In what direction does this EM wave transport momentum?
Does this agree with the form of the Maxwell stress tensor
you just deduced?
ANSWER:
If Tij represents the force per unit area acting in the
direction on a surface whose normal is in the
direction, then the diagonal elements are
pressures and T33 is the radiation pressure
on a surface normal to
. In the same way
-T33 represents the the momentum current density
transported by the fields, and is (as expected) in the same
direction as
and is, in fact, equal to
.
This was a tedious problem; it took me all day to get it right. I will be duly impressed if you managed to grind through it successfully. Now you know why we like our plane waves so much, Huygens' principle notwithstanding!