In particular, calculate
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!