Chapt. 34 Maxwell’s Equations, Electromagnetic Radiation and Special Relativity 263 a) For analytic results, one frequently wants to use a dimensionless (i.e., unitless) variable in place of λ . The conventional choice is x = hc kTλ . Write B λ in terms of x eliminating all explicit λ ’s. b) Find the formula for a non-zero, ±nite x that makes B λ stationary with respect to λ . Use the chain rule. Note NO explicit analytic formula exists for x . The best you can do is ±nd a simple implicit formula for x : i.e., implicit in this case means that x occurs on both sides of an equal sign. Is the stationary point going to be a maximum, minimum, or in²ection point? Explain why. c) By roughly plotting both sides of the formula found in the part (b) answer or by any other means determine the x that makes B λ stationary. d) From the results of foregoing parts, derive Wien’s displacement law with an approximate value for Wien’s displacement constant (i.e., the constant in Wien’s displacement law).
This is the end of the preview. Sign up
access the rest of the document.
This note was uploaded on 11/16/2011 for the course PHY 2053 taught by Professor Buchler during the Fall '06 term at University of Florida.