How can a refrigerator magnet be stronger than the Earth's magnetic field?

Question

This Wikipedia page lists examples of magnets and magnetic fields of different strengths.

I don't understand why it claims that the Earth's magnetic field is less strong ($31.869 \ \mu\text{T}$) than a refrigerator magnet ($5 \ \text{mT}$).

I'm assuming that the first value is the intensity of the Earth's magnetic field on the surface ($6,371 \;\text{km}$ away from its center), but in that case, how does it make sense to measure the strength of a magnet without also specifying the distance from the magnet at which the measurement was made? How can the same unit measure both the intensity of a magnetic field at a certain distance, and also the overall (distance-independent) strength of a magnet?

Answer 1

As you are saying, the magnetic field strength for the Earth is at its surface (that is normally available without digging), that is the closest available connection between the Earth and the magnet/metal.

The other magnet's strength is the same way, a refrigerator magnet's strength is meant by attaching it to the surface of the refrigerator, thus creating the closest possible connection between the magnet and the metallic surface of the refrigerator (without damaging the refrigerator or the magnet).

Now your question is, how can a refrigerator magnet be stronger then the Earth's magnetic field? The EM force of the Earth is different from the gravitational field. In case of the gravitational field, the Earth stress-energy (not mass directly) is very much important, and in some ways, the huge mass (in reality stress-energy) of the Earth makes you feel it should have a very strong gravitational field.

Now with the EM field, it is very different. It does not matter in reality how huge a mass (or stress-energy) the Earth has, even a small sized magnet can be (and in your example it is) stronger then the Earth's magnetic field. It is an intrinsic property of the EM force, where it can be canceled out inside the body by opposite charges. That is what happens, thought the Earth is huge, it is full of opposite charges that cancel out, and you only feel the net force (which is not even as strong as a small magnet).

Now with the magnetic field it is a little bit more complicated, because the Earth's magnetic field is due to a liquid outer core, that moves and creates electric currents. The rotation of the Earth on its axes causes these currents to create a magnetic field.

Now the magnetic field strength drops with distance very quickly, and since you cannot touch the liquid outer core inside the Earth, you are far away from the actual magnet of the Earth itself when you are on the surface.

When you attach the magnet to the refrigerator, that is as close at it gets to the magnetic field of the refrigerator magnet. But the refrigerator magnet is far away from the Earth's liquid core that generates the magnetic field of the Earth.

Your experiment would have a different result if you tried it very close to the liquid core (disregarding other effects like heat etc).

Answer 2

As @Árpád Szendrei noted, "Your experiment would have a different result if you tried it very close to the liquid core"

Indirect estimate of magnetic field inside the Earth gives a value of 2.5 mT (Nature, v. 468, 16 Dec. 2010, p. 952), which is of the same order of magnitude as the magnetic field of the refrigerator magnet.

The article's abstract: "Magnetic fields at the Earth’s surface represent only a fraction of the field inside the core 1. The strength and structure of the internal field are poorly known 2,3,4,5, yet the details are important for our understanding of the geodynamo. Here I obtain an indirect estimate for the field strength from measurements of tidal dissipation. Tidally driven flow in the Earth’s liquid core develops internal shear layers, which distort the internal magnetic field and generate electric currents. Ohmic losses damp the tidal motions and produce detectable signatures in the Earth’s nutations. Previously reported evidence of anomalous dissipation in nutations 3,6 can be explained with a core-averaged field of 2.5 mT, eliminating the need for high fluid viscosity 6 or a stronger magnetic field at the inner-core boundary 3. Estimates for the internal field constrain the power required for the geodynamo 7,8."

Answer 3

If you stand on the moon's surface you will also be attracted to the moon although earth's mass is much larger, the same goes for magnets; the force is inversely proportional to the square of the distance.

Only in close range to the magnet a compass will point in the direction of the magnet, if you move it away from the magnet it will of course point in the direction of earth's pole, and not the magnet.

Also see How strong would the Earth's "magnet" be if it was the size of a fridge magnet?