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3
votes
4answers
168 views

Energy density with complex permittivity?

Question What is the correct form of the energy density when we have a complex permittivity (such as in a dielectric)? Additional information A complex permittivity means that we have: $$\vec ...
3
votes
3answers
349 views

Electromagnetism boundary condition

The dielectric slab surrounded by air as shown in diagram has permittivity $\epsilon$ different from air and permeability almost same as air. Electric field everywhere within the slab is given to be ...
0
votes
3answers
58 views

Nonlocal dielectric function - what does it mean?

I'm reading this* article and in the second sentence of introduction I encountered a term I haven't heard of before. Namely: nonlocal dielectric function. What does this nonlocality mean? And how does ...
2
votes
2answers
811 views

Dielectric slab counter-intuitive formula?

For the calculation of force on one of the two equal(in magnitude, opposite in sign) point charges separated by $r$ with a dielectric slab of dielectric constant $K$ and width $d$ in between, the ...
0
votes
2answers
186 views

Dielectric boundary

I am trying to determine why electric field may be confined to a certain region if there is a large difference in the permitivity for example if electric field flows through water and then reaches a ...
6
votes
1answer
194 views

Why is $\textbf{D}$ the response to $\textbf{E}$?

In the text Wooten, equation 2.69 shows $\textbf{D}$ being the response to $\textbf{E}$ with $\epsilon$ as the response function: $$ \textbf{D}(\textbf{r},t) = \int d\textbf{r}^{\prime} \int ...
2
votes
1answer
49 views

Why there are spikes in permittivity Vs. frequency curve?

When the frequency is increased the permittivity of a dielectric material decreases. But in the way of decrease there are some spikes which indicates sudden increase of permittivity for certain ...
1
vote
1answer
29 views

Relation between dipole moment and polarisaton

In the Landau's book "Electrodynamics of Continuous Media" he derives the relation between the polarisation $\vec P$ and the dipole moment $\vec p$. Starting with the definition of the dipole moment: ...
1
vote
1answer
258 views

Dielectric sphere placed in another dielectric medium with uniform external field: is there a surface charge density?

Consider a dielectric sphere placed within a dielctric medium. There is a uniform electric field $E_0$ present throughout in the medium. Would there be surface charge on the sphere?
0
votes
1answer
23 views

Confusion about the total bound charge of a sphere placed in dielectric

There is a solved exercise in which a charged sphere of radium $r=a$ is inside a dielectric material. The surface bound charge and the volume bound charge are respectively: $$p_{sp}=\vec{P}\cdot ...
0
votes
1answer
28 views

How to find the polarization of a dielectric sphere with charged shell surrounding it?

A shell with negligible thickness has a given charge density as a function of theta, and is filled with a dielectric material with a given electric susceptibility. Using lovely legendre polynomials ...
0
votes
1answer
28 views

Work done when applying an electric field?

On these example questions from MIT in the solution to 4.1 they write the work done by applying the electric field to be: $$W=V_0 \int \vec E \cdot d \vec D$$ Where does this equation come from and ...
0
votes
1answer
93 views

Surface bound charge in the electric displacement

In Griffiths, the electric displacement is written with just volume charge density, and that is because, he says, 'we cannot apply gauss law precisely at the surface of a dielectric, for here volume ...
0
votes
1answer
71 views

Dielectric heating - does EM field transfer energy to polar molecules?

In AC field, polar molecule are trying to align with external field. At high freguencies, changes of field are so quict, that molecules cannot align with it. This leads to increasing kinetic energy of ...
0
votes
1answer
105 views

Charged dieletric/conductor in capacitor

It is a standard problem to consider a dielectric or a conductor between the parallel plates of a capacitor. But what happens to capacity, voltage, charge, inserting between the plates of an ideal ...
0
votes
1answer
51 views

Why defects reduce electric field?

I am running a simulation with drift-diffusion equation, Poisson equation and Fourier heat equation with a metal/insulator/metal structure. In my simulation, initially electric field is at the top of ...
3
votes
0answers
75 views

What is the origin of the “polarization catastophe”?

According to the Clausius-Mossotti relation, $$ \frac{\epsilon_r - 1}{\epsilon_r + 2}=\frac{n\alpha}{3\epsilon_0} $$ So when $n\alpha = 3\epsilon_0$, the relative permittivity $\epsilon_r$ ...
3
votes
0answers
176 views

Electric field of a capacitor in dielectric medium with weird size

I have been learning gauss's law in capacitor recently, recently I come up with this problem that I couldn't solve myself. If we have a capacitor,and a dielectric medium with half the volume between ...
2
votes
0answers
64 views

Validity of the static limit of a dielectric function

In general, the dielectric function $\epsilon(q,\omega)$ reflects the spatial and temporal response of a condensed matter system to an applied potential. If we put an electron into an electron sea, ...
2
votes
0answers
83 views

Multiple meanings of polarizability?

There's a concept in linear response theory called the polarizability $\chi$ $$\tag{1} \rho_{ind}=\int \chi(\vec{r},\vec{r}',t-t') V_{ext} \: d\vec{r}' dt' $$ where $\rho_{ind}$ is the induced charge ...
1
vote
0answers
32 views

Dielectric field in a homogenous electric field

I'm working through my workbook right now and currently am stuck on the chapter about dielectrics. The term $\vec{E}=\frac{3}{\epsilon_r +2}\vec{E_0}$ was introduced without a proper proof. Instead ...
1
vote
0answers
29 views

Calculate characteristic frequency from atomic polarizability

With Lorentz model, the plasma frequency can be calculated from electron density $$\omega_p=\sqrt\frac{4\pi N e^2}{3m}$$ But I also found in this paper that it could also be calculated from atomic ...
1
vote
0answers
44 views

Lindhard function for surface plasmon

Is there anybody that knows how to calculate the Lindhard function for the surface plasmon (between the surface of two metals of different dielectrics)? What I'm looking for is to find this function ...
1
vote
0answers
66 views

Dielectric constant of gases - constant?

A number of questions related to the topic: Is the dielectric constant actually constant as a function of temperature and frequency (when used in a capacitor)? Is it constant as a function of field ...
1
vote
0answers
60 views

What is the most effective dielectric material known to man?

What is the most effective dielectric medium/material (highest breakdown voltage) known to man? Is it the vacuum? or are there any materials which could be more effective than the vacuum?
1
vote
0answers
79 views

Is the dielectric constant of an insulator always positive?

I know there are many examples of metals with a negative dielectric constant at optical frequencies. But what about insulators?
1
vote
0answers
45 views

Intensity Poynting

Take a plane wave propagating in the $\hat{z}$ direction in a non-magnetic linear dielectric. The real electric field is then given by $$\vec{E}(r,t) = E_0\, e^{-k_i z}\cos(k_R - \omega t)\, \hat{x} ...
1
vote
0answers
75 views

Does all electrical insulator can be electrostatically charged?

Does all electrical insulator can be electrostatically charged, or insulator with only dielectric property can? Thank you.
1
vote
0answers
509 views

Complex polarizability of a dielectric sphere in a homohenious electric field

It is well known that complex polarizability of uniform dielectric sphere with radius $r$ and complex permittivity $\hat\epsilon_{in}(\omega)$ placed in a medium with complex permittivity ...
0
votes
0answers
18 views

Relation between displacement current, dielectric and time varying Electric field

I know that displacement current is produced in dielectric material due to dipole moment. I also know that displacement current is produced by time varying electric field (according to maxwell ...
0
votes
0answers
20 views

Can we lock electric charges in dielectric cells?

Suppose next. We using Wimshurst machine and gathering charges in dielectric cells such as mica .Before discharge we put whole machine in vacuum chamber.Question is next. Can we storage those charges ...
0
votes
0answers
11 views

Electric field in a sphere embedded in a medium

Consider a system where a sphere of conductivity $\sigma_i$ is embedded in a large medium of conductivity $\sigma_e$. An electric field $E_0$ is applied and the question is, what is the electric field ...
0
votes
0answers
9 views

Calculating pressure on a dielectric kept inside a capacitor

Firstly, the pressure is because of the opposing forces acting on both sides of the dielectric slab. On the left side of slab, the field due to the left plate is $\frac{\sigma}{2\epsilon_0}$ and ...
0
votes
0answers
55 views

dielectric polarization

Suppose a small solid sphere made of an isotropic dielectric is introduced in the field of some given system of remote charges. Assuming that the polarization in the dielectric does not affect the ...
0
votes
0answers
26 views

Direction of polarization in dielectrics

Our teacher just taught us polarization in dielectric materials. I have some doubts that he wasn't able to clear. Is the direction of polarization, for any non-linear dielectric, in the direction of ...
0
votes
0answers
68 views

Effect of a dielectric medium on electric field and electric flux

What is the effect of dielectric medium in comparison to vacuum on electric field and electric flux. I read that higher dielectric constant means higher relative permittivity which means more ...
0
votes
0answers
39 views

what can be the BG and dielectric constant of monolayer MoS2 in semiconducting state (2H) and in metallic state (1T)

Monolayer MoS2 is a semiconductor that can undergo an MIT (Metal to insulator) or semiconducting state to insulating state transition. The semiconducting state is referred as 2H State and the metallic ...
0
votes
0answers
74 views

Quantitative understanding of excess heat capacity in ferroics

I'm looking to understand what an excess heat capacity in a ferroelectric (FE) can correspond to qualitatively. Typically one starts with a Landau expansion of the free energy if you want to study the ...
0
votes
0answers
57 views

Calculating rise in water surface due to a charged capacitor

Two metal plates separated by a distance d & initially charged with charge +Q & -Q are kept so that it just touches the surface of a very large water tank as shown in figure a. Thus water ...
0
votes
0answers
30 views

Does water absorb microwaves above of beneath its relaxation frequency

I am a bit confused about the concept of relaxation frequency. In my course text we derived a model with the help of Newton's law to describe the movement of polar molecules in an electromagnetic ...
0
votes
0answers
52 views

Density of polarisation charge is zero always for linear isotropic homogeneous dielectrics?

It seems to me that the volumetric density of polarisation charge in a linear homogeneous isotropic dielectric in an external field is always zero, but I find this rather surprising. Consider such ...
0
votes
0answers
21 views

Inhomogeneous scattering from a dielectric box in 2D?

I wrote an E&M simulator and need to verify the accuracy. My simulator evaluates a 2D grid (which is what my camera measures), and would like to test an object that is minimally perturbed by ...
0
votes
0answers
59 views

Speed of light in a medium as superposition of dipole radiation

Studying electromagnetism I know that the speed of light in a medium is $v = c/\eta$ and that it's possible to derive this from the Maxwell equations in the medium. But I wanted to find a microscopic ...
0
votes
0answers
18 views

Electrodynamics of a single ion transport between a dielectric slab

I am trying to solve the mean passage time for a single solvated ion to diffuse through a pore. This pore is surrounded by the medium with a low dielectric permittivity, i.e. around 10. The solvent ...
0
votes
0answers
270 views

Finding potential of conducting sphere coated by a dielectric shell

An uncharged conducting sphere of radius $a$ is coated with a thick insulating shell (dielectric constant $\epsilon_r$ out to radius $b$. This object is now placed in an otherwise uniform electric ...
0
votes
0answers
44 views

Mosotti-Clausius formula from the first principles

I would like to understand how to get the Mosotti-Clausius formula for the dielectric susceptibility of a dielectric material with spherically symmetric molecules from the first principles, where by ...
0
votes
0answers
24 views

Why breakdown voltage decreases with increasing FWHM of an asperity?

I am running a simulation for a dielectric breakdown. I am getting breakdown voltage decreases with FWHM, which does not make sense as field enhancement is higher for a small width. Simulations solve ...
0
votes
0answers
815 views

How are band gap energy, dielectric constant (permittivity) and resistance related to each other?

The following three properties are related to current flow: Band gap energy Dielectric constant Resistance I would expect them all to have the same trend (i.e. higher band gap energy would cause ...
0
votes
0answers
40 views

Addition of forces in dielectric material

In this paper (page 2 of document) it is said that: Because this calculated force was comparable to the gravitational force, they assumed that the same would be true for the forces on a ...