Discussion question A.Discussion question B.Discussion questions C and
D.a single thing traveling in a single direction, whereas no such as-
sumption was made in arguing for theE×Bform. For instance, if
two light beams of equal strength are traveling through one another,
going in opposite directions, their total momentum is zero, which is
consistent with theE×Bform, but not withU/c.
Some examples were given in chapter 3 of situations where it
actually matters that light has momentum. Figure q shows the first
confirmation of this fact in the laboratory.Angular momentum of light waves
For completeness, we note that since light carries momentum, it
must also be possible for it to have angular momentum. If you’ve
studied chemistry, here’s an example of why this can be important.
You know that electrons in atoms can exist in states labeled s, p,
d, f, and so on. What you might not have realized is that these
are angular momentum labels. The s state, for example, has zero
angular momentum. If light didn’t have angular momentum, then,
for example, it wouldn’t be possible for a hydrogen atom in a p state
to change to the lower-energy s state by emitting light. Conservation
of angular momentum requires that the light wave carry away all
the angular momentum originally possessed by the electron in the
p state, since in the s state it has none.
Discussion Questions
A Positive charges 1 and 2 are moving as shown. What electric and
magnetic forces do they exert on each other? What does this imply for
conservation of momentum?
B 1. The figure shows a line of charges moving to the right, creating
a currentI. An Amperian surface in the form of a disk has been superim-`
posed. Use Maxwell’s equations to find the fieldBat point P.
- A tiny gap is chopped out of the line of charge. What happens when
this gap is directly underneath the point P?
C The diagram shows an electric field pattern frozen at one moment in
time. Let’s imagine that it’s the electric part of an electromagnetic wave.
Consider four possible directions in which it could be propagating: left,
right, up, and down. Determine whether each of these is consistent with
Maxwell’s equations. If so, infer the direction of the magnetic field.
D What happens if we use Maxwell’s equations to analyze the behavior
of the wave in a frame of reference moving along with the wave?
Section 11.6 Maxwell’s equations 733