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 nonzero, ±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).
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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.
 Fall '06
 Buchler
 Physics, Special Relativity, Radiation

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