362 Week 10: Maxwell’s Equations and Light
to suggest that the power that appears as heat in a resistor is actuallyelectromagnetic
energy that flows in through the sides of the resistor, quite contrary to at leastmynaive
expectations. But it gets the answers we obtained other ways precisely correct – it is
difficult to argue with the conclusion.
The electromagnetic field doesn’t just carry energy – it carriesmomentum^105. If you
recall our arguments way back when we discussed the failure of Newton’s Third Law,
we knew even then that it must be so – the missing momentum has to gosomeplaceor
momentum violation would be ubiquitous in electromagnetism – but now we have to run
it down.
This is actually rather tricky. It isn’t easy to derive the momentum carried by the
electromagnetic field, because it has no mass. The easiest way to see what it must be is
to examine the net force exerted on a point charge in an electromagnetic field. We’ll do
this (and define the associatedradiation pressurein the next section.10.4: Radiation Pressure and Momentum
There are two arguments that make it comparatively simple to see that an electromag-
netic wave must exert a force on charged matter that it strikes ata surface. Let’s take
the simplest one first – an electromagnetic wave incident on the surface of a perfect
conductor at right angles.B (out)
E
E I (surface)
F F
Figure 142: An electromagnetic wave incident on a conducting surface penetrates a short distance
into the conductor, inducing asurface currentin the direction of the electric field at the surface.
Although it is beyond the scope of this course to treat waves incident on conductors, it
is a True Fact(tm) that while conductors screen theirbulkinterior from electromagnetic
fields (including electromagnetic radiation) they do not do thisinstantlyat the surface.
Just as static fields build up a static surface charge density that cancels the field on the
interior that is afew atoms thick, time varying fields penetrate a small distance into
a conductor (called theskin depth) before being cancelled by a time-varying charge-
current distribution confined to the surface. The skin depth depends on the frequency of
the wave and the conductivity of the material (getting smaller as either one gets larger)
but is usually at least a few atoms thick (and can be centimeters thickat very low
frequencies such as that of household current).
In figure 142 an electromagnetic wave is incident at right angles on a conducting surface.
The wave penetrates a short (grey-shaded) distance into the conductor before being
attenuated, and within this distance the electric field pushes asurface current in the(^105) And often angular momentum as well, but that is beyond the scope of this course.