Does Water Really Repel Magnets?
— A Living Frog Floated Above a Strong Magnet
We tend to think that things a magnet won't stick to have nothing to do with magnets. Water, though, is trying to flee from a magnet with a tiny force. The force is so weak that we normally never notice it. But make the magnet extremely strong, and a living creature made of water simply floats in the air.
Take the magnet that holds a note on your fridge door and bring it close to a glass of water. Nothing seems to change.
But in 1997, at a laboratory in the Netherlands, a small living frog was placed inside a huge tube-shaped magnet. Inside the tube, the frog floated, with nothing holding it up.
There was no iron in the frog. What lifted it was the water that makes up most of its body.
Two reasons the frog floated
When a magnet comes near, the electrons in water turn into tiny magnets that point the opposite way and push the magnet back. So water repels a magnet with a very weak force.
Double the magnet's strength and the repelling force becomes about 4 times larger. Make it 10 times stronger and the force becomes about 100 times larger. With an extremely strong magnet, it finally beats the body's weight.
In other words, the repelling force is always there. An ordinary magnet is just too weak, and weight wins.
Why does water repel a magnet?
Everything is made of atoms. Inside atoms, electrons are moving around. When electrons move, they create a tiny magnetic effect around them.
Bring a magnet close from outside, and the motion of the electrons changes very slightly. The change follows a rule: it shifts in the direction that "cancels" the influence of the approaching magnet.
As a result, water becomes a very weak magnet pointing the opposite way to the one coming near. If you bring a north pole close, the water side presents a north pole facing it. That is why it is pushed back.
This is not a property of water alone. Wood, plastic and our own bodies all repel weakly in the same way. For things like iron, which are strongly attracted, this weak repulsion is simply hidden beneath a much stronger pull.
Why don't we notice it every day?
The force with which water repels a magnet is incredibly weak compared with the force with which iron is pulled toward one. Water's response to a magnet is said to be only about one hundred-millionth of iron's.
This is where the second reason comes in. The repelling force is proportional to the square of the magnet's strength. Look at the right side of Figure 1. A fridge magnet is about 0.005 tesla (the tesla is a unit of magnet strength). The magnet that floated the frog was 16 tesla, about 3,200 times stronger. Because the force goes with the square, the difference in push is about 10 million times.
Strength alone is not enough to float something. The strength also has to change sharply from place to place. As on the left of Figure 1, at the exit of the tube the field lines spread out, and the magnet gets weaker the higher you go. Water is pushed toward the weaker region, so an upward force appears.
The water inside the body is pushed in the same way everywhere. So the frog is thought to have been supported evenly throughout its body, in a state where it hardly felt its weight. The frog is said to have been fine after the experiment.
Andre Geim, one of the physicists who floated the frog, received the Ig Nobel Prize in 2000 for this experiment. The prize goes to research that "makes people laugh, then think". In 2010 he also received the Nobel Prize in Physics for different work. He is said to be the only person to have won both.
Liquid oxygen is known to cling to a strong magnet when brought close. Oxygen molecules have a property of strong "attraction" that outweighs the weak repulsion. Even among liquids, the way electrons are arranged inside can make the response to a magnet the exact opposite.
Summary
Things that a magnet won't stick to are, in fact, all trying to flee from it with a very weak force. Water is one of them. Because the force grows with the square of the magnet's strength, raising it to thousands of times that of a fridge magnet can float even a creature made of water. We don't normally see it, not because the force is absent, but because it is too weak and hidden by weight.
Things a magnet won't stick to are not unrelated to it.
They dislike it, just a little.
How a magnet's force passes through paper and hands is explained in "Why does a magnet stick even through paper or your hand?", and what happens when you break a magnet is covered in "If you cut a magnet in half, do you get a magnet with only a north pole?".
- Stick one grape on each end of a drinking straw. Rest the middle of the straw on top of a plastic bottle cap so that it balances.
- Surround it with a box or similar to keep out the wind, and wait until the straw settles and stops moving.
- Slowly bring a strong neodymium magnet as close to a grape as you can without touching it. The grape begins to turn, slowly drifting away from the magnet.
Grapes are mostly water, so the same repulsion as in this article occurs. The movement is very slow, so be patient. Neodymium magnets are very strong, and two of them can pinch your fingers and injure you. They are dangerous if a small child swallows them, so keep them out of reach.
For those who want to know more — terms, formulas and links to textbooksWe state clearly what level each part belongs to, from middle school science to university courses
- Middle schoolCovered in middle school science
- High schoolCovered in high school physics
- High school+Advanced high school material, or treated as a textbook sidebar
- UniversityNot taught in high school; university courses (electromagnetism, condensed matter physics)
- ResearchNot yet taught even at university as settled fact; being studied by researchers right now
Middle schoolTerms: this phenomenon has a name
- Diamagnetism: the property of becoming a weak opposing magnet and being repelled when a magnet comes near. Many things have it, including water, wood, copper and bismuth.
- Paramagnetism and ferromagnetism: the property of being attracted to a magnet. Weak attraction is paramagnetism (liquid oxygen, for example); strong attraction is ferromagnetism (iron, for example).
- Diamagnetic levitation: floating an object in mid-air using the repulsion of diamagnetism. The frog experiment is the best-known example.
Middle schoolHigh schoolChecking with a formula: how strong a magnet does it take to float water?
We set up the condition where the "push-back force" and the "weight" on each cubic metre of water balance, and estimate the magnet strength needed.
| In symbols | B × ( dB ／ dz ) ＝ μ0 × ρ × g ÷ |χ| |
| In words | magnet strength × how fast the strength drops going up = permeability of vacuum × density of water × gravitational acceleration ÷ how easily water repels |
| Where it comes from | The balance between the upward force on a diamagnetic object (per volume: |χ| × B × gradient ÷ μ0) and its weight per volume (ρ × g) |
| Symbol | Meaning and unit |
| B | Magnet strength (magnetic flux density). Unit: tesla |
| dB ／ dz | How much the strength changes over 1 metre going up. Unit: tesla per metre |
| μ0 | Permeability of vacuum. About 1.26 × 10⁻⁶ (unit: tesla metre per ampere) |
| ρ | Density of water. Unit: kilograms per cubic metre |
| g | Gravitational acceleration. Unit: metres per second squared |
| χ | Volume magnetic susceptibility (how easily it repels). Negative for water; no unit |
| Size of water's volume susceptibility | About 9.0 × 10⁻⁶, as commonly stated |
| Permeability of vacuum | About 1.26 × 10⁻⁶ |
| Density of water | 1000 kilograms per cubic metre |
| Gravitational acceleration | 9.8 metres per second squared |
| Distance over which the strength changes a lot inside the magnet (a rough tube size) | About 0.1 metre |
| Repulsiveness ÷ permeability (the 10⁻⁶ factors cancel) | 9.0 ÷ 1.26 ≒ 7.14 |
| Weight per volume | 1000 × 9.8 ＝ 9800 |
| Required "strength × rate of drop" | 9800 ÷ 7.14 ≒ 1373 |
| Treating the drop as "strength ÷ 0.1 metre", the square of the strength is | 1373 × 0.1 ≒ 137 |
| Square root of 137 | About 11.7 tesla, as the value works out |
| Compared with a fridge magnet (0.005 tesla) | 11.7 ÷ 0.005 ＝ 2340 |
The required strength is on the order of 10 tesla. This agrees well with the 16-tesla magnet used in the real experiment. It is about 2,000 times a fridge magnet or more, and over 200,000 times Earth's magnetic field. Floating water takes a magnet that extreme.
High schoolHigh school+Why does it go with the "square"?
High schoolIn high school physics you learn Lenz's law: when a magnetic field changes, a current flows in the direction that cancels the change. Diamagnetism can be roughly understood as the motion of electrons in atoms shifting slightly in a similar direction.
High school+The response of water to a magnet (its magnetization) is proportional to the magnet's strength B. That magnetization then feels a force from the "slope" of the magnet's strength. Two things that are proportional multiply together, so the force is proportional to B times the slope, which is roughly the square of the strength. This is why the magnetic energy is written in the form |χ| × B² ÷ ( 2 × μ0 ) per volume.
UniversityOrdinary magnets can't float things stably
Even by combining permanent magnets, you cannot keep an object floating steadily. This is shown by Earnshaw's theorem. Diamagnetic objects, however, tend to settle toward the magnet's "weak spots", so they escape this restriction. This is also called the Braunbek extension. The origin of diamagnetism itself is explained as Larmor diamagnetism (Langevin diamagnetism), which treats the orbital motion of electrons with quantum mechanics. The paper that explains the frog experiment, "Of flying frogs and levitrons", discusses the conditions for this stability in detail.
📖 Derivations and further reading: Diamagnetism (Wikipedia) ／ Earnshaw's theorem (Wikipedia)
ResearchWhat is still not well understood
- How well can weightlessness be reproduced? Diamagnetic levitation is used to mimic a "weightless state" for cells and small creatures. But the components inside a body repel by slightly different amounts, so how closely it matches the weightlessness of space is said to be still debated.
- Effects of long stays in strong fields What happens when living things stay for a long time in a field above 10 tesla is still being investigated.
- Materials that float on weaker magnets Things such as graphite, which repels tens of times more than water, are known to float even above neodymium magnets. Research is under way to make materials that repel even more strongly.
So the content of this article, too, is "an explanation of what is known so far". In theory the human body should also float, but at present there is said to be no magnet able to produce that strength over a space big enough for a person.
Links to textbooks (by level)
| Level | Subject and unit | Where in this article |
|---|---|---|
| Middle school | Science, year 2: "Electric current and magnetic field" | Magnet strength, spreading of field lines |
| High school | Physics: "Electromagnetic induction and Lenz's law" | Repulsion arising in the "cancelling direction" |
| High school+ | Physics (advanced): "Magnetism of matter" | The force growing with the square of the strength |
| University | Electromagnetism and condensed matter physics | Earnshaw's theorem, Larmor diamagnetism |
| Research | Biophysics and materials science | Reproducing weightlessness, new diamagnetic materials |
| ― | Links to daily life | Strong fields in hospital scanners, handling neodymium magnets |
- M. V. Berry, A. K. Geim, "Of flying frogs and levitrons", European Journal of Physics 18 (1997)
- NobelPrize.org, "Andre Geim – Facts"
- Wikipedia (Japanese), "Diamagnetism" (反磁性)
- National Astronomical Observatory of Japan (国立天文台), ed., Rika Nenpyo (理科年表, Chronological Scientific Tables), Maruzen Publishing (magnetic susceptibilities of materials)
* This article is a general-audience science explainer. The figures given are rough guides to help you understand how things work. Magnets above 10 tesla are special devices in research facilities and cannot be reproduced at home. Handle neodymium magnets with care to avoid pinching and swallowing.