MOTION MOUNTAIN

Vol. IV, page 231
Chapter 2
THE DESCRIPTION OF
ELECTROMAGNETIC FIELD
EVOLUTION
Electric and magnetic fields change: simply said, they move. How
xactly does this happen? In the 1860s, James Clerk Maxwell* collected all
xperimental knowledge he could find, and deduced the precise description of
electromagnetic field motion. Twenty years later, Heaviside and Hertz extracted the
main points of Maxwell ideas, calling their summaryMaxwell’stheoryoftheelectromagneticfield.
The motion of the electromagnetic field is described by a set of evolution equations.
In the relativistic description, the set consists of two equations, in the non-relativistic
case of four equations. All observations of classical electrodynamics follow from these
equations. In fact, if quantum effects are properly taken into account,all electromagnetic
effects of nature are described.
The first field equation of electrodynamics
The first relativistic field equation of electrodynamics is the precise statement that electromagneticfieldsoriginateat
charges,andnowhereelse.Itcan variously be written**
dF=jμ 0 or
∇⋅E= ρ ε 0
and
∇×B− 1 c 2 ∂E
∂t =μ 0j . (28)
*JamesClerkMaxwell(b.1831Edinburgh,d.1879Cambridge) isoneofthemostimportant andinfluential
physicists.Hefoundedelectromagnetismbytheoretically unifying electricityandmagnetism,asdescribed
inthischapter.Hisworkonthermodynamicsformsthesecondpillar ofhisactivity.Inaddition,hestudied
the theory of colours and developed the colour triangle; he was one of the first people to make a colour
photograph. He is regarded by many as the greatest physicist ever. Both ‘Clerk’ and ‘Maxwell’ were his
familynames.
** There is a certain freedom in writing the equations, becausedifferent authors absorb different combinations
of the constantscandμ 0 into the definitions of the quantitiesF,Aandj.The one given here is the
most common version. The equations can be generalized to cases where the charges are not surrounded
by vacuum, but located inside matter. We will not explore these situations in our walk because,as we will
discoverlater on,theseeminglyspecialcaseofvacuuminfactdescribesall ofnature.
Motion Mountain – The Adventure of Physics copyright © Christoph Schiller June 1990–November 2015 free pdf file available at www.motionmountain.net