Non-metal objects are attracted to the Earth due to gravity. So the weight of non-metal objects can be only dependent on their mass.
On the other hand metals can be attracted to the Earth's magnetic field, with the Earth acting as a giant magnet; causing metals to weight more than they normally should.
In other words the weight of metals and magnetic objects would be the sum of the magnetic force plus the gravitational force, is that correct?
If that effect is true, would it be more clear as we go closer to the magnetic poles, and metals would weigh different in different locations on Earth?
Best Answer
Reformulating your question: do metals feel a force of attraction to the earth due to the earth's magnetic field - and does that force depend on the position on earth?
It is not the magnetic field itself that causes the attraction, it is the gradient of the magnetic field. In a uniform magnetic field you will get some magnetization (more so in ferromagnetic materials), and there will in general be a torque as the dipole moment in the material tries to align with the external magnetic field. This is the principle behind a magnetic compass, but in itself does not result in a net force (of the kind that you could measure on scales).
In a non-uniform field,
$$F = (\mu \cdot \nabla) B$$
Now with the magnetic field of a dipole scaling roughly with $\frac{1}{r^3}$, we know that the gradient will be approximately $3B/r$. Since $r$ is the radius of the earth, dividing $B$ by a large number makes a very, very small number. And because you are taking the dot product, with the magnetization being aligned with the magnetic field and the gradient being at right angles (at the equator), it will be zero. But as you approach the poles, the magnetization and the gradient will start to align somewhat.
So yes - there will be a force on ferromagnetic objects due to the earth's magnetic field, and that force changes with position on earth - greatest near the magnetic poles, smallest near the equator. But it will be absolutely tiny, and you will have a very hard time measuring it.