MOTION MOUNTAIN

234 6 classical electrodynamics
Challenge 238 s
Challenge 239 d
of a drop of water?
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When a voltage is applied to a resistor, how long does it take until the end value of the
current, given by Ohm’s ‘law’, is reached? The first to answer this question was Paul
Drude* in the years around 1900. He reasoned that when the current is switched on,
the speedvof an electron increases asv=(eE/m)t, whereEis the electrical field,e
the charge andmthe mass of the electron. Drude’s model assumes that the increase of
electron speed stops when the electron hits an atom, loses its energy and begins to be
accelerated again. Drude deduced that the average timeτup to the collision is related to
the specific resistance by
ρ= E j =E env =2m τe 2 n , (92)
withnbeing the electron number density.The right side does not depend onEany more;
it is a constant. Drude had thus explained Ohm’s ‘law’U=RI (orE=jρ) from material
properties, by assuming that resistance is due to moving electrons that continuouslycollideandspeedupagain.Insertingnumbers
forcopper(n=8.5⋅10 28 /m −3 and
ρ=0.16⋅10 −7 Ωm), we get a timeτ=51 ps. This time is so short that the switch-on
processcanusually beneglected.
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Does it make sense to write Maxwell’s equations in vacuum? Both electrical and magneticfieldsrequirechargesinordertobemeasured.Butin
vacuum there are no charges
at all. And fields are defined by using infinitesimally small test charges. But, as wementioned
already, infinitesimally small charges do not exist. In fact, only quantum theory
solves this issue. Are you able to imagine how?
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We have seen that in cases ofmid-sizedfields,classicalelectrodynamicsisagoodapproximation,
despite charge discreteness.One practical systemmakes use ofdiscrete charge
but can nevertheless be described in many of its aspects with classical electrodynamics.
It merits a separate discussion: our brain.
*PaulKarlLudwigDrude(b.1863Braunschweig,d.1906Berlin),physicist,predictedwithhiselectrongas
model of metals – that the ratio between the thermal conductivity and the electric conductivity at a given
temperature should be the same for all metals; this is roughly correct. Drude also conceived ellipsometry
andintroducedcasthesymbol forthespeedoflight.
Motion Mountain – The Adventure of Physics copyright © Christoph Schiller June 1990–November 2015 free pdf file available at www.motionmountain.net