Gravity and Levity

How strong would a magnetic field have to be to kill you?

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There’s a great joke in Futurama, the cartoon comedy show, about a horror movie for robots.  In the movie, a planet of robots is terrorized by a giant “non-metallic being” (a monsterified human).  The human is finally defeated by a makeshift spear, which prompts the robot general to say:

“Funny, isn’t it?  The human was impervious to our most powerful magnetic fields, yet in the end he succumbed to a harmless sharpened stick.”

The joke, of course, is that the human body might seem much more fragile than a metallic machine, but to a robot our ability to withstand enormous magnetic fields would be like invincibility.

But this got me thinking: how strong would a magnetic field have to be before it killed a human?

 

Unlike a computer hard drive, the human body doesn’t really make use of any magnetic states — there is nowhere in the body where important information is stored as a static magnetization.  This means that there is no risk that an external magnetic field could wipe out important information, the way that it would for, say, a credit card or a hard drive.  So, for example, it’s perfectly safe for a human (with no metal in their body) to have an MRI scan, during which the magnetic fields reach several Tesla, which is about  times stronger than the normal magnetic fields produced by the Earth.

 

A computer hard drive stores information in a sequence of magnetically aligned segments.

 

But even without any magnetic information to erase, a strong enough magnetic field must have some effect.  Generally speaking, magnetic fields create forces that push on moving charges.  And the body has plenty of moving charges inside it: most notably, the electrons that orbit around atomic nuclei.

As I’ll show below, a large enough magnetic field would push strongly enough on these orbiting electrons to completely change the shape of atoms, and this would ruin the chemical bonds that give our body its function and its structure integrity.

What atoms look like

Before I continue, let me briefly recap the cartoon picture of the structure of the atom, and how to think about it.  An atom is the bound state of at least one electron to a positively charged nucleus.  The electric attraction between the electron and the nucleus pulls the electron inward, while the rules of quantum mechanics prevent the electron from collapsing down completely onto the nucleus.

 

In this case, the relevant “rule of quantum mechanics”  is the Heisenberg uncertainty principle, which says that if you confine an electron to a volume of size , then the electron’s momentum must become at least as large as .  The corresponding kinetic energy is , which means that the more tightly you try to confine an electron, the more kinetic energy it gets.  [Here, is Planck’s constant, and is the electron mass$.]  This kinetic energy is often called the “quantum confinement energy.”

In a stable atom, the quantum confinement energy, which favors having a large electron orbit, is balanced against the electric attraction between the electron and the nucleus, which pulls the electron inward and has energy . [Here is the electron charge and is the vacuum permittivity].  In the balanced state, these two energies are nearly equal to each other, which means that meters.

This is the quick and dirty way to figure out the answer to the question: “how big is an atom?”.

The associated velocity of the electron in its orbit is , which is about m/s (or about a million miles per hour).  The attractive force between the electron and the nucleus is about , which comes to ~100 nanoNewtons.

Who pulls harder: the nucleus, or the magnetic field?

Now that I’ve reminded you what an atom looks like, let me remind you what magnetic fields do to free charges.

They pull them into circular orbits, like this:

 

The force with which a magnetic field pulls on a charge is given by , where is the strength of the field.  For an electron moving at a million miles per hour, as in the inside of an atom, this works out to be about 1 picoNewton per Tesla of magnetic field.

Now we can consider the following question.  Who pulls harder on the electron: the nucleus, or the external magnetic field?

The answer, of course, depends on the strength of the magnetic field.  Looking at the numbers above, one can see that for just about any realistic situation, the force provided by the magnetic field is much much smaller than the force from the nucleus, so that the magnetic field essentially does nothing to perturb the electrons in their atomic orbitals.  However, if the magnetic field were to get strong enough, then the force it produces would be enough to start significantly bending the electron trajectories, and the shape of the electron orbits would get distorted.

Setting from above gives the estimate that this kind of distortion happens only when  Tesla.  Given that the strongest static magnetic fields we can create artificially are only about 100 Tesla, it’s probably safe to say that you are unlikely to experience this any time soon.  Just don’t wander too close to any magnetars.

Distorted atoms

But supposing that you did wander into a magnetic field of 100,000 Tesla, what would happen?

The strong magnetic forces would start to squeeze the electron orbits in all the atoms in your body.  The result would look something like this:

 

 

So, for example, an initially spherical hydrogen atom (on the left) would have its orbit squeezed in the directions perpendicular to the magnetic field, and would end up instead looking like the picture on the right.  This squeezing would get more and more pronounced as the field is turned up, so that all the atoms in your body would go from roughly spherical to “cigar-shaped,” and then to “needle-shaped”.

Needless to say, the molecules that make up your body are only able to hold together when they are made from normal shaped atoms, and not needle-shaped atoms.  So once the atomic orbitals got sufficiently distorted, their chemistry would change dramatically and these molecules would start to fall apart.  And your body would presumably be reduced to a dusty, incoherent mess (artist’s conception).

 

But for those of us who stay away from neutron stars, it is probably safe to assume that death by magnetic field-induced disintegration is pretty unlikely.  So you can continue lording your invincibility over your robot coworkers.

 

UPDATE:

A number of people have pointed out, correctly, that if you really subjected a body to strong magnetic fields, something would probably go wrong biologically far before the field got so ludicrously large fields as 100,000 Tesla.  For example, the motion of ions through ion channels, which is essential for nerve firing, might be affected.  Sadly, I probably don’t know enough biology to give you a confident speculation about what, exactly, might go wrong.

There is another possible issue, though, that can be understood at the level of cartoon pictures of atoms.  An electron orbiting around a nucleus is, in a primitive sense, like a tiny circular electric current.  As a result, the electron creates its own little magnetic field, with a “north pole” and “south pole” determined by the direction of its orbital motion.   Like so:

Normally, these little electron orbits all point in more or less random directions.  But in the presence of a strong enough external magnetic field, the electron orbit will tend to get aligned so that its “north pole” points in the same direction as the magnetic field.  By my estimate, this would happen at a few hundred Tesla.

In other words, a few hundred Tesla is what it would take to strongly magnetize the human body.  This isn’t deformation of atoms, just alignment of their orbits in a consistent direction.

Once the atomic orbits were all pointed in the same direction, the chemistry of atomic interactions might start to be affected.  For example, some chemical processes might start happening at different rates when the atoms are “side by side” as compared to when they are “front to back.”  I can imagine this subtle alteration of chemical reaction rates having a big effect over a long enough time.

Maybe this is why, as commenter cornholio pointed out below, a fruit fly that grows up in a ~ 10 Tesla field appears to get mutated.

 

 

Footnote

I have been assuming, of course, that we are talking only about static magnetic fields.  Subjecting someone to a magnetic field that changes quickly in time is the same thing as bombarding them with radiation.  And it is not at all difficult to microwave someone to death.

[Update: A number of people have brought up transcranial magnetic stimulation, which has noticeable biological effects at relatively small field strengths.  But this  works only because it applies a time-dependent magnetic field, which can induce electric currents in the brain.]

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