MOTION MOUNTAIN

226 5 electromagnetic effects
Challenge 223 s
Page 46
Challenge 224 s
Vol. I, page 340
Challenge 225 s
Challenge 226 s
Challenge 227 s
Ref. 198
Challenge 228 e
Ref. 199
Can you guess whatNis physically? (Hint: think about quantum theory.)
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Faraday discovered, as told above, how to change magnetism into electricity, knowing
that electricity could be transformed into magnetism.The issue is subtle. Faraday’s law
is not the dual of Ampère’s, as that would imply the use of magnetic monopoles; neither
is it the reciprocal, as that would imply the displacement current. But he was looking for
a link and he found a way to relate the two observations – in a novel way, as it turned
out.
Faraday also discovered how to transform electricity into light and into chemistry. He
then tried to change gravitation into electricity. But he was not successful. Why not?
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At high altitudes (60 km to1000 km) above the Earth, gases are partly or completely
ionized; no atom is neutral. One speaks of the ionosphere, as space is full of positive
ions and free electrons. Even though both charges appear in exactly the same number, a
satellite moving through the ionosphere acquires a negative charge. Why? How does the
charging stop?
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A capacitor of capacityCis charged with a voltageU. The stored electrostatic energy is
E=CU 2 /2. The capacitor is then detached from the power supply and branched on to
an empty capacitor of the same capacity. After a while, the voltage obviously drops to
U/2. However, the stored energy now isC(U/2) 2 , which is half the original value. Where
did the energy go?
How can you give somebody an electric shock using a4.5 V battery and some wire?
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An old puzzle about electricity results from the equivalence of mass and energy. It is
known from experiments that the sizedof electrons is surely smaller than10 −22 m. This
means that the electric field surrounding it has an energy contentEgiven by at least
E nergy = 1 2 ε 0∫E 2 ∞
lectric field dV=1 2 ε 0∫ ( 1 2
q
d 4πε o r 2) 4πr 2 dr
= q2 1
>1.2 µJ . (88)
8πε o d
On the other hand, the mass of an electron, usually given as511 keV/c 2 , corresponds
to an energy of only82 fJ, ten million times less than the value just calculated. In other
words, classical electrodynamics has considerable difficulty describing electrons.
In fact, a consistent description of charged point particles within classical electrodynamicsisimpossible.
Thistopicreceives only a rare – but then often passionate – interest
nowadays, because the puzzle is solved in a different way in the quantum parts of ourad-
Motion Mountain – The Adventure of Physics copyright © Christoph Schiller June 1990–November 2015 free pdf file available at www.motionmountain.net