= Lorenz-gauge potentials for a circularly polarized plane wave
{c}
{title2=$\Phi=0,\quad\mathbf A=\omega^{-2}\partial_t\mathbf E$}
For a transverse monochromatic <electromagnetic wave> with angular <frequency> $\omega\ne0$, $\partial_t^2\mathbf E=-\omega^2\mathbf E$. The displayed <electric potential> and <magnetic vector potential> therefore give $-\nabla\Phi-\partial_t\mathbf A=\mathbf E$. Transversality gives $\nabla\cdot\mathbf A=0$, so the <Lorenz gauge> holds. For $\mathbf E=E_0(\cos\theta,\sin\theta,0)$ and $\theta=\omega t-Kz$, taking a <curl> yields $\mathbf B=(K/\omega)\widehat{\mathbf z}\times\mathbf E$. The vacuum <Maxwell equations> require $K^2=\omega^2/c^2$. The field has <circular polarization>, with $|\mathbf B|=|\mathbf E|/c$ and perpendicular electric and magnetic directions.
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