Why Do Magnets with Different Field Homogeneities Experience Equal Attraction?

[Antony Kolarov]

I've been looking for that question for months but no luck.

According to the classical electrodynamics the attraction between two magnets is due to the inhomogeneous magnetic field acting on the atomic loop currents (through Lorenz forces). The homogenous field does not produce any attraction but the not homogenous field produces forces that have some component not laying in the current loop plane, resulting in attraction or repulsion.

Let's imagine that one of the two interacting magnets may produce very inhomogeneous field. And the other - very homogenous. That could be due to the shape of the magnets. Why the attraction that the two magnets feel is the same (3-rd principle of Newton) since the degree of homogeneity may be very different at the places where the 2 magnets reside?

Thanks in advance to anyone that may want to discuss that matter!

 

[PietKuip]

On the scale of the compass, the Earth's field is homogeneous. It only exerts a torque on the compass, otherwise there is no force between the two.
(I am not entirely sure if this is relevant as an answer.)

 

[Antony Kolarov]

On the scale of the compass, the Earth's field is homogeneous. It only exerts a torque on the compass, otherwise there is no force between the two.
(I am not entirely sure if this is relevant as an answer.)

Yes, right! Thank you for the help!
But the compass needle provide a non-homogenous field. So the Earth current loops (probably) have to feel a tiny attraction?

 

[PietKuip]

If you look at the Earth's field as produced by a current loop, you are looking on a scale where the field is inhomogeneous. Then there is a force between the two. But a current loop cannot produce a homogeneous field.

(It may also help to remember that the gravitational attraction from an apple on the Earth is not "tiny". It is just as large as the other way around, a few Newton.)

 

[Antony Kolarov]

If you look at the Earth's field as produced by a current loop, you are looking on a scale where the field is inhomogeneous. Then there is a force between the two. But a current loop cannot produce a homogeneous field.

(It may also help to remember that the gravitational attraction from an apple on the Earth is not "tiny". It is just as large as the other way around, a few Newton.)

Maybe the "scale" would be the key to the answer. Thank you for that! I have to think about.

But if we leave the magnetic field of the Earth and go back to the original issue: Two permanent magnets (small metal peaces), the same size, one of them producing more inhomogeneous field (e.g. having one side sharpened). I still wonder:
- If field of Magnet 1 more homogeneous than field of Magnet 2 then: should not Magnet 2 fill stronger attraction force (caused by Magnet 1's field) than fills Magnet 1 (caused by Magnet 2's field)?

Or that way of thinking is totally wrong?

 

[Philip Wood]

Do you think that a large current loop and a small current loop would be an example of what you're concerned about? Suppose they were coaxial. Then the field produced by the large loop would be nearly uniform over the small loop , but the reverse would not be true. It's possible though, by using the B-S rule and the Lorentz force rule to show that the forces on the loops are equal and opposite (even if the loops are neither circular nor co-axial).