= Plane electromagnetic wave
{title2=$\mathbf B=\widehat{\mathbf k}\times\mathbf E/c$}
{wiki}
A monochromatic vacuum <plane electromagnetic wave> has phase $\mathbf k\cdot\mathbf r-\omega t$, where $\mathbf k$ is the <wavevector>, $\omega>0$ the <angular frequency>, and $\omega=c|\mathbf k|$. Its field amplitudes obey $\mathbf k\cdot\mathbf E_0=\mathbf k\cdot\mathbf B_0=0$ and $\mathbf B_0=\mathbf k\times\mathbf E_0/\omega$.
For the <linear polarization> and orientation in the visualization, choose a right-handed <Cartesian coordinate system> and put
$$
\mathbf E(z,t)=E_0\cos(kz-\omega t)\widehat{\mathbf x},\qquad
\mathbf B(z,t)=\frac{E_0}{c}\cos(kz-\omega t)\widehat{\mathbf y},\qquad
k>0,\quad\omega=ck.
$$
Constant phase means $z=ct+\text{constant}$, so propagation is along $+z$. The <cross product> $\widehat{\mathbf x}\times\widehat{\mathbf y}=\widehat{\mathbf z}$ fixes the positive <Poynting vector>. Both fields reverse together every half-period and are in phase. Reversing the propagation direction with the same electric orientation reverses the magnetic orientation.
These fields are spatially uniform across every transverse plane. An infinite <plane electromagnetic wave> is an idealization with infinite total <electromagnetic energy>; it is useful as a local approximation and as a building block for <superposition>. For <frequency> $f=100\,\mathrm{MHz}$, $\omega=2\pi f$ and <wavelength> $\lambda=c/f\simeq3.00\,\mathrm m$, independently of $E_0$.
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