MOTION MOUNTAIN

electromagnetic effects and challenges 225
Challenge 221 e
Challenge 222 s
Ref. 197
This connection is also used to make fractured bones heal more rapidly: by applying
pulsed magnetic fields to a broken bone, the healing is stimulated and accelerated. (Static
magnetic fields obviously do not work for this aim.) Also teeth are piezoelectric, and the
effect plays also a role in their growth.
∗∗
In shops, one can buy piezoelectric devices – similar to a gas lighter – that are applied to
mosquito bites and are said to reduce itching and even swelling. (Some product names
are ‘zanza click’ and ‘skeeter click’) Can these claims be true?
∗∗
A team of camera men in the middle of the Sahara were using battery-driven electrical
equipment to make sound recordings. Whenever the microphone cable was a few tens
of metres long, they also heard a50 Hz power supply noise, even though the next power
supply was hundreds of kilometres away. An investigation revealed that the high voltage
lines in Europe lose a considerable amount of power by irradiation; these50 Hz waves
are reflected by the ionosphere around the Earth and thus can disturb recording in the
middle of the desert. Can you estimate whether this observation implies that living directlynearahigh
voltage line is dangerous?
∗∗
When solar plasma storms are seen on the Sun, astronomers first phone the electricity
company.They know that about 24 to 48 hours later, the charged particles ejected by the
storms will arrive on Earth, making the magnetic field on the surface fluctuate. Since
power grids often have closed loops of several thousands of kilometres, additional electric
currents are induced, which can make transformers in the grid overheat and then
switch off. Other transformers then have to take over the additional power, which can
lead to their overheating, etc. On several occasions in the past, millions of people have
been left without electrical power due to solar storms. Today, the electricity companies
avoid the problems by disconnecting the various grid sections, by avoiding large loops,
by reducing the supply voltage to avoid saturation of the transformers and by disallowing
load transfer from failed circuits to others.
∗∗
If the electric field is described as a sum of components of different frequencies, its socalledFouriercomponents,theamplitudes
aregiven by
̂ E(k,t)=
1
(2π) 3 /2 ∫E(x,t)e−ikx d 3 x (86)
and similarly for the magnetic field. It then turns out that a Lorentz invariant quantity
N, describing the energy per circular frequencyω, can be defined:
N= 1 +|B(k,t)| 2
8π ∫|E(k,t)|2 d 3 k . (87)
c|k|
Motion Mountain – The Adventure of Physics copyright © Christoph Schiller June 1990–November 2015 free pdf file available at www.motionmountain.net