Simple Nature - Light and Matter

i/An impossible wave pattern.

and Maxwell’s equations become

ΦE= 0

ΦB= 0

ΓE=−

∂ΦB

∂t

c^2 ΓB=

∂ΦE

∂t

.

The equation Φ = 0 has already been verified for this type of
wave pattern in example 39 on page 652. Even if you haven’t learned
the techniques from that section, it should be visually plausible that
this field pattern doesn’t diverge or converge on any particular point.

Geometry of the electric and magnetic fields
The equationc^2 ΓB=∂ΦE/∂ttells us that there can be no such
thing as a purely magnetic wave. The wave pattern clearly does have
a nonvanishing circulation around the edge of the surface suggested
in figure g, so there must be an electric flux through the surface.
This magnetic field pattern must be intertwined with an electric
field pattern that fills the same space. There is also no way that the
two sides of the equation could stay synchronized with each other
unless the electric field pattern is also a sine wave, and one that
has the same wavelength, frequency, and velocity. Since the electric
field is making a flux through the indicated surface, it’s plausible
that the electric field vectors lie in a plane perpendicular to that
of the magnetic field vectors. The resulting geometry is shown in
figure h. Further justification for this geometry is given later in this
subsection.

h/The geometry of an electromagnetic wave.

One feature of figure h that is easily justified is that the electric

and magnetic fields are perpendicular not only to each other, but

also to the direction of propagation of the wave. In other words, the

vibration is sideways, like people in a stadium “doing the wave,”

not lengthwise, like the accordion pattern in figure i. (In standard

Section 11.6 Maxwell’s equations 725