Taking the curl of Faraday's law and substituting Ampère–Maxwell gives a second-order PDE whose solutions propagate at v = 1/√(μ₀ε₀).
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Flick one end of a rope and a bump runs along it. This says the electric field does the same through empty space, and the speed of the bump comes out as 1/√(μ₀ε₀). That's the speed of light.
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