# Magnets Floating in the Earth's Field

Q:
People say that the earth is a big magnet. We are wondering if a strong piece of magnet can float in the air, based on the principle that like poles of a magnet repels each other.
- Wu Fan and Qihan
A:
Hi Wu Fan and Qihan,

That is a very good question, because it addresses a feature of magnetic forces which normally does not arise in our experience with small magnets.

The force on an object is related to the change in the energy of a system (not including the kinetic or thermal energy of the object) when the object is moved. We write

F = (change in Energy)/(change in position)

For static fields. The change in position has a direction, and so the force does too (you need some vector algebra with a dot product to express this exactly).

Two small magnets placed together with like poles close to each other feel a repulsive force because of the energy stored in the magnetic field. The energy density in space is proportional to the magnetic field squared, and when the close-by poles are the same, their fields add in more places than they subtract, and so the total energy is higher for this case than when opposite poles are closer, where the field is smaller in more places.

There are two things about the Earth’s magnetic field which makes this effect much smaller. For one, the field is very weak at the surface (about a gauss or less). The more important reason is that because the field extends over such a large space and because we on the surface are far away from the center of the Earth’s dipole, the Earth’s magnetic field strength is very uniform if you look at it over a region of space that is reasonable in size (like the size of the magnet you propose to use).

If you put these two pieces together, you find that the force on a magnet due to the Earth’s field is very small -- if you move the magnet from one place to another, its field adds to the Earth’s field in almost the same way because the Earth’s field is very little different from one place to another, and the total magnetic energy changes by a very very tiny amount. In fact, the total magnetic force on a magnet in a uniform magnetic field is exactly zero, and the forces we normally associate with magnets repelling or attracting are proportional to the rate of change of the field strength with position.

This isn’t the end of the story, however, because the magnetic energy of the system depends on which way the magnet is pointing, relative to the Earth’s field. If it points along the field, the fields add, for a higher energy. If it points the other way, the fields subtract, for a lower energy, and so the magnet prefers to turn to point in this way. Magnets in uniform fields feel torques which make them turn around if they are not pointing in the right direction, but there is no net force making the magnet want to levitate.

That having been said, if you had a really really big magnet, whose field extended over such a large region that the Earth’s field changes noticeably over that region (you might need another Earth-sized bar magnet), then yes, a noticeable force can be produced.

As for actual levitation, that can only happen with materials whose magnetic moment actually points the wrong way, increasing the energy in a magnetic field. These are called diamagnets. Diamagnetism is purely a quantum mechanical effect, with no classical explanation. By far the most intense diamagnets are superconductors. You may have seen superconductors levitating over magnets, or vice-versa. The Earth’s magnetic field does not change rapidly enough from place to place to levitate even a superconductor.

Tom (w Mike)

(published on 10/22/2007)

## Follow-Up #1: followup to magnetic levitation

Q:
I am working on a Science Fair Project idea based around this concept, trying to figure out if it is possible to make a feasable vehicle using the Earth’s magnetism to levitate it and give it the power to move around. As your answer said, that is pretty much impossible. But, is there any reasonable way to energize the earth’s magnetism in a certain place without spending more than it costs to pave the road in that same unit of area? I really want to know is if there is any way to naturally make a lightweight vehicle levitate 1-2 feet off the ground (maybe less...) and have the ability to move multi-directionally. Thanks, Wade
Houston, TX, USA
A:

The Earth’s magnetism isn’t causing any sort of energy to flow  up to the surface of the Earth, so it can’t be used as a power supply. The difference in strength of the field between different heights is also far, far too weak to be used as the field in a superconducting levitation scheme, in which the field doesn’t have to supply energy.

(published on 10/22/2007)

## Follow-Up #2: Magnetic levitation?

Q:
Hello, What if we lay down a magnetic sheet on the road and fit some solenoids under a vehicle to change the strength and to oppose it to levitate .
- Jai (age 16)
India
A:
Great idea Jai.    It works and in fact train systems have been constructed using this idea.
Take a look at for some examples.
Our web site has answered many questions on this subject.  I suggest you type maglev into the search box and see what other people have asked.

LeeH

(published on 08/10/2012)

## Follow-Up #3: permanent magnet contrasted with Earth

Q:
What are the difference between permanent magnet and earth? Why permanent magnet attract only iron but earth attract all things ?
- dhilipkumar (age 19)
A:

Any magnet, including a permanent magnet or the Earth, will attract any ferromagnetic material, not just iron. Some other examples include cobalt and nickel. Magnets magnetically attract paramagnetic materials more weakly and repel diamagnetic materials. A good permanent magnet has a high density of aligned magnetic spins  and thus has a strong magnetic field nearby. The Earth has a weaker magnetic field from electrical currents driven by thermal convection, in a complicated process that I don't really understand.

Both the Earth and the permanent magnet will also attract all other materials by gravity. The strength of the gravity depends on the mass of the source. The Earth's mass is much bigger so it has much stronger gravity than your permanent magnet, even allowing for how far we are from the center of the Earth.

Mike W.

(published on 09/06/2013)

## Follow-Up #4: Do magnetic monopoles exist?

Q:
has anyone ever observed a monopole magnetic field resignating from either the earth or a permanent magnetic fields???
- London (age old)
Modesto, Ca, Stanislaus
A:

Hi London,

The answer is no.   Many careful searches have been made but without success.  Too bad, they would fit nicely into Maxwell's equations.  We have answered many questions of this sort.   I suggest you type  magnetic monopoles  into the search box and browse several of the former questions and answers.

LeeH

(published on 10/07/2014)

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