# Blackbody Radition in Flatland

Blackbody Radiation in Flatland

a) Carry out the derivation of u(v,t), the energy per unit area per unit frequency in the electromagnetic field, for the 2-dimensional case, i.e. inside a square cavity of side L held at temperature T. Find the total energy in the square and show that it's of the form:

U(T) = (L^2)a(T^n)

and determine n and a in mks units.

(v is frequency)

*note: in Stefan-Boltzmann expression U(T)=aT^4

where a = 705662 x 10^(-16) J/m^(3)*K^4

b) Carry out the derivation of the factor f that allows the total radiation per second per unit length of the edge of the square to be written:

E(f) = fcu(T)

c) Determine the frequency v,max where u(vT) is a max when T = 300K

You can use handwriting in the explanation if necessary.

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#### Solution Summary

Blackbody Radiation in Flatland. Carry out the derivation of u(v, t), the energy per unit area per unit frequency in the electromagnetic field, for the 2-dimensional case, i.e. inside a square cavity of side L held at temperature T.