the same goes for quantum particles that are subject to the strong force.

6. Jan 7, 2008

### Tanja

Possibly the trouble with the lack of a magnetic dipol isn't as much dependen on the concept "force", which is just a mathematical idea for the energy derivative in space.

- On the one hand the magnetic field in a solid like iron is the result of spin couplings.
- On the other hand it apears with electromagnetic waves and current flows in rings.

Would be interesting to find similarities or a superior explanation for these two systems ending up with the same force (effect).

Does anyone have an idea?

7. Jan 7, 2008

### Staff: Mentor

I wouldn't call it "radiation" which implies that the energy escapes to infinity. Most books (and those lecture notes) discuss electromagnetic field energy and momentum in the context of electromagnetic waves because that's a very practical application. But the field energy and momentum also exist in any other situation where $\vec E \times \vec B$ is nonzero (for momentum) and $E^2 + B^2$ is nonzero (for energy). Just calculate the total $\vec E$ and $\vec B$ at any given moment (produced for example by two charges moving past each other) and calculate the energy and momentum from those.

8. Jan 7, 2008

### Tanja

Isn't there a big, big difference between the two appearances of a magnetic field as I wrote above and the electrical and magnetical field vectors as the amplitude of electromagnetic waves?
I regard the E and B vector in an electromagnetic wave as the possibility or the potential to couple and interact with matter. Or does anyone here knows an example where B, let's say of light, really has an effect in such a way that a particle gets attracted, just because of the presence of a light beam?