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Lorentz
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Lorentz
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Lorentz Forces and Other Magnetic Effects
There are several means by which magnetic fields can interact with living beings: Faraday currents, Lorentz forces, magneto-mechanical effects and quantum spin interaction. Faraday currents produced by the rapidly changing fields of electromagnets were discussed in the previous section. For permanent magnets, Lorentz and other forces may be more important and they are explored below.
Lorentz Forces: When an atom gains or
loses an electron in a
chemical reaction, it becomes electrically charged and is called an
ion.
If you dissolve table salt in water, sodium and chlorine atoms separate
to
become Na+ and Cl- ions. In living tissue, sodium
and
potassium ions are very common. When a charged particle moves in a
magnetic
field, a force pushes the particle at a right angle to its motion. This
is
called a Lorentz force and it's magnitude is given by F
= qvB, where force equals
charge times
velocity times
magnetic field. It seems like such
forces
should be important players in biology and many websites that sell
magnets proudly allude to
Lorentz forces. Unfortunately, when
you actually perform the calculation, the magnitudes of such forces are
so
pitifully tiny that it's hard to believe they are relevant. This is one
reason
so many people in the scientific community think permanent magnets are
a
health fraud. Let's take a closer look and you can make up your own
mind.
First, we have to decide how an ion might be in motion
inside your body.
It could be carried by your blood and a velocity of 1 cm/sec might
apply
to smaller vessels in your arms or legs. At your heart, the peak flow
rate
in the aorta may be as high as 63 cm/sec. Outside of the circulatory
system,
things don't flow as fast. What about movements when you flex a
muscle?
If a magnet were banded to your arm and if your biceps were of
Terminator
quality, you might be able to flex centimeter movements in a tenth of a
second.
This would move cells and ions at 10 cm/sec. Let's do a calculation
with
a velocity of 1 cm/sec remembering that in some circumstances it could
be
ten or more times higher. Second, we can consider a sodium ion with a
positive
charge of one missing electron. And third, we can choose the magnetic
field
strength to be 240 gauss. This is the strength of a typical rare earth
magnet
at a distance of 1 inch from the pole face. Using this information,
Lorentz
calculations are summarized in the table below. I include the details
so
you can be assured that I am presenting the facts without any fiction.
If
you don't have a technical background, skip over the table for a
discussion
of the relative magnitude of the forces.
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Lorentz Force on a Blood Ion (Lorentz Force) = (Charge)(Velocity)(Gauss) = qvB |
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Lorentz Work Across a Vessel (Work) = (Increase in Energy) = (Force)(Distance) = FD |
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Thermal Energy of a Blood Ion (Thermal Energy) = (3/2)(k)(Temperature) = 3/2kT |
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Electric Field Balance (Electric Force) = (Charge)(Electric Field) = qE |
For the Lorentz calculation, we have assumed a sodium ion moving with blood under the influence of a rare earth magnet. The Lorentz force is 3.84x10-23 newton, where newton is a metric unit similar to a pound. Scientific notation is used and it means 3.84 divided by ten 23 times. It is a very small force. Of course, the sodium ion is also small, so we must compare forces to get an idea of its relevance. One approach is to assume the Lorentz force pushes the ion halfway across the blood vessel or about 1 mm. In so doing, work will be performed which will raise the energy level of the ion. How does this increase compare to the thermal energy due to temperature vibrations? Well, as you can see from the table, the thermal energy is 167,000 times greater than the Lorentz contribution. Based on this result, it would appear that any chemical reaction would be dominated by temperature alone, making the Lorentz force insignificant.
Another calculation can further test this conclusion. Lorentz forces move positive charges one way and negative charges the other. This would create a small electric field across the blood vessel. A balance would be reached when the electric field was strong enough to counter the Lorentz forces. Refering to the table above, balance occurs at an electric field strength of 0.00024 volts per meter. Of course, a blood vessel is much smaller than a meter, so across a 1 mm width, the voltage difference would be a mere 0.24 microvolts. Compare this to the voltage difference across a human cell membrane which is typically 80 millivolts. The membrane potential is 333,000 times greater than the Lorentz voltage. Again, we must conclude that Lorentz forces cannot play a significant role under our assumed conditions. If the velocity were higher or the magnetic field greater, more of an effect would be expected. But remember, we are orders of magnitude away from matching the other forces and energies. You can now see why so many physical scientists are skeptical of magnetic health hype.
To
counter this pessimism,
let's take a look at some unusual
creatures. Sharks, skates and rays are able to use the Earth's magnetic
field
for guidance. They accomplish this feat with special organs in their
heads
called "Ampullae of Lorenzini." Interesting name, don't you think? The
ampullae
are long, jelly-filled canals that use Lorentz forces to separate ions
and
create low level electric fields. These are very specialized sensors
capable
of detecting less than 1 microvolt. As the fish swim across the Earth's
magnetic
field lines, the microvoltages in their sensors change, allowing them
to
tell north/south from east/west. Sharks actually do what we just
calculated
to be impractical. Let's compare our blood flow assumptions to the
environment
of the shark. For blood flow, we assumed a velocity of 1 cm/sec and a
field
of 240 gauss. For a shark, perhaps we could estimate a swimming speed
of
1 m/sec in the Earth's field of 1/2 gauss. Comparing these numbers, the
blood
flow Lorentz forces would actually be 4.8 times greater than the shark
Lorentz
forces. At faster blood speeds, the situation could be 48 times
more
favorable. So if the biology is arranged just right, magnetic Lorentz
forces
can make a difference. Fancy calculations and dumb sharks contrast the
opinions
in the debate over permanent magnets and health. For a discussion of a
possible mechanism whereby Lorentz forces could play a role at cell
membranes, see the next chapter.
Magneto-Mechanical Effects: Nature's building blocks can be divided into three magnetic categories: ferromagnetic, diamagnetic and paramagnetic. Ferromagnetic material usually contains iron that may be magnetized and strongly attracted by magnets, including the Earth's magnetic poles. Magnetite is a common ferromagnetic substance which may be found in living organisms. Magnetotactic bacteria contain large amounts of magnetite with up to 2% of their dry mass as iron. The magnetite is arranged in chains of 20-30 single magnetic domain crystals which allow these bacteria to sense both the north/south and up/down components of the Earth's field. The bacteria tend to migrate in the north/south directions with strains in the northern hemisphere preferring north and southern strains preferring south. Although magnetite is present at trace levels in humans, organs that actually utilize magnetite have never been found in you or me.
Most material is diamagnetic or
paramagnetic which means it
is very weakly repulsed or attracted by magnets. Hemoglobin is
diamagnetic
and therefore very weakly repulsed by a magnetic pole. The few iron
atoms
in hemoglobin are individually attracted to a magnet but the
overall
effect simply reduces hemoglobin's diamagnetism. Some macro-molecules
are
very asymmetric, both physically and magnetically. Rhodospin is a
photo-pigment
in the retinal rods of eyes that exhibits diamagnetic asymmetry. That
means
it responds to magnetic forces in an unbalanced fashion. When placed in
a
static magnetic field, rhodospin turns to minimize the diamagnetic
stress.
In a 1 tesla field (10,000 gauss), it will rotate a full 90o
in
four seconds. Of course, that's quite a large field and four seconds is
a
long time in the world of molecules. Again, we are faced with the
dilemma
of a real effect that is real weak.
Quantum Spin Interaction: Electrons have a magnetic characteristic called spin. Loosely speaking, they are like little electromagnets. If they spin one way, the north magnetic pole is up. If the spin the other way, the pole is down. As a pair of electrons, the spins are usually opposite and their little magnets cancel one another. When they are unpaired, this results in diamagnetic and paramagnetic properties. When chemicals react, electrons are shared or traded. A strong static magnetic field can affect the speed of such reactions. In special cases, this can affect the outcome. Evidence that such quantum effects are relevant to biological processes is very slim. The most discussed candidates for such effects are chemical reactions that involve oxygen plus iron and have an intermediate stage with unpaired electrons. They include the enzymes cytochrome P450, lipoxygenase and cyclo-oxygenase. There is no proof that these enzymes are affected by magnetics in the real world. It is just theory. When it comes to magnetism and health, there is plenty of room for opinion.
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