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While going through the proof of the transverse nature of electromagnetic waves using gauss' law for electricity, I encountered a statement that I couldn't comprehend.

They used an argument that since the wave has a finite wavelength, it could not be propagated by a UNIFORM electric field. But why?

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    $\begingroup$ Could you add the full quote from the reference and include title & author? $\endgroup$ – Kyle Kanos Jan 8 '16 at 11:30
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A uniform field will have no change in its magnitude or direction.

Since there is no change in magnitude, the wave will essentially be a straight line on the graph. This the wavelength will be infinite.

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