Unformatted text preview: 10.10. SIMPLE DIELECTRICS 10.21 For N molecules per unit volume, we have the dipole moment per unit volume, 2
P=Np=NTEE We normalize to so as follows and, for isotropic materials, write the relation between
P and E as where
Xe — K50 is called the normalized electric susceptibility to polarization. In vector form, we have
the polarization P = (50er (as in Chapter 5) and we write 5— (1+ )-s 1+N22
—~€o Xe — 0 K50 For a different species in the gas, 1 + Z i:::] = 50 [1 ‘i‘ ZXea] This is the regime we have been discussing for 5 real (in a nonconducting material). 8:80 Now we extend this model to forced oscillations under the inﬂuence of an electromag-
netic wave E = Eoeiw‘ and let to be arbitrary. To make a realistic model, we must
include damping within the molecule as well as resonance effects. Now the equation
of motion becomes that of a damped, forced harmonic oscillator:
(£211: dx - t 7 in? = —mFa — K5.“ — eEoe’”
where F is the damping coefﬁcient. As with springs, the natural frequency we =
\lK/m can be found from solving this equation with l" = 0 and E = 0. We can
introduce we, and replacing d/dt by jw and det2 by —w2 we have: 8 t=———m Eef'wt
a:() wg—w2+jwl‘ 0 The electron vibrates at u: but the damping term changes the phase and affects the
amplitude of x(t) relative to E. Again, the dipole moment per unit volume is: N_e’
__ _ = m In!
P — New (LI—#3 _ (4)2 + jwl" E001 We use 15. = onEE and E = 50(1 + Xe) to write: N82 5 = so + (10.19) _me._.
wg —w2 +ij ...
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- Fall '06