This question might be trivial but I have a conceptual confusion regarding permittivity and susceptibility of a dielectric  According to Wikipedia, permittivity is the ability to resist external electric field. This means a substance with high permittivity requires high external electric field to polarize. On the other hand, susceptibility is defined as the ability to polarize. So a substance with higher susceptibility should polarize easily. This means both the quantities are inversely proportional to each other but mathematically they are linearly dependant  Where am I going wrong?    I get it that there is a similar question but the answer for that question did not answer mine and I still did not get the privilege of commenting as I am a newbie. That's why I posted it as a separate question   I understood the definitions but couldn't understand the mathematical relation
124307
I want to ask a question about the meaning of the names of some dielectric properties. I'm not a native English speaker, so I don't know why the name of the properties are susceptibility and permittivity. It could be trivial, but I want to understand why they are named this way.  As far as I understand, susceptibility is about how susceptible the material is. Atoms are susceptible to electric fields.  Then what about permittivity? Do they permit something? Permittivity is about total field and polarization ($\mathbf{D}= \epsilon_0 \mathbf{E} + \epsilon_0 \chi_e \mathbf{E}$ $=\epsilon_0 \mathbf{E}+\mathbf{P}$).  But to me, both look almost the same. Why don't you call susceptibility permittivity, and permittivity susceptibility?
90011
Consider the diagram below:  (Author: Joshua Hykes )  From this diagram we can see that the absorption coefficient for the photoelectric effect generically decreases with the increase in energy of the photon. What is the physical reason for this decrease. (i.e. why does the probability of photoelectric absorption decreases with increasing photon energy).  Note: I am aware that the large spin is due to more inner electrons been able to be lifted.  Edit For Clarity  I will here rephrase the question: in the above diagram there is a general decrease in the absorption coefficient due to the photoelectric effect (i.e. the absorption of a photon by an electron and subsequent emission of that electron) with energy (ignoring the occasional absorption edge). This is of course linked to a decrease in the probability of the photoelectric effect occurring (and a corresponding decrease in the cross section). My question is: what is causing this decrease with increasing energy. (For the purpose of this question I am ignoring the contribution due to the Compton effect and pair production and simply focusing on the cross section due to the photoelectric effect.)
97012
I am self-studying Griffiths's Introduction to Electrodynamics (4th edition) and all has been smooth sailing except for section 4.2.3 in which Griffiths argues for why we can compute (at least at the elementary level of classical electrodynamics that I am currently studying) the field due to a polarized dielectric chunk of material by simply adding up the potential (or field) due to each tiny volume element times the polarization per unit volume $\mathbf{P}$, treating each volume element as containing a perfect dipole. I have attached the page and a half of the chapter here, as well as the Eq. 4.8 alluded to there. I'll explain what I understand and where I lose track of his argument, and I'm hoping someone can help me sort things out. After a very gentle qualitative intro, Griffiths essentially says that we are going to define the macroscopic field $\mathbf{E(r)}$ at the point $\mathbf{r}$ in space as the average electric field over a sphere of radius a &quot;thousand times the size of a molecule&quot; about the point $\mathbf{r}$, which I'll call $V$. Fine, this is just a definition, and he says that analogous definitions using ellipsoids etc. yield the same answer, which I'm willing to accept. Now by superposition, the average field on $V$ can be found as the average field due to charges inside and outside of the sphere. With (4.17), he gives the average potential over $V$ due to all charges (dipoles) outside of $V$, and with (4.18) he gives the average field inside $V$ due to the charges inside $V$. I'm still following up to here, but now he loses me. He says that what is left out of the integral &quot;corresponds&quot; to the field at the centre of a uniformly polarized sphere, but what does this correspondence mean? I see how the integral in (4.17) doesn't include $V$, but why does that mean that $\mathbf{E}_{in}$ adds back what is missing (what does it even mean for an average field to source potential? We can speak of charge sourcing potential, or taking a line integral of a field giving a potential, but this is just some field value?). The best I can come up with is to say that if you take (4.19), split the integral out into $V$ and outside $V$, and then apply the (negative) gradient to the integral, one should be able to show that $\mathbf{E}_{in}$ is recovered for the former term, and so that would seem to imply that our coarse graining calculation does indeed give the correct macroscopic field as we have defined it (but I couldn't see how to DO this derivative, so I couldn't prove it). I've tried to look at other resources on this (eg. Zangwill), but none were digestible for me unfortunately. Please let me know if this is unclear, and I can try to rephrase. But essentially I'm hoping someone can, in detail, walk me through Griffiths's arguments. Eq 4.8 (note that Griffiths's script vector r equals $\mathbf{r} - \mathbf{r'}$, and hats have their usual unit vector meaning):  Griffiths text:
63642
Is there a substance that doesn't reflect or absorb visible light but may reflect light from another spectrum? Is there a theoretical substance that would have these properties?  EDIT: Sorry I wasn't quite clear with my original question. I've updated it to express more what I was thinking. Would a substance be "invisible" if it didn't reflect or absorb light? Does a real or theoretical substance like that exist? I assume we can see glass and so on because it refracts light and to a certain extent reflects it.
51000
Polarisation, spin, helicity, chirality and parity keep confusing me. They seem to be related, but exactly how they are related is unclear to me. Can someone maybe give a short overview about what these quantities mean and how they are related? What are the values for e.g. basic particles like electron or photon?
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There was some discussion on this question        which I don't see as being conclusively resolved:   "turns out that what might LOOK like two ordinary electrolytics are not, in fact, two ordinary electrolytics." "No, do not do this. It will act as a capacitor also, but once you pass a few volts it will blow out the insulator." 'Kind of like "you can't make a BJT from two diodes"' "it is a process that a tinkerer cannot do"   So is a non-polar (NP) electrolytic cap electrically identical to two electrolytic caps in reverse series, or not?  Does it not survive the same voltages?  What happens to the reverse-biased cap when a large voltage is placed across the combination?  Are there practical limitations other than physical size?  Does it matter which polarity is on the outside?  I don't see what the difference is, but a lot of people seem to think there is one.  Summary:   As posted in one of the comments, there's a sort of electrochemical diode going on:     The film is permeable to free electrons but substantially impermeable to ions, provided the temperature of the cell is not high. When the metal underlying the film is at a negative potential, free electrons are available in this electrode and the current flows through the film of the cell. With the polarity reversed, the electrolyte is subjected to the negative potential, but as there are only ions and no free electrons in the electrolyte the current is blocked. —    Normally a capacitor cannot be reverse-biased for long, or large currents will flow and "destroy the center layer of dielectric material via electrochemical reduction":     An electrolytic can withstand a reverse bias for a short period, but will conduct significant current and not act as a very good capacitor. —    However, when you have two back-to-back, the forward-biased capacitor prevents a prolonged DC current from flowing.  :     For circuit positions when reverse voltage excursions are unavoidable,   two similar capacitors in series connected “back to back” ... will create a   non-polar capacitor function ... This works because almost all the circuit voltage   is dropped across the forward biased capacitor, so that the reverse   biased device sees only a negligible voltage.   :     The oxide dielectric construction that is used in tantalum capacitors   has a basic rectified property which blocks current flow in one   direction and at the same time offers a low resistance path in the   opposite direction.
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I was looking for an equation that could show the relationship between the range of frequencies of an EM wave, and its Maximum data transfer rate. I know that ranges of shorter wavelengths can have a larger bitrate/symbol rate, but could not find an equation relating the two variables.   Thanks in advance for the help.  EDIT: I refined my wording above. Also, no one answered my question over at amateur radio SE. As for the nyquist rate wiki page, I still could not find the answer I was looking for.
90607
When you are inside some non uniformly and non radially polarized sphere, why do the dipoles from outer shells don't affect you (the potential there is only due to inner dipoles from what I have seen)?
73549
I understand how one associates the spin of a quantum particle, e.g. of a photon, with intrinsic angular momentum. And in electromagnetism I have always understood the polarization of an EM wave as the oscillations of the E and M field, not necessarily being  aligned with the direction of propagation of the wave.     Questions:   But when one talks about the polarization of a photon in Quantum Mechanics, how does it really differ from its spin?  Are they somehow related and what's the physical idea behind photon polarization in contrast to photon-spin? Feel free to use mathematical reasonings as well if you see it fit!
15021
Say we had a circuit with a cell (with internal resistance)and an external resistor of $10 \Omega$ as shown:  The $10\Omega$ resistor then increases in temperature, leading to an increase in resistance in this resistor. My thinking was that since $10 \Omega$ resistor now has a value higher than $10\Omega$, more voltage drops across this resistor. Since your emf is constant, less voltage must drop across the internal resistor. Less voltage drop means less resistance. Where is the flaw in my logic?
15195
I mean to ask why there is $4\pi$ present in force equations governing electricity? Though all objects in universe are not spherical and circular, the constant of proportionality in both equations contain $4\pi$. Why?
13207
I was wondering (since I've looked pretty hard and haven't been able to find anything)-  are there any models that explain the polarization of light upon reflection? Everywhere I've looked I've seen things like the Brewster angle mentioned, and empirical data, but I haven't yet found any theoretical models that explain this type of polarization. Can anybody point me in the right direction? Or have no such models been made?
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If polarization is interpreted as a pattern/direction of the electric-field in an electromagnetic wave and the frequency as the frequency of oscillation, how can we interpret polarization and frequency when we are dealing with one single photon?
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It is well known that a  can "split light" by separating different frequencies of light:    Many sources state that the reason this happens is that the  is different for different frequencies.  This is known as .  My question is about why dispersion exists.  Is frequency dependence for refraction a property fundamental to all waves?  Is the effect the result of some sort of non-linearity in response by the refracting material to electromagnetic fields?  Are there (theoretically) any materials that have an essentially constant, non-unity index of refraction (at least for the visible spectrum)?
91415
In a classical electrodynamics textbook (Griffiths), it is mentioned that even though the electric field function, $E:\mathbb{R}^{3}\rightarrow \mathbb{R}^{3}$, is a (3D) vector valued function, the amount of information needed to fully describe it is equivalent to the amount needed to describe a scalar valued function, and this is because it is the gradient of an electric potential function, $U:\mathbb{R}^{3}\rightarrow \mathbb{R}$ and so is completely determined by it. The author goes on to explains that this is so because $E$ has the property that its curl is zero evevrywhere, and this is what restricts the freedom in determining $E$ (and what enables it to be the gradient of a scalar function in the first place).     This is all fine (and fun), but I find myself unable to answer this question: why does the imposition of zero curl provide an amount of information exactly equivalent to two scalar-valued functions (no more, no less)?   An example of the sort of reasoning that leads me to other conclusions: since zero curl is equivalent to equating three pairs of partial derivatives ($\partial E_{x}/\partial y = \partial E_{y}/\partial x$ and so on), leaving 6 out of 9 partial derivatives "free", it seems that "one third of the amount of information" required to describe $E$ has been taken up, as opposed "two thirds"... I am of course assuming here that the first order partial derivatives determine the behavior of the function (perhaps up to a constant as in the 1D case?), and that these partial derivatives are independent of each other and thus provide equal amounts of information. Is either of these assumptions wrong? Is my whole reasoning off?  Any insight into this question and a possible answer would be appreciated.  *The question is, of course, a general one about vector-valued functions, with $E$ just being a particular case.  **I have not mentioned all the obvious assumption of smoothness necessary for everything to be defined..  ***I realise that I'm playing fast-and-loose with the word "information", and that my whole question is very un-formal. Any reference to an area of mathematics which may perhaps put such intuitions on rigorous footing are more then welcome.   Edit: I am not asking why (or when) a vector field having zero curl is equivalent to it being a gradient of some scalar field. I am asking about the amount of information we get about a vector field when we determine its curl.
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Is it an accurate statement to say that free electrons in a metal experience NO restoring force when they interact with electromagnetic waves? I understand that the electrons exist in a space filled with ions, and doesn't the cumulative potential that is present due to the presence of the ions exert an electric field on the electrons. Even in the case of simple metals, where you can say that the nucleus is shielded by the valence electrons, so called Coulomb shielding, how significant is the shielding. Naively, it seems to me that because the charge in the nucleus is not balanced by the charge in the bound electrons, there should be some net potential that the free electron sees.
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In the derivation of the , there is nothing whatsoever that relates to a particular/specific material. But we nonetheless use this formula for several distinct sources in nature, such as the Sun and the CMB. How can it be applicable to so many different things? As far as I understand, the emitted photons come from the rotational and vibrational levels. But shouldn't these levels depend on the particular material/elements that the object is made of?   Summarising:   Is the black body radiation formula applicable to an macroscopic object composed of different elements only?  How can it describe so different things (eg Sun spectrum, CMB) if there is nothing in the formula that relates to a specific material/element? If the photons come from vibrational/rotational levels transitions, shouldn't these depend on the object in question? Also, what's the actual reason why there are no contributions from translational motion? And what about excited electrons?