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Elements of Solid State Physics

J.P. Srivastava

Chapter 10

Theory Of Dielectrics: Applications To Plasmons, Polaritons And Polarons - all with Video Answers

Educators

Chapter Questions

00:23

Problem 1

Find the components of the electric field resulting from charges $+q$ and $-q$ in the following figure. Add them vectorially to show that the resultant is given by

Mayukh Banik
Mayukh Banik
Numerade Educator
03:10

Problem 2

Assuming that an atom consists of a uniform sphere of negative charge with radius $R$ surrounding a point positive charge, show that the polarizability is equal to $4 \pi \in_{0} R^{3}$. Assume that the negative charge remains uniform even under the action of a field. If the diameter of argon atom be $3 \AA$, calculate the index of refraction of argon gas at NTP.

Adriano Chikande
Adriano Chikande
Numerade Educator
11:36

Problem 3

An infinite dielectric medium with dielectric constant $\in$ has a spherical cavity of radius $R$ cut within it. If a very small conducting sphere of radius $r$ is placed at the centre of the cavity and a uniform electric field $E_{0}$ is produced within the main body of the dielectric, what will be the induced dipole moment of the sphere?

Linda Winkler
Linda Winkler
Numerade Educator
01:29

Problem 4

The resonance absorption exhibited by a medium shows a single absorption line at $6000 \AA$ (in vacuum). When a beam of light of this wavelength travels through $2.5 \mathrm{~cm}$ in the medium, the intensity of light drops to $1 / \mathrm{e}$ of its initial value. Calculate the maximum value of the imaginary part of the index of refraction.

Surendra Kumar
Surendra Kumar
Numerade Educator
06:29

Problem 5

The complex index of refraction of a metal for infrared radiation ( $\omega \tau<<1$ ) is expressed as
$$
\sqrt{\epsilon(\omega)}=(n+i k)=1+4 \pi i \sigma_{0} / \omega \quad \text { (C.G.S) }
$$
where $\sigma_{0}$ is the electrical conductivity for static fields. Check that $\sigma_{0}$ has the unit $\mathrm{s}^{-1}$ in e.s.u. Assuming $\sigma_{0} \gg \omega$ (leading to $n=k$ ), show that the reflectance of the metal approximately equals
$$
\left[1+\left(2 \omega \pi \sigma_{0}\right)^{1 / 2}\right]
$$

Prachita Kush
Prachita Kush
Numerade Educator
01:48

Problem 6

Assume that the electrons and the nucleus of an atom form a spherical cloud of uniform density and radius $r_{0}$. Taking $r_{0}$ as the Bohr radius, calculate the polarizability of hydrogen atom based on this model. How does it compare with the true polarizability?

Sai Chaitanya Tadepalli
Sai Chaitanya Tadepalli
Numerade Educator
01:51

Problem 7

Complete the following table, which lists the typical parameters for electrons in four different types of plasma.
$$
\begin{array}{lcccc}
\hline & \begin{array}{c}
N_{0} \\
\left(\mathrm{~m}^{-3}\right)
\end{array} & \begin{array}{c}
T \\
(\mathrm{~K})
\end{array} & \begin{array}{c}
\omega_{\mathrm{p}} \\
\left(\mathrm{rad} \mathrm{s}^{-1}\right)
\end{array} & \begin{array}{c}
\lambda_{\mathrm{D}} \\
(\mathrm{m})
\end{array} \\
\hline \text { Solar atmosphere } & 10^{18} & 10^{4} & & \\
\text { Solar corona } & 10^{13} & 10^{6} & & \\
\text { Ionosphere } & 10^{10} & 10^{3} & & \\
\text { Tokamak } & 10^{19} & 10^{8} & & \\
\hline
\end{array}
$$

Zachary Warner
Zachary Warner
Numerade Educator