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The Solid State: An Introduction to the Physics of Crystals for Students of Physics, Materials Science, and Engineering

Harold Max Rosenberg

Chapter 13

DIELECTRIC PROPERTIES - all with Video Answers

Educators


Chapter Questions

02:38

Problem 1

Assuming that an atom consists of a unform sphere of negative charge with radius $R$ surrounding a point positive charge, show that the polarizability is equal to $4 \pi \varepsilon_0 R^3$. (The negative charge may be taken to reman uniform in an applied field.) The diameter of an argon atom is $0.3 \mathrm{~nm}$. Estimate the refractive index of gaseous argon at S.T.P.

David Zhang
David Zhang
Numerade Educator
02:48

Problem 2

The dielectric constant of a solid is 5 . It is placed between the plates of a condenser which are $1 \mathrm{~mm}$ apart and which is charged to $100 \mathrm{~V}$. Calculate the local field acting on an atom in the dielectric.

Prabhu Ramji
Prabhu Ramji
Numerade Educator
11:36

Problem 3

A spherical cavity of radius $R$ is cut in an infinite dielectric which has dielectric constant $\varepsilon$. A very small conducting sphere of radius $r$ is placed at the centre of the cavity and a uniform electric field $E_0$ is set up in the main body of the dielectric. Calculate the induced moment of the sphere.

Linda Winkler
Linda Winkler
Numerade Educator
02:48

Problem 4

$\mathrm{KH}_2 \mathrm{PO}_4$ is a colourless crystalline material which has a relative dielectric constant at low frequencies of 100 . On the assumption that the low-frequency dielectric constant is due predominantly to the vibration of the $\mathrm{H}^{-}$ions (of which there are $2 \times 10^{28}$ per cubic metre) about their equilibrium positions. estimate the frequency at which the peak of the dielectric absorption will occur.

Prabhu Ramji
Prabhu Ramji
Numerade Educator
01:31

Problem 5

Show that in a material which has a dielectric relaxation mechanism the dielectric power loss at very high frequencies is independent of the frequency.

cm
Charles Magnusen
Numerade Educator
03:30

Problem 6

If the dielectric relaxation time of a medium is $10^{-10} \mathrm{~s}$ estimate the width of the relaxation peak between points where the energy dissipation is reduced by one half.

Vishal Gupta
Vishal Gupta
Numerade Educator
01:18

Problem 7

The amplitude of a light wave which is travelling in a medium can be represented by $A \exp \{i(n \omega x / c-\omega t)\}$, where $n$ is the refractive index and $c$ is the velocity of light in vacuo. Show that if the light is attenuated as it passes through the medium then this can be represented by taking $n$ as complex, i.e. in the form $n+i k$. Express $\varepsilon^{\prime}$ and $\varepsilon^{\prime \prime}$ in terms of $n$ and $k$.

Ajay Singhal
Ajay Singhal
Numerade Educator
05:48

Problem 8

A medium which exhibits resonance absorption has a single absorption line centred on $600 \mathrm{~nm}$ (in racuo). If the intensity of a beam of light of that wavelength falls to $\exp (-1)$ of its initial value in $0-025 \mathrm{~m}$, find the maximum value of the imaginary part of the refractive index

Prachita Kush
Prachita Kush
Numerade Educator