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
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Please find the solution in the attachments. Since the problem involved lot of explaination, I prefered my own writing.
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