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While seeing the derivations of the Rayleigh Jeans law and the Planck's Law for a Blackbody Radiation, I came across a fact that they assumed that Electromagnetic Radiation inside a cavity would form standing waves only.

Why is it that the blackbody radiations inside the metal box should be a standing wave only in the derivation of Rayleigh Jeans law and Planck's law?

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The boundary conditions for the electric field demand that it is continuous across an interface between two media.

When a wave is incident on a perfect conductor, there is no transmitted E-field - i.e. the electric field is zero inside the metal. This means the sum of the electric fields of the incident and reflected waves must be exactly zero immediately on the other side of the interface.

But the sum of two waves, with equal amplitude but moving in opposite directions is a standing wave, with a node at the metallic boundary.

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