MOTION MOUNTAIN

Chapter 6
SUMMARY AND LIMITS OF
CLASSICAL ELECTRODYNAMICS
Ref. 39
All of classical electrodynamics can be summarized in three principles. Every
dventurer should know them, because they will help us later on, when we
pproach the top of Motion Mountain. We will discover that we can arrive at the
top only if we express things as simply as possible.The three principles of classical electrodynamicsare:
⊳Electricchargesexertforcesonothercharges;forchargesatrest,theforce
fallsoffastheinverse square of the distance.* Equivalently, charges are surroundedbyanelectromagneticfield.
⊳Electricchargesareconserved.
⊳ Charges move more slowly than light. Equivalently, all charged particles
have mass.
From these three principles we can deduce all of electrodynamics. Electrodynamics is
thus built on the definition of charge, the conservation of charge, and the invariance of
the speed of light. In particular, we can deduce the followingbasicstatements:
— The electromagnetic field is a physical observable, as shown e.g. by compass needles.
— The sources of the electromagnetic field are the (moving) charges, as shown by amber,
lodestone or mobile phones.
— The electromagnetic field changes the motion of electrically charged objects via the
Lorentz expression as shown, for example, by electric motors.
— The electromagnetic field can exist in empty space and moves in it as a wave, as
shown, for example, by the light from the stars.
— The electromagnetic field behaves like a continuous quantity and is described by
Maxwell’s evolution equations, as shown, for example, by mobile phones and electrictoothbrushes.
Moreprecisely,themotionoftheelectricfieldEandofthemagneticfieldBisdescribed
bytheLagrangian density
L= ε 0
2 E2 − 1 B 2 . (89)
2μ 0
* Quantum theory will show that this principle, Coulomb’s ‘law’, can be rephrased as: electric charges at
restemit virtual photons with aconstant averagerate.
Motion Mountain – The Adventure of Physics copyright © Christoph Schiller June 1990–November 2015 free pdf file available at www.motionmountain.net