Consider a bound atomic electron of charge q in a dielectric medium with a complex, fre-
quency dependent, atomic polarizability a(w). We can write O = as + i02, where as and a
are the real and imaginary parts of O respectively. The dielectric function may be taken to
be E(W) = 1 + 41TNa(w) where N is the density of polarizable atoms. We take H = 1 for this
medium. Note: for this problem you should not assume any particular functional form for
An oscillating electric field E(t) = Re Ew ] exerts a force on the bound electron cloud.
Assume Ew is a real valued vector and s is an arbitrary phase factor.
a) [5 pts] The resulting velocity of the electron cloud center of mass can be written as
v(t) = Re Find Vw in terms of Ew and a(w).
b) [10 pts] If W is the work done on the electron by the electric field in one period of
oscillation T, then find the average work done over one period, i.e. W/T, where T = 2TT/W.
This is the energy absorbed by the electron. Express your answer in terms of Ew and a(w).
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