Technology

# How mighty would a magnetic field must clean be to waste you?

There’s a huge silly memoir in Futurama, the cartoon comedy level to, a pair of dismay film for robots.  In the film, a planet of robots is drastically very a lot surprised by a huge “non-metal being” (a monsterified human).  The human is finally defeated by a makeshift spear, which prompts the robot long-established to voice:

“Comical, isn’t it?  The human used to be impervious to our most extremely effective magnetic fields, but within the discontinuance he succumbed to a harmless sharpened stick.”

The silly memoir, of route, is that the human body could presumably perhaps presumably also seem necessary extra fragile than a metal machine, but to a robot our ability to withstand mighty magnetic fields would be contend with invincibility.

Nevertheless this got me pondering: how mighty would a magnetic field must clean be sooner than it killed a human?

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Now not like a pc laborious force, the human body doesn’t genuinely blueprint expend of any magnetic states — there’s nowhere within the body where main data is kept as a static magnetization.  Which ability that that there’s not any such thing as a be troubled that an external magnetic field could presumably perhaps presumably also wipe out main data, the methodology that it could presumably perhaps presumably for, scream, a bank card or a laborious force.  So, let’s scream, it’s completely protected for a human (with out a steel in their body) to believe an MRI scan, by which the magnetic fields attain a complete lot of Tesla, which is about $10^5$ times stronger than the long-established magnetic fields produced by the Earth.

A computer laborious force retail outlets data in a sequence of magnetically aligned segments.

Nevertheless even with none magnetic data to erase, a mighty sufficient magnetic field will should believe some fabricate.  In general talking, magnetic fields develop forces that push on spirited charges.  And the body has a great deal of spirited charges interior it: most seriously, the electrons that orbit around atomic nuclei.

As I’ll level to below, a fleshy sufficient magnetic field would push strongly sufficient on these orbiting electrons to fully exchange the form of atoms, and this is in a position to discontinuance the chemical bonds that give our body its feature and its structure integrity.

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## What atoms stare contend with

Sooner than I continue, let me briefly recap the cartoon protest of the structure of the atom, and be taught the map in which to mediate about it.  An atom is the certain voice of as a minimum one electron to a positively charged nucleus.  The electrical appeal between the electron and the nucleus pulls the electron inward, while the foundations of quantum mechanics forestall the electron from collapsing down fully onto the nucleus.

In this case, the relevant “rule of quantum mechanics”  is the Heisenberg uncertainty realizing, which says that in case you confine an electron to a quantity of size $r$, then the electron’s momentum must become as a minimum as fleshy as $p sim hbar/r$.  The corresponding kinetic vitality is $p^2/2m sim hbar^2/mr^2$, which implies that the extra tightly you are trying to restrict an electron, the extra kinetic vitality it gets.  [Here, $hbar$ is Planck’s constant, and $m$ is the electron mass\$.]  This kinetic vitality is often called the “quantum confinement vitality.”

In a stable atom, the quantum confinement vitality, which favors having a fleshy electron orbit, is balanced towards the electrical appeal between the electron and the nucleus, which attracts the electron inward and has vitality $sim -e^2/epsilon_0 r$. [Here $e$ is the electron charge and $epsilon_0$ is the vacuum permittivity].  In the balanced voice, these two energies are nearly equal to every varied, which implies that $r sim hbar^2 epsilon_0/me^2 sim 10^{-10}$ meters.

Here’s the rapid and dirty methodology to identify the answer to the attach an relate to: “how huge is an atom?”.

The associated speed of the electron in its orbit is $v sim p/m sim hbar/m r$, which is about $10^6$ m/s (or a pair of million miles per hour).  The sparkling force between the electron and the nucleus is about $F_E sim -e^2/epsilon_0 r^2 sim m^2 e^6/hbar^4 epsilon_0^3$, which involves ~100 nanoNewtons.

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## Who pulls extra tough: the nucleus, or the magnetic field?

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

They pull them into round orbits, contend with this:

The force with which a magnetic field pulls on a price is given by $F_B sim e v B$, where $B$ is the energy of the field.  For an electron spirited at a million miles per hour, as within the within of an atom, this works out to be about 1 picoNewton per Tesla of magnetic field.

Now we are in a position to win into narrative the next attach an relate to.  Who pulls extra tough on the electron: the nucleus, or the external magnetic field?

The answer, of route, is dependent on the energy of the magnetic field.  Having a stare at the numbers above, one can salvage out about that for factual about any realistic subject, the force provided by the magnetic field is necessary necessary smaller than the force from the nucleus, in divulge that the magnetic field essentially does nothing to perturb the electrons in their atomic orbitals.  On the replacement hand, if the magnetic field were to procure mighty sufficient, then the force it produces would be sufficient to beginning drastically bending the electron trajectories, and the form of the electron orbits would procure distorted.

Atmosphere $F_B > F_E” src=”https://s0.wp.com/latex.php?latex=F_B+>+F_E&bg=ffffff&fg=333333&s=0&c=20201002″> from above affords the estimate that this extra or much less distortion happens most efficient when  Tesla.  Provided that the strongest static magnetic fields we are in a position to develop artificially are most efficient about 100 Tesla, it’s doubtlessly protected to voice that you just should not going to ride this any time rapidly.  Merely don’t stir too end to any magnetars.

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## Distorted atoms

Nevertheless supposing that you just did stir accurate into a magnetic field of 100,000 Tesla, what would happen?

The mighty magnetic forces would beginning to squeeze the electron orbits for your complete atoms for your body.  The pinnacle result would stare something contend with this:

So, let’s scream, an initially spherical hydrogen atom (on the left) would believe its orbit squeezed within the directions perpendicular to the magnetic field, and would discontinuance up as a replace having a stare contend with the image on the magnificent.  This squeezing would procure an increasing selection of pronounced as the field is turned up, in divulge that every person the atoms for your body would walk from roughly spherical to “cigar-formed,” and then to “needle-formed”.

Needless to voice, the molecules that blueprint up your body are most efficient ready to retain collectively when they are made of long-established formed atoms, and not needle-formed atoms.  So as soon as the atomic orbitals got sufficiently distorted, their chemistry would exchange dramatically and these molecules would beginning to collapse.  And your body would presumably be diminished to a dusty, incoherent mess (artist’s idea).

Nevertheless for those of us who keep far off from neutron stars, it’s far presumably protected to win that death by magnetic field-prompted disintegration is ravishing not going.  So it’s good to perhaps presumably perhaps presumably continue lording your invincibility over your robot coworkers.

UPDATE:

A vary of of us believe pointed out, precisely, that in case you genuinely subjected a body to mighty magnetic fields, something would doubtlessly walk harmful biologically far sooner than the field got so ludicrously fleshy fields as 100,000 Tesla.  As an illustration, the motion of ions through ion channels, which is crucial for nerve firing, could presumably perhaps presumably even be affected.  Sadly, I doubtlessly don’t know sufficient biology to give you a confident speculation about what, exactly, could presumably perhaps presumably also walk harmful.

There is one other doable location, even though, that can presumably perhaps presumably also merely be understood at the stage of cartoon photos of atoms.  An electron orbiting around a nucleus is, in a worn sense, contend with a tiny round electrical recent.  Consequently, the electron creates its possess little magnetic field, with a “north pole” and “south pole” particular by the course of its orbital motion.   Admire so:

Typically, these little electron orbits all level in additional or much less random directions.  Nevertheless within the presence of a mighty sufficient external magnetic field, the electron orbit will are inclined to procure aligned in divulge that its “north pole” factors within the identical course as the magnetic field.  By my estimate, this is in a position to happen at a number of hundred Tesla.

In varied phrases, a number of hundred Tesla is what it could presumably perhaps presumably win to strongly magnetize the human body.  This isn’t deformation of atoms, factual alignment of their orbits in a fixed course.

Once the atomic orbits were all pointed within the identical course, the chemistry of atomic interactions could presumably perhaps presumably also beginning to be affected.  As an illustration, some chemical processes could presumably perhaps presumably also beginning going down at varied rates when the atoms are “aspect by aspect” as when compared with when they are “front to relief.”  I will take into account this delicate alteration of chemical reaction rates having a huge fabricate over a long sufficient time.

Maybe here’s why, as commenter cornholio pointed out below, a fruit flee that grows up in a ~ 10 Tesla field looks to procure mutated.

## Footnote

I genuinely had been assuming, of route, that we are talking most efficient about static magnetic fields.  Subjecting somebody to a magnetic field that changes posthaste in time is the identical element as bombarding them with radiation.  And it’s far in no map complex to microwave somebody 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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