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\sect{Radiation from 1D balckbody fiber}
Given an optic fiber with length ${L}$ and it's section area is
${A}$. The fiber is in thermic equilibrium in temperature ${T}$.
Assume the fiber is a one dimensional medium for the electromagnetic
field (relate to the magnetic radiation as a photon gas).
\begin {itemize}
\item[(a)]
What is the condition (on temperature)so the one dimensional
proximity will be valid?
\item[(b)]
What is the electromagnetic energy density per length unit?
\item[(c)]
What is the radiation pressure on the fiber edges?
\item[(d)]
Assuming that the radiation can emit from the boundary of the fiber,
what is the emitting radiation flow (energy per time unit)?
\item[(e)]
What is the spectral distribution ${J\left(w\right)}$ of the
emitting radiation flow?
\item[(f)]
What is the entropy and what is the heat capacity of the system?
\end {itemize}
Given:
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\[\int_{0}^{\infty}\frac{x}{e^{x}-1}dx=\frac{\pi^{2}}{6}\]