= Solution
Using $\nabla\times\mathbf E=-\partial_t\mathbf B$ directly with the specified <plane wave> gives
$$
-ik\hat{\mathbf x}\times\mathbf E_0=-i\omega\mathbf B_0,
\qquad
\boxed{\mathbf B_0=\frac{E_0}{c}\hat{\mathbf z}.}
$$
The <electric field>, <magnetic flux density> and propagation direction form a right-handed triad, and for a nonzero <wave amplitude>
$$
\boxed{\frac{|\mathbf E_0|}{|\mathbf B_0|}=c.}
$$
The <electric field> and <magnetic field> have the same <wave phase> in vacuum.
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