= Solution
In empty space the fields are divergence-free. Taking the curl of <Faraday's law> and using
$$
\nabla\times(\nabla\times E)=\nabla(\nabla\cdot E)-\nabla^2E
$$
gives
$$
\nabla^2E-\mu_0\epsilon_0\frac{\partial^2E}{\partial t^2}=0.
$$
The same calculation, starting from the <Ampère-Maxwell equation>, gives the corresponding equation for $B$. Thus every component satisfies the <electromagnetic wave equation> with speed
$$
c=\frac1{\sqrt{\mu_0\epsilon_0}}
\simeq3.0\times10^8\ \mathrm{m\,s^{-1}}.
$$
Its agreement with the measured speed of light identifies light as an <electromagnetic wave>.
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