Regarding the Magnetic Field Associated with A Wave

1. Jun 5, 2012

AMG56

1. The problem statement, all variables and given/known data

An electromagnetic wave propagating in free space in the x-axis direction between two planes z=0 and z=a has an electric field given by

$$\vec{E} = E_0 \mathrm{sin}(\frac{\pi z}{a}) \mathrm{cos} (\omega t -kx) \vec u_y$$

Is this wave a plane wave? Based on the answer, compute the magnetic field associated to this wave.

2. Relevant equations

$$\Delta \vec{E} - \mu_0\epsilon_0 \frac{\delta^2E}{\delta t^2} =0$$

3. The attempt at a solution

My problem comes from that the wave is not a plane wave since it's motion is defined in two directions. After starting with the wave equation I get stuck since I cannot make any substitutions into the equation. I really just need help getting started on where to go from here, any assistance would be much appreciated.