How Do Eo and Bo Relate in Maxwell's Equations for a Vacuum?

[SaveFerris]

1. Show that:

electric field E(x,t) = [0, Eo, 0] * f(kx-wt)

magnetic field B(x,t) = [0, 0, Bo] * f(kx-wt)

(where k, w, Eo, Bo are constants) satisfy the Maxwell equations in a vacuum where
charge and current densities are zero.

What relation between k and w must hold for a solution with Bo and Eo not equal to 0? How are Bo and Eo related in this case?


3. The Attempt at a Solution

I have finished the first part of this question proving that the Maxwell equations are solved, but am a little stuck on the second part!

i thought that if kx = wt then the equation would still equal zero, but as it's a function of kx-wt I am not sure this works? if i could do that i thought finding k in terms of w might be the relationship but I am not sure. this would give k = wt/x.

Thank you for any help!

 

[George Jones]

What is, for example,

$$\frac{\partial B_z}{\partial t}?$$