MOTION MOUNTAIN

78 2 the description of electromagnetic field evolution
m, q m, q
v
v
0 distance r
F I G U R E 44 Charged particles after a collision.
Challenge 75 ny
Ref. 42
Challenge 76 s
Ref. 43
Page 116
antpropertythatwementionedrightatthestart:thefielditselfcanmove. In particular,
the field can carry energy, linear momentum and angular momentum.
Colliding charged particles
Electromagnetic fields move. A simple experiment clarifies the meaning of motion for
fields: When two charged particles collide, their total momentum is not conserved. Let
us check this.
Imagine two particles of identical mass and identical charge just after a collision, when
they are moving away from one another. The situation is illustrated in Figure 44. Imagine
also that the two masses are large, so that the acceleration due to their electrical
repulsionissmall. Foran observer at the centre of gravity of the two, each particle feels
an acceleration from the electric field of the other. This electric fieldEis given by the
so-calledHeavisideformula
E= q(1−v2 /c 2 )
4πe 0 r 2 . (33)
Inotherwords,thetotalsystemhasavanishing total momentum for this observer.
Take a second observer, moving with respect to the first with velocityv, so that the
first charge will be at rest. Expression (33) leads to two different values for the electric
fields, one at the position of each particle. In other words, the system of the two particles
is not in inertial motion, as we would expect; the total momentum is not conserved for
this observer.The missing momentum is small, but where did it go?
This at first surprising effect has even been put in the form of a theorem by Van Dam
and Wigner. They showed that, for a system of particles interacting at a distance, the total
particle energy–momentum cannot remain constant in all inertial frames.
The total momentum of the system is conserved only because the electromagnetic
field itself also carries some momentum. In short, momentum is conserved in the experiment,butsomeofitiscarriedbythefield.Thepreciseamountdependsontheobserver.
Two colliding charged particles thus show us that electromagnetic fields have momentum.Ifelectromagneticfieldshave
momentum, they are able tostrike objects and to
be struck by them. As we will show below, light is also an electromagnetic field.Thus we
should be able to move objects by shining light on to them. We should even be able to
suspend particles in mid air by shining light on to them from below. Both predictions
are correct, and some experiments will be presented shortly.
Motion Mountain – The Adventure of Physics copyright © Christoph Schiller June 1990–November 2015 free pdf file available at www.motionmountain.net