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Power for a blackbody radiation

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If a blackbody is in equilibrium with the surrounding electromagnetic field, the power emitted by the surface of the blackbody will be related to the energy density of the electromagnetic field by [itex]P=\frac{cu}{4}[/itex]. Try as I might, I haven't found a good derivation for this equation (the Hyperphysics one has several problems). I thought that it shouldn't be too hard to derive, but playing with Poynting's theorem led me nowhere, so now I humbly turn to physicsforums for help.

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