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Permittivity $\varepsilon$ is what characterizes the amount of polarization $\mathbf{P}$ which occurs when an external electric field $\mathbf{E}$ is applied to a certain dielectric medium. The relation of the three quantities is given by
$$\mathbf{P}=\varepsilon\mathbf{E},$$
where permittivity can also be a (rank-two) tensor: this is the case in an ...
18
If $\varepsilon$ or $\mu$ are tensors (read, matrices), then so is $c_m$:
$$
\overbrace{\varepsilon}^\mathrm{matrix} \underbrace{\mu}_\mathrm{matrix}=c_m^{-2}\ \leftarrow\ \text{matrix as well}
$$
In other words, if the permeability and/or permittivity are matrices, then the speed of light is a matrix as well. In this case, the $\_^{\color{red}{-1}}$ is ...
answered Dec 26 '16 at 19:43
AccidentalFourierTransform
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You cannot totally avoid quantum mechanics, but it may suffice to say that reflections by free electrons are not the only way to prevent transmission. Any situation where light can promote an electron from a low energy state to a higher one will cause absorption, regardless of DC conductivity. Or even with little absorption, massive scattering of light by ...
16
Just because the material doesn't conduct currents on a macroscopic scale, does not mean it doesn't contain any movable charges at all. In fact, as the very name “dielectric” suggests, such a material contains charges which can be to some degree separated – electrons move a bit to one side or the other, never actually bidding their parent atom farewell but ...
15
What you are describing is anomalous dispersion. This happens when a material becomes strongly absorbing, typically near an absorption line, and the refractive index becomes complex.
In these circumstances the phase and group velocities are different and indeed the group velocity can be greater than $c$. This isn't a problem since the group velocity is no ...
11
A dielectric effectively behaves as if it was thicker than it is. If the dielectric constant is $K$ and the thickness of the dielectric is $t$, then for calculating the force it behaves as if the thickness was $t\sqrt{K}$.
To see this let's take the example we know about where the dielectric fills the space between the charges:
In (a) the thickness of the ...
9
In a microwave the EMW energy is transferred to the water molecules, but, since they are in immediate contact with other molecules (as in any food), the whole volume gets heated. You will not have a two-temperature mixture.
9
At sufficiently high voltages almost everything conducts due in part to quantum tunneling of electrons. An insulator has a breakdown voltage which is the field strength required before it will start conducting.
Related to the breakdown voltage is the dielectric strength which is the minimum voltage over distance ($\mathrm{V}/\mathrm{m}$) before a material ...
7
The Kramers-Kronig relations are the expression, in the Fourier frequency domain, of the fact that the linear susceptibility $\chi(\tau)$ is a causal function, i.e. that the dielectric response of the signal $f$ to a forcing $F$ has the form
$$
f(t)
= \int_0^\infty \chi(\tau) F(t-\tau) \mathrm d\tau
= \int_{-\infty}^\infty \theta(\tau)\chi(\tau) F(t-\tau) \...
6
Your professor is right. Capacitors K2 and K3 are not parallel and then in series with capacitor K1, because the vertical line that is separating K1 on left and K2 and K3 on right is not an equipotential line. That is, potentials on the left side of K2 and on the left side of K3 are not the same!
You actually have upper half of K1 and K2 in series and ...
6
$D$ is the electric displacement field or commonly the flux density and $E$ is the field intensity. There is a fundamental difference between them which will be understood to certain extent as you go through the following answer. Consider a point charge of $Q$ coulombs. This means that the number of flux lines emitted by the charge is $Q$ coulombs. .
Let ...
6
There are two contributions to the electric field in a dielectric:
The field generated by the 'free' charges, i.e the ones on the capacitor plates. Call it $E_0$
$E_0$ polarizes the dielectric, which in turn adds to the total electric field. Call that polarization $P$.
The total electric field is $$E=E_0-\epsilon_0^{-1}P$$ (The factor of $\epsilon_0^{-1}$ ...
6
First make a parallel plate capacitor with plates of area A and spacing d. Fill the space between the plates with the dielectric whose complex permittivity $\epsilon(\omega)$ you wish to measure.
The formula for this capacitance is a complex function of frequency because the permittivity is a complex function of frequency.
$$
C(\omega)={{\epsilon(\omega)A}\...
6
I believe you are talking aboug the Goos-Hänchen shift which is described in this paper.
From there, the following diagram:
That link also gives a detailed mathematical description. The original paper (referenced from the above) is
F. Goos and H. (Lindberg-)Hänchen, Ein neuer und fundamentaler Versuch zur Totalreflexion,
Ann. Phys. 1, 333 (1947),
http://...
5
In a liquid mixture such as ethanol-water, both components vaporize to some extent. If the combined vapor pressure of the two equals the external pressure, say 1 atm, the mixture will boil. The components DO NOT boil separately. Further, the composition of the vapor and the composition of the liquid will be different from each other. This is the basic ...
5
As Pygmalion points out, the flaw in your reasoning is assuming that the surface of the $K_1$ dielectric is an equipotential, which it need not be. At the triple junction there will be some accumulation of charge and the accompanying electric fields, which will result in a potential difference between the two sides of dielectric 1's surface.
Let me explain ...
5
You are correct: there is no free charge so $\vec{D}=0$ which means
$$
\vec{E}=-\frac{1}{\epsilon_0}\vec{P}=-\frac{k}{\epsilon_0r}\hat{r}
$$
But this is for $R_1\leq r\leq R_2$.
Inside the shell, $r<R_1$, there are no enclosed charges, so $\vec{E}=0$ there. Outside the shell, there is also no charge. Recall that the total charge for dielectrics can be ...
5
Imagine a blob of liquid water. Each molecule is polar because the electrons are closer to the oxygen than the hydrogens. Without a large external electric field, the water is moving around bumping this way and that way with basically random orientations.
Now while in orbit make a very large parallel plate capacitor,charge it up and put your blob of water ...
5
The only property of metals used in deriving $C=\varepsilon A/d$ is that they are perfect conductors. Ideally, all metals have this property. So even if you change the metal, it should not matter.
But if you use something other than metal, then it will of course change the capacitance.
5
The permittivity of a conductor is infinite.
Let the value of an external electric field in free space (relative permittivity = 1) be $E$.
If this is applied to a material of relative permittivity $\epsilon_r$ then the electric field in the material is $\dfrac {E}{\epsilon_r}$
Inside a conductor the electric field is zero hence its relative ...
5
When you have a dividing line which is between two dielectrics parallel to the plates you have to ask yourself; is the dividing line an equipotential?
That is relatively easy for diagram B as there is no change of dielectric on either side of the dividing line.
In diagram A there is a change of dielectric on either side of the dividing line and so in ...
5
Permittivity and permeability are not just constants, but instead are complex functions that depend on a number of other quantities, including the wavelength of the light. In fact, the refractive index $n$ is only half the story - there is also a related quantity, the extinction coefficient $k$, that describes the absorption in a medium. To put it more ...
5
. . . . why don't we just put these metal plates as close as possible without touching each other . . . .
How is this going to be done?
One of the functions of a solid dielectric is to keep the plates separated.
Air as with other dielectric is an insulator but if the electric field is to large it "breaks down" and becomes a conductor.
So for a given ...
4
So, this is an old post that I came across when I had a similar question. Here's a paper where they dissolve different amounts of ions in the water and found that the ability for the microwave oven to heat the water actually reduces as more ions are introduced.
So from this study, you could conclude that ion drag is not source of heating in the water.
4
About the autoionization of water ...
Wikipedia (http://en.wikipedia.org/wiki/Debye_length) gives a formula for water
$$\text{debye length in nm} = \frac{0.304}{\sqrt{I\text{ in molar}}}$$
where $I$ is ionic strength, which is 1E-7 for pure, pH-neutral water. That gives a screening length of 1$\mu$m.
So at DC, there will be an electric field in the bottom ...
4
Use a setup that looks like this:
The level of the water in the fine tube changes with the average density of the ice/water mixture so as the ice mets it will go down and as water freezes to ice it will go up.
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The energy is used to polarize the dielectric, i.e.: Moving charges inside the dielectric.
4
First of all that's $U=\frac{1}{2}CV^2$.
But there is also another relation : $U=\frac{1}{2C}Q^2$.
And I think your confusion will be gone if you realize when to use which relation. If you have a capacitor with a constant voltage source connected across it, then you use the first relation. But when a capacitor is already charged and is not part of a circuit,...
4
It is all about wavelength versus tunnel diameter. The wavelength of GPS is about 20cm it would happily propagate in any normal tunnel if it could get in but the earth and other structures absorb it. AM radio (600kHz - 1500kHz) cannot propagate in any normal tunnel because the wavelength is too long (500m-200m) relative to the diameter, and thus gets ...
4
I think the answer is clearer if you consider the equipotential as shown in the diagram below. Forgive their straight line nature as they were easier to draw that way.
Given that $\vec E$ must be perpendicular to an equipotential surface then in your computation of potential difference $\displaystyle V_{AB}=-\int_B^A\vec{E\,}\cdot\mathrm d\vec{r\,}$ the ...
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