Interpreting ##\hat{e}_z## in Maxwell's equations

[flintbox]

Hi, I'm trying to interpret a form of Maxwell's equations, but I can't seem to figure out where the term $\^{e}_z$ comes from in the following equation:
$\frac{\partial{\vec{E}_t}}{\partial{z}}+i\frac{\omega}{c}\hat{e}_z\times \vec{B}_t=\vec{\nabla}_tE_z$

 

[Paul Colby]

This is a guess because more background on the source of this equation is needed. My guess is that the problem being worked is assuming a plane wave field dependence?

 

[Korak Biswas]

Will you please clarify the notations? What does $t$ stand for?

 

[nrqed]

Hi, I'm trying to interpret a form of Maxwell's equations, but I can't seem to figure out where the term $\^{e}_z$ comes from in the following equation:
$\frac{\partial{\vec{E}_t}}{\partial{z}}+i\frac{\omega}{c}\hat{e}_z\times \vec{B}_t=\vec{\nabla}_tE_z$

It comes from taking the curl of the B field (here they are assuming a plane wave). But the equation is not completely correct, the term on the rhs does not make any sense.