11.7 Electromagnetic properties of materials
Different types of matter have a variety of useful electrical and mag-
netic properties. Some are conductors, and some are insulators.
Some, like iron and nickel, can be magnetized, while others have
useful electrical properties, e.g., dielectrics, discussed qualitatively
in the discussion question on page 614, which allow us to make
capacitors with much higher values of capacitance than would oth-
erwise be possible. We need to organize our knowledge about the
properties that materials can possess, and see whether this knowl-
edge allows us to calculate anything useful with Maxwell’s equations.11.7.1 Conductors
A perfect conductor, such as a superconductor, has no DC elec-
trical resistance. It is not possible to have a static electric field
inside it, because then charges would move in response to that field,
and the motion of the charges would tend to reduce the field, con-
trary to the assumption that the field was static. Things are a little
different at the surface of a perfect conductor than on the interior.
We expect that any net charges that exist on the conductor will
spread out under the influence of their mutual repulsion, and settle
on the surface. As we saw in chapter 10, Gauss’s law requires that
the fields on the two sides of a sheet of charge have|E⊥,1−E⊥,2|
proportional to the surface charge density, and since the field inside
the conductor is zero, we infer that there can be a field on or im-
mediately outside the conductor, with a nonvanishing component
perpendicular to the surface. The component of the field parallel
to the surface must vanish, however, since otherwise it would cause
the charges to move along the surface.
On a hot summer day, the reason the sun feels warm on your
skin is that the oscillating fields of the light waves excite currents
in your skin, and these currents dissipate energy by ohmic heating.
In a perfect conductor, however, this could never happen, because
there is no such thing as ohmic heating. Since electric fields can’t
penetrate a perfect conductor, we also know that an electromag-
netic wave can never pass into one. By conservation of energy, we
know that the wave can’t just vanish, and if the energy can’t be
dissipated as heat, then the only remaining possibility is that all of
the wave’s energy is reflected. This is why metals, which are good
electrical conductors, are also highly reflective. They are notperfect
electrical conductors, however, so they are not perfectly reflective.
The wave enters the conductor, but immediately excites oscillating
currents, and these oscillating currents dissipate the energy both by
ohmic heating and by reradiating the reflected wave. Since the parts
of Maxwell’s equations describing radiation have time derivatives in
them, the efficiency of this reradiation process depends strongly on
frequency. When the frequency is high and the material is a good
conductor, reflection predominates, and is so efficient that the wave734 Chapter 11 Electromagnetism