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# Model of dielectric with frequency dependent dielectric cons

(See attached file for full problem description)

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Frequency dependent dielectric constant
The polarization of a dielectricum P(r,t) is given by calculating the mean of the induced dipole moment of the bound charge in a small volume V(r) in the neighbourhood of r, i.e P(r,t) = (1/V(r))&#61523;j pj(t)
In a simple model for a linear dielectric we make the assumption that there are N charged particles (with mass m and charge q) per unit volume, which are bound to their equilibrium positions rj´ through a harmonic potential &#966;(rj) = a² (rj - rj´)². An electric field E(r,t) acts such that it tends to push the particles out of their equilibrium position
In addition there is there is a damping force acting, Fj = &#61485;b²drj
dt
which is proportional to velocity.
a) Give the equation of motion for rj(t).
b) Calculate the polarisation P(r,t) for an electric field with time dependence exp(&#61485;i&#969;t). What is the complex dielectric constant &#949;(&#969;) in this case
c) Sketch the real and imaginary parts of &#949; as a function of frequency
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#### Solution Preview

The calculation is in the attached file freq.pdf and the sketches are in the attached ...

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