Active questions tagged electromagnetism - Physics Stack Exchange most recent 30 from physics.stackexchange.com 2019-08-17T13:33:11Z https://physics.stackexchange.com/feeds/tag/electromagnetism http://www.creativecommons.org/licenses/by-sa/3.0/rdf https://physics.stackexchange.com/q/493119 2 Are there any real-world examples of refraction of light by magnetic permeability? uhoh https://physics.stackexchange.com/users/83380 2019-07-23T05:56:48Z 2019-08-17T12:31:21Z <p>The question <a href="https://physics.stackexchange.com/q/493117/83380">Fresnel Transmission Coefficient for Magnetic Field</a> is interesting.</p> <p>Thinking about it led me to reflect upon what little I know of the history of optics, with refraction by lenses and prisms being expressed in terms of an index of refraction, which at lower frequencies (microwaves) was related to the dielectric polarizability.</p> <p>Today in optics texts it's usually the electric field amplitude rather than the magnetic field amplitude that's calculated, though we could just as well use either one with the proper conversions.</p> <p>This led me to wonder <em>Are there real-world examples of refraction due to magnetic permeability?</em> </p> <p>You can't focus light with an iron lens because it's opaque and possibly wouldn't have much permeability at such a high frequency. You might be able to make a microwave lens out of ferrite or some other low-loss medium, but <em>for the purposes of this question only</em> I won't call microwaves "light".</p> <p><strong>Question:</strong> In the wavelength range of IR (say about 10 microns or shorter) to near-UV (say about 100 nm or longer) are there any practical <em>examples or demonstrations of</em> refraction by the magnetic permeability of a material?</p> https://physics.stackexchange.com/q/197994 5 Maxwell Stress Tensor at material boundaries Fork2 https://physics.stackexchange.com/users/26017 2015-08-06T08:56:27Z 2019-08-17T06:00:36Z <p>I am trying to grasp the meaning of the Maxwell Stress tensor $T_i^j$ at material boundaries. Concretely, I am trying to calculate the force between two waveguides. The results are given in <a href="http://math.mit.edu/~stevenj/papers/PovinelliLo05.pdf" rel="nofollow">an article by Povinelli et al.</a></p> <p>The problem is, I get the same results when I evaluate the stress tensor IN the material and integrate this over the boundary of the waveguide. $$F_i=\int n_j T_{i,in}^j dS$$ However, since there is a discontinuity of the Maxwell tensor at the boundary, I would expect an extra surface force $f_i=n_j (T_{i,out}^j-T_{i,in}^j)$. This would essentially mean that I would have to calculate: $$F_i=\int n_j T_{i,out}^j dS$$</p> <p>What is wrong with this reasoning?</p> https://physics.stackexchange.com/q/497200 0 How much energy, momentum, and/or angular momentum are lost to radiation in Rutherford scattering? Michael Seifert https://physics.stackexchange.com/users/81133 2019-08-16T17:04:49Z 2019-08-16T19:04:12Z <p>Inspired by <a href="https://physics.stackexchange.com/questions/497176/will-momentum-be-conserved-in-case-of-electrostatic-force/">this question:</a></p> <p>Consider two charged particles, of masses <span class="math-container">$m_1$</span> &amp; <span class="math-container">$m_2$</span> and charges <span class="math-container">$q_1$</span> and <span class="math-container">$q_2$</span>. They approach each other from a great distance, interact via their electromagnetic fields, and end up going in different directions. (For simplicity, let's work in the CM frame.) Usually when we analyse this problem, we assume that the two particles interact via a potential energy <span class="math-container">$$V(\vec{r}_1, \vec{r}_2) = -\frac{q_1 q_2}{4 \pi \epsilon_0 r_{12}}.$$</span> Under these assumptions, via standard arguments, the total mechanical energy <span class="math-container">$E_\text{mech} = \sum_i \frac{1}{2} m_i \vec{v}_i^2$</span>, mechanical momentum <span class="math-container">$\vec{p}_\text{mech} = \sum_i m_i \vec{v}_i$</span>, and mechanical angular momentum <span class="math-container">$\vec{L}_\text{mech} = \sum_i m_i \vec{r}_i \times \vec{v}_i$</span> of the two particles are conserved in the scattering event.</p> <p>However, we also know that these charges are accelerating during their collision, and accelerating charges (can) radiate. This radiation can in principle carry energy, linear momentum, and angular momentum away from the particles.</p> <ol> <li>Do scattering charges radiate net energy? If so, how much?</li> <li>Does the total mechanical momentum of the charges change in the scattering process? If so, what is <span class="math-container">$\Delta \vec{p}_\text{mech}$</span>?</li> <li>Does the total mechanical angular momentum of the charges change in the scattering process? If so, what is <span class="math-container">$\Delta \vec{L}_\text{mech}$</span>?</li> </ol> <p>It seems like this is a natural enough question that someone should have already addressed it, so pointers to the literature (in lieu of a full answer here) would still be helpful. I have a nagging suspicion that there is a nice symmetry argument to be made for question 2 (and possible question 3 as well), but I can't quite put my finger on it.</p> <p>I'm most interested in an answer couched in the language of classical electrodynamics, though if insight can be gleaned from quantum probabilities I'd be happy to hear about it. </p> https://physics.stackexchange.com/q/496976 0 What exactly happens when a charged conductor comes into contact with an electric insulator? Hilbert https://physics.stackexchange.com/users/134777 2019-08-15T14:59:37Z 2019-08-16T11:25:03Z <p>Let us say we have a negatively charged conducting sphere:</p> <p><a href="https://i.stack.imgur.com/exNuD.png" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/exNuD.png" alt="enter image description here"></a></p> <p>If we put an insulator into contact with the sphere: <a href="https://i.stack.imgur.com/nF7oM.png" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/nF7oM.png" alt="enter image description here"></a></p> <p>Would the negative charges located in the contact region transfer from the surface of the conductor onto the surface of the insulator that's in contact with sphere? Would the outcome be any different if the insulator was a dielectric?</p> https://physics.stackexchange.com/q/497105 0 Why is there a negative sign in the (non-relativistic) bivector formulation of the Lorentz force? Draconis https://physics.stackexchange.com/users/221326 2019-08-16T05:32:12Z 2019-08-16T05:32:12Z <p>I'm currently trying to update my understanding of basic (Newtonian, non-relativistic) physics to use bivectors and Clifford products instead of pseudovectors and cross products. And I've come up against that most famous use of cross products, magnetic fields.</p> <p>In the cross product formulation, the B-field is a pseudovector, and the force it exerts on a moving charged particle is <span class="math-container">$\vec{F}_{mag} = q \vec{v} \times \vec{B}$</span> .</p> <p>In the bivector formulation, the B-field is a bivector, and the force it exerts on a moving charged particle is <span class="math-container">$\vec{F}_{mag} = -q\vec{v} \vee \mathbf{B}$</span> (where <span class="math-container">$\vee$</span> is the inner product).</p> <p>Where does this extra negative sign come from? Why doesn't it show up in the cross product formulation?</p> https://physics.stackexchange.com/q/497076 0 The physics of microwave vacuum tubes Physicist137 https://physics.stackexchange.com/users/57094 2019-08-16T02:27:13Z 2019-08-16T05:16:55Z <p>I've searched this extensively, but I couldn't find anything (the only thing I found was <a href="http://www.tubebooks.org/Books/Spangenberg_vacuum_tubes.pdf" rel="nofollow noreferrer">this one</a>). I know this question seems to be more of engineering than physics, but I've found some <a href="https://physics.stackexchange.com/q/202985/">engineering</a> questions in here, so, I'll give a try.</p> <p>I'd like a book which explains vacuum tubes (their design: diodes, triodes, cathode-ray tubes, klystrons, magnetrons, etc). I do not want a book which teaches how to manufacture circuits with these tubes, I want to know about the tube themselves: <em>especially the physics of how they work</em>. And, most importantly, I do not want books who hide the math. Additional points for high power tubes and microwave tubes (especially high powered microwave tubes! :D). My preference goes for rigorous books.</p> <p>Well, I'm comfortable with classical electrodynamics at a graduate level, so, it would be nice to have a book that actually would assume this knowledge (I am asking a lot.. I know.... its okay if the book you recommend doesn't meet all the requirements).</p> https://physics.stackexchange.com/q/435354 0 Coaxial cable with compound dielectric SantiMontouliu https://physics.stackexchange.com/users/185257 2018-10-18T16:00:29Z 2019-08-16T00:01:40Z <p>I'm trying to solve a problem from Reitz and Milford's Foundations of Electromagnetic Theory (3rd ed, problem 4-8), and don't know how to start:</p> <p>A coaxial cable of circular cross section has a compound dielectric. The inner conductor has an outside radius <span class="math-container">$a$</span>; this is surrounded by a dielectric sheath of dielectric constant <span class="math-container">$K_1$</span> and of outer radius <span class="math-container">$b$</span>. Next comes another dielectric sheath of dielectric constant <span class="math-container">$K_2$</span> and outer radius <span class="math-container">$c$</span>. If a potential difference <span class="math-container">$V_0$</span> is imposed between the conductors, calculate the fields <span class="math-container">$\vec{E}(\vec{r}), \, \vec{D}(\vec{r}), \, \vec{P}(\vec{r})$</span> in both dielectrics.</p> <p>I'm assuming I have to use the solution to Laplace's equation in cylindrical coordinates, but I'm not sure about how to use the border conditions.</p> <p>Thanks in advance.</p> https://physics.stackexchange.com/q/336176 0 Finding the induced current in a loop and force acting on the conductor Pame https://physics.stackexchange.com/users/152574 2017-05-29T14:31:29Z 2019-08-15T22:00:50Z <p><img src="https://snag.gy/fKpl0H.jpg" alt="loop"></p> <p>The conductor has a velocity to the right and is part of a closed loop (see the picture). Find the direction of the induced current and the direction of the magnetic force on the conductor</p> <p>There must be induced a magnetic field going into the plane of the paper to counteract the increase in flux going out of the plane of the paper. The force must be going in the opposite direction of the velocity, so using the right-hand rule: straight fingers pointing upwards through the conductor, curled fingers down and thumb to the left, giving a current going counterclockwise. Why is this not correct?</p> <p>When it comes to the force, we know it must be going in the opposite direction of the conductor (Lenz' law), but what if we wanna find it using the right-hand rule? To get that right i have to use that the current goes clockwise (which is correct), but now i have to use the exterior magnetic field to get the force right? Why is this? Why do i have to use the induced magnetic field when finding the induced current, but when im finding the <strong>induced</strong> magnetic force, i have to use the <strong>exterior</strong> magnetic field. Why?</p> <p>In addition, could i use that the direction of the charges is to the right, and use that to find the direction of the current? Whats the difference between a force acting on the conductor, and a force acting on electrons inside the conductor?</p> https://physics.stackexchange.com/q/193337 3 Physical cause of Negative Permittivity user85503 https://physics.stackexchange.com/users/74426 2015-07-09T22:19:09Z 2019-08-15T18:03:05Z <p>What is the physical cause behind a material having a negative real part of its dielectric function? Given the complex permittivity, $\epsilon(\omega)=\epsilon(\omega)'+i\epsilon(\omega)''$, the Drude model gives \begin{align} \epsilon'=1-\frac{\omega_{P}^2}{\omega^2+\omega_{\tau}^2} \end{align} where $\omega$ is the frequency of the incoming light, $\omega_{P}=\sqrt{\frac{Ne^2}{m\epsilon_0}}$ is the plasma frequency, $N$ is the electron density, $m$ is the electron's mass, $e$ is the electronic charge, and $\omega_{\tau}$ is the frequency of collisions between conduction electrons and the ion lattice.</p> <p>If $\omega$ is small enough, then $\epsilon'&lt;0$. But how does this physically happen?</p> https://physics.stackexchange.com/q/496925 0 Potential Drop across Inductor VS Potential drop across Rotating coils in $B$-Field VKJ https://physics.stackexchange.com/users/219729 2019-08-15T06:18:15Z 2019-08-15T15:54:06Z <p>I was trying to understand the difference between the <strong>Back emf generated across Inductor</strong> due to change in current and <strong>Back Emf Generated across a coil</strong> that is rotating in presence of B Field.</p> <p>Intuitively, a potential drop is quantifying the amount of energy dropped by a unit charge moving in a field. I hope this understanding is right.</p> <p><strong>Case1: Inductor</strong></p> <blockquote> <p>Is it correct to say that potential drop in the inductor (due to self-inductance) is to the energy that is dropped by unit charges to build magnetic field around it? This drop-in energy of the electron is modelled as emf across inductor right?</p> </blockquote> <p><strong>Case2: Rotating Machine</strong></p> <p>When current flows through a coil due to a voltage source the rotational force(Torque) comes into picture due to the motion of charges along the conductor. So the coils start to rotate. Back Emf comes into the picture. The potential drop across the coil that is rotating in Presence of External B Field commonly referred to as Back emf in rotating machines.</p> <p><a href="https://i.stack.imgur.com/2aDap.jpg" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/2aDap.jpg" alt="enter image description here"></a></p> <blockquote> <p>Is this the energy spent by electrons to overcome the Lorentz Magnetic force** <strong>acting on electrons</strong> in the opposite direction of electron flow due to the fact that coil moves perpendicular to the field when rotating?</p> </blockquote> <p>**The Lorentz Magnetic force opposing the flow of electron due to the coil(indirectly electron moving in the external B field: The force on the electron is given by F is given by in the below diagram: </p> <p><a href="https://i.stack.imgur.com/b3bMj.jpg" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/b3bMj.jpg" alt="enter image description here"></a></p> <p>Here Consider velocity <strong>v</strong> as the velocity of conductor of the coil due to coils under rotational motion. Since the conductor is moving the Charge is also moving.</p> https://physics.stackexchange.com/q/419958 1 Assistance with visualization of alternating current Steve T. https://physics.stackexchange.com/users/191342 2018-07-28T22:54:15Z 2019-08-15T12:02:40Z <p>Sorry, I'm already ashamed to ask for your help. But I'm feel that I needed in some hints about how to imagine alternating current. I really realize I have trouble with it during reading <a href="http://www1.astrophysik.uni-kiel.de/~hhaertel/PUB/Quality-Electricity.pdf" rel="nofollow noreferrer">this</a> document (full but old version is <a href="https://files.eric.ed.gov/fulltext/ED287730.pdf" rel="nofollow noreferrer">here</a>). There is image on p.29:</p> <p><a href="https://i.stack.imgur.com/W67Cs.png" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/W67Cs.png" alt="enter image description here"></a> </p> <p>At first, this simple circuit consisting of a battery and a resistor was in some steady state with constant voltage and current all around. Then source voltage is doubled. And there is this transient phase on the image during which a new voltage is forming. Pluses/minuses represent surface charges on the wires. The change in charge distribution travels like a wave-front through the circuit with speed of light.</p> <p>I explicitly divide all these states apart. Like, 1st steady state with some current in accordance with Ohm's law > transient phase > new steady state after doubled voltage reached resistor with increased current in wires and the resistor.</p> <p>My problem is that when I try to image AC voltage source instead of DC the mess begins. Since, roughly speaking, there is no steady states now, voltage and charge distribution on the wires is constantly changing. Because of this its hard for me to imagine alternating current in the circuit.</p> <p>Maybe it would be a little easier for me if I knew the following. On the image above, there are 2 regions, behind "wave front", where a new doubled voltage has already been formed and ahead of it, where voltage is still old.</p> <p>So my question is about currents in these regions. Is there in the region behind "wave front" already increased current and its value satisfying I = V/R and ahead the front, correspondingly, old value of current ?</p> <p>If so, I can imagine AC more or less as follows: as voltage propagates down the wires it cause appropriate currents (according to Ohm's law), lets say, in vicinity of wave front. And since length of wires is small in this case, one can think as in some instant of time wave front "ran" through all wire and reach it end. And so we have some concrete equal value of potential for entire length of the wire and appropriate current's value in it.</p> <p>If this is a wrong idea then I'm lost and would like to hear some tips about how to imagine it. Thanks for the help. </p> <p>Updated: Now I think this is most likely incorrect because in that case even in an open AC circuit there would be a "normal" current. Well, after a couple of days of reflection and re-reading I realize I'am confuse charge redistribution processes with "main" current so nevermind. I'm going to rephrase the question. </p> https://physics.stackexchange.com/q/496899 3 Charge distribution for three connected conductor spheres iluvatar https://physics.stackexchange.com/users/82610 2019-08-15T02:41:49Z 2019-08-15T06:55:50Z <p>In the auxiliary material of the physics textbook of Halliday, first chapter about electrostatics, there is an example that has the following statement and solution: </p> <p>basically there are three identical conducting spheres. One has a charge <span class="math-container">$Q$</span>, the others have no charge. The spheres are away from each other. They are now connected by two thin conducting wires (one from sphere 1 to sphere 2. The other from sphere 2 to sphere 3). Then the wire from 2 to 3 is cut, then the wire from 1 to 2 is cut. What is the final charge of sphere 1 ? The surprising answer is <span class="math-container">$Q/4$</span>. </p> <p>It is surprising because one expects it to be <span class="math-container">$Q/3$</span> since that is the only way to guarantee that all spheres are at the same potential when they are all connected. But the original answer, <span class="math-container">$Q/4$</span>, seems to suggest that the charge actually separates as much as possible, going to the extremes (sphere 1 and 3, each one with <span class="math-container">$Q/2$</span>, and the center with null charge) and then, when the first wire is cut, the net charge <span class="math-container">$Q/2$</span> divides among the two still connected spheres. We think is a mistake in the book, because it does not take into account the potential when all spheres are connected, but maybe we are overlooking something. Any guidance for the sake of learning is welcome. Thanks </p> https://physics.stackexchange.com/q/496917 -2 What force per unit of length does each line charge exert on the other? [on hold] Obit11 https://physics.stackexchange.com/users/155863 2019-08-15T05:37:16Z 2019-08-15T05:56:35Z <p>What force per unit of length does each line charge exert on the other? </p> <p>I have Two identical uniform line charges that are <span class="math-container">$d=0.8\,\rm m$</span> apart. They are parallel to the z axis. They have an identical linear density of <span class="math-container">$\rho = 75 \,\rm nC\,m^{-1}$</span>. The picture below is I guess how I visualise this. </p> <p><a href="https://i.stack.imgur.com/RHvX0.png" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/RHvX0.png" alt="How I&#39;m visualising this"></a> </p> <p>So, force per unit length <span class="math-container">$= \frac 12 \rho^2\,\pi\,0.8\,\epsilon_0$</span> </p> <p>So, force per unit length <span class="math-container">$= \dfrac{(7.5\times10^{-8})^2}{2\,\pi\,8.854\times10^{-12}\,0.8}$</span></p> <p>So, per unit length <span class="math-container">$= 1.26\times 10^{-4} \,\rm N\, mC^{-1}$</span></p> <p>Is my logic correct? or flawed? And correct answer with units for answer? </p> <p>Thank you. </p> https://physics.stackexchange.com/q/496915 0 Energy stored in a sphere of variable charge density user208480 https://physics.stackexchange.com/users/208480 2019-08-15T05:33:27Z 2019-08-15T05:33:27Z <p>I have seen a derivation of the energy stored in a uniformly charged sphere. However, I would like to generalize this derivation to include a variable charge density (varying with radius). The derivation starts by fixing a small spherical charge of radius <span class="math-container">$r$</span> at the origin and then adds more charge in a shell over this sphere over and over in an integral using <span class="math-container">$dW = Vdq$</span> where <span class="math-container">$V$</span> is the potential caused by the initial sphere. I am not sure if it follows that we can use the same method for a variable charge density. If not, why not? Is there a preferred method for this without following this derivation?</p> https://physics.stackexchange.com/q/496913 0 RF Transmission Loss Dustin K https://physics.stackexchange.com/users/234450 2019-08-15T05:30:06Z 2019-08-15T05:30:06Z <p>I am aware that an <strong>ideal</strong> 3rd order circuit with R=0 will oscillate forever, but even this this is not true. Power is dissipated through the em waves. </p> <p>How does one calculate the losses due to these emissions? </p> https://physics.stackexchange.com/q/496844 0 Forces between particles rotating and how to represent their effect on them mathematically in 3D ijk-1 https://physics.stackexchange.com/users/239026 2019-08-14T18:52:39Z 2019-08-14T19:51:30Z <p>If 4 atoms are represented in three dimensions, with each particle having coordinates <span class="math-container">$(x,y,z)$</span>, one can compute the rotations around their nucleus with the Rodrigues Rotation formula. I’m now left with the electric and magnetic forces between the particles to finally model mathematically all the particles. Is there any simple way which I can approach the issue with forces acting between particles without having to figure out many angles and partial derivatives to know how it will affect the trajectory of electrons and protons (I’m considering only hydrogen atoms)?</p> https://physics.stackexchange.com/q/496663 6 Are photons emitted by a magnet? Luke https://physics.stackexchange.com/users/106906 2019-08-13T21:30:41Z 2019-08-14T18:14:33Z <p>If you put a photon detector near a magnet (with the magnetic field static in time), is there some probability that the photon detector will detect a photon?</p> <p>Does QFT not predict that a photon could be detected? If we have a uniform static classical <span class="math-container">$\vec{B}$</span> field in the <span class="math-container">$z$</span> direction, e.g. <span class="math-container">$A_{classical}^{\mu}=(0,-By,0,0)$</span> and we couple electrons to this classical field by adding the term <span class="math-container">$H_{interaction}=\bar{\psi}\gamma_{\mu}\psi A^{\mu}_{classical}$</span> to the QED Lagrangian, then there are then Feynman diagrams which seem to indicate that the classical field can produce real photons. (e.g. the Feynman diagram where the classical source emits a photon which fluctuates into an <span class="math-container">$e^{+}e^{-}$</span> bubble with a real photon emitted off of the bubble). </p> https://physics.stackexchange.com/q/496833 0 About fixing the potential on the surface of a conductor Hilbert https://physics.stackexchange.com/users/134777 2019-08-14T17:18:58Z 2019-08-14T17:53:49Z <p>In Purcell's Electricity and Magnetism, p.116 section 3.3, the author spoke about Laplace's equation and said that the boundary conditions for the potential<span class="math-container">$\,\phi$</span> on the surface of the conductor may be fixed:</p> <blockquote> <p>In a real system the potentials may be fixed by permanent connections to batteries or other constant-potential "power supplies."</p> </blockquote> <p>Does it mean then if I had a conductor like this one:</p> <p><a href="https://i.stack.imgur.com/qtIYG.png" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/qtIYG.png" alt="enter image description here"></a></p> <p>I would be able to set the potential <span class="math-container">$\phi$</span> on its surface to a given value by connecting it in the way below?</p> <p><a href="https://i.stack.imgur.com/8neje.png" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/8neje.png" alt="enter image description here"></a></p> https://physics.stackexchange.com/q/477236 0 Net bound current with uniform magnetization sangstar https://physics.stackexchange.com/users/153135 2019-05-01T18:55:55Z 2019-08-14T14:57:34Z <p>My confusion stems from the following:</p> <p><a href="https://i.stack.imgur.com/hSPxD.png" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/hSPxD.png" alt="enter image description here"></a></p> <p>Can I reason the answer being (D) analogous to... for instance:</p> <p>If this was instead a solid cylinder with uniform polarization <span class="math-container">$\mathbf P$</span> pointing in the z-direction, I'd believe the net bound charge would be on the top/bottom surface only. That's because the constituents atoms in the volume will have their electron clouds and nuclei polarize along an external electric field such that the nuclei will tend to move towards the 'tails' of vector field <span class="math-container">$\mathbf P$</span> and the electron clouds away from it. For each electron cloud, there will thus be a neighboring nuclei canceling out its bound charge contribution, except at the top/bottom surfaces where there can be no neighboring charge for the bound charges there.</p> <p>Can I apply this logic here? I also feel like my explanation was a bit confused or muddy. </p> https://physics.stackexchange.com/q/33621 26 How do electrons know which path to take in a circuit? Swapnanil Saha https://physics.stackexchange.com/users/9244 2012-08-07T12:16:16Z 2019-08-14T11:19:06Z <p>The current is maximum through those segments of a circuit that offer the least resistance. But how do electrons know beforehand that which path will resist their drift the least?</p> https://physics.stackexchange.com/q/145954 2 Polarization of a transverse wave travelling in ionosphere with polarization direction perpendicular to earths magnetic field seeking_infinity https://physics.stackexchange.com/users/57676 2014-11-10T17:52:55Z 2019-08-14T07:01:45Z <p>Assume a transverse electromagnetic wave entering ionosphere such that its electric field is perpendicular to Earth's magnetic field. Now, I read that as it will enter plasma, the wave will tend to be elliptically polarized.</p> <p>In other words: if Earth's magnetic field $B$ is in $z$-direction, electric field $E$ of the wave is in $y$-direction and propagation vector $k$ lies in $x$-direction, then it says that $E$ will develop a component along $x$ too.</p> <p>How does that happen?</p> https://physics.stackexchange.com/q/493456 0 Modifying the Hamiltonian when there is a presence of the Coulomb interaction TangBear https://physics.stackexchange.com/users/176782 2019-07-25T01:24:05Z 2019-08-14T02:57:30Z <p>Referring to the Hamiltonian of a system of free electrons,</p> <p><span class="math-container">$$H_0= \sum_{\sigma} \int d^3rd^3r' \psi_{\sigma}^{\dagger}(\mathbf{r})\left(- \frac{\hbar^2}{2m}\nabla^2\right)\delta(\mathbf{r}-\mathbf{r'})\psi_\sigma (\mathbf{r'})$$</span></p> <p>When the Coulomb interaction is turn on, we can modify this Hamiltonian by imposing</p> <p><span class="math-container">$$\partial^\mu\rightarrow\partial^\mu + i \frac{q}{\hbar c} A^\mu$$</span></p> <p>I expected the new Hamiltonian to contain the term like</p> <p><span class="math-container">$$H_{\mathrm{Coulomb}} = \frac{1}{2}\sum_{\sigma,\sigma'}\int d^3rd^3r' \psi_\sigma^\dagger(\mathbf{r})\psi_\sigma(\mathbf{r})\left( \frac{q^2}{4\pi\epsilon_0|\mathbf{r}-\mathbf{r'}|}\right)\psi_{\sigma'}^\dagger(\mathbf{r'})\psi_{\sigma'}(\mathbf{r'})$$</span></p> <p>However, when I substituted this to the free Hamiltonian, I could not see anyway to obtain this result at all.</p> https://physics.stackexchange.com/q/179570 2 Difference between electric and magnetic field (relating to EEG & MEG) Gennadiy Gurariy https://physics.stackexchange.com/users/79280 2015-05-02T02:08:02Z 2019-08-13T23:01:20Z <p>I study cognitive neuroscience and I periodically run into physics related questions in the context of neuroimaging technologies. </p> <p>My question specifically refers to electric and magnetic fields that can be measured by electroencephalography (EEG) and Magnetoencephalography (MEG), respectively. </p> <p>One interesting difference between the EEG and MEG signal is that unlike the electric field, the magnetic field is unimpeded by differing conductances across brain, skull, scalp and other tissues. I was wondering if somebody could explain what differences between the two fields account for these phenomena.</p> https://physics.stackexchange.com/q/496616 0 Is the passage of lightning on a transmission line? [on hold] Goldname https://physics.stackexchange.com/users/95956 2019-08-13T15:56:12Z 2019-08-13T18:02:26Z <p>If so, then shouldn't lightning be reflected back into the sky everytime it hits the earth, due to an impedance change?</p> https://physics.stackexchange.com/q/496606 0 Electromagnetic wave and skin depth, skin effect Harsh Nigam https://physics.stackexchange.com/users/166853 2019-08-13T14:46:23Z 2019-08-13T16:33:56Z <p>In EM theory concept of skin depth is induced which is a measure of how much a EM wave can penetrate the medium, from it arises the concept of skin effect which is for EM wave but we use this to explain flow of current in conductor (most of the current flows over the skin of conductor at high frequency). But all this was derived for EM wave then why are we using it to explain flow of current,which is not em wave ???</p> https://physics.stackexchange.com/q/354333 3 Does a homemade evacuated tube produce X rays? Chemistry4all https://physics.stackexchange.com/users/167718 2017-08-29T11:06:27Z 2019-08-13T16:01:20Z <p>Recently, I've bought a tiny USB powered spark gap bipolar Tesla coil (rated at 15 mA and (35-50)kV). I am a pretty interested in spectroscopy, so I played around with the tesla coil and a couple of Neon bulbs (among others) from which I could get a pretty decent Ne spectrum.</p> <p>The other day , I was wondering if I could build myself a partially evacuated Argon tube which could be powered by the tesla coil.And so I went to the lab to pick a "gas collector tube", I purged it with pure Ar several times, then I connected it to the vacuum pump and I sealed it.</p> <p>Surprisingly, it worked! (see photo below).</p> <p>Then I wondered if it might be producing some low energy X rays (I really doubt it but I decided to test it with an old Ludlum Geiger counter)and indeed the Geiger counter showed quite a high reading.</p> <p>So my question is: <strong>was it really producing x rays as a consequence of the electron impact towards one of the electrodes?</strong> or <strong>was it simply the static interference of the tesla coil with the Geiger counter?</strong></p> <p>Honestly, I really doubt that it was really producing x rays, due to the following points:</p> <ul> <li><p>The vacuum pump used is not a high efficient rotary vacuum pump , so the final pressure is far from an ideal vacuum.</p></li> <li><p>The plasma is very faint (the picture is a 5 second exposure shot)</p></li> <li><p>The Geiger counter shows the similar response whenever it is close to the tesla coil (even if the vacuum tube is not connected)</p></li> <li><p>The signal response is very drastic, that is, the Geiger counter only shows a significant reading when it's just a few cm form the tesla coil, if not there is no signal at all.</p></li> </ul> <p>What do you think?</p> <p><a href="https://i.stack.imgur.com/ojF3V.jpg" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/ojF3V.jpg" alt="enter image description here"></a></p> https://physics.stackexchange.com/q/496613 -2 Pronunciations of Law of Biot & Savart [on hold] StackUpPhysics https://physics.stackexchange.com/users/204000 2019-08-13T15:16:53Z 2019-08-13T15:16:53Z <p>I was studying the Chapter in Magnetic Field due to Current from the Book Principles of Physics by Walker, Hallisay and Resnick. It had the following line-</p> <blockquote> <p>The vector equation and it's scalar form, Eq. 29-1 are known as Law of Biot and Savart (rhymes with "Leo and bazaar").</p> </blockquote> <p>This was mentioned after introducing Biot Savart Law but I couldn't understand what is rhyming here as the words are too different and don't have similar pronunciations at all.</p> https://physics.stackexchange.com/q/496581 0 Finding magnetic flux density of a point a certain distance away from the curved face of a disc magnet [on hold] Max https://physics.stackexchange.com/users/238071 2019-08-13T11:11:12Z 2019-08-13T13:07:22Z <p>I have used this website <a href="http://https:www.supermagnete.de/eng/faq/How-do-you-calculate-the-magnetic-flux-density" rel="nofollow noreferrer">here</a> because I am trying to find a formula that will tell me the magnetic field strength (B) of a point a certain distance away from the <strong>curved part/round face</strong> of a circular/disc-shaped magnet.</p> <p><a href="https://i.stack.imgur.com/Q4h4J.png" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/Q4h4J.png" alt="enter image description here"></a></p> <p>So far on the website, I have found one formula (refer to image) but the formula only gives the B field with respect to Z (magnetic flux along the magnetization axis), Because Z is with reference to a pole face I don't think it will work when trying to find the strength of the B field from X (shown in red on the diagram). How can I modify the equation above to give me the B-Field strength at point X? I'm going to predict that I will need to use Biot-Savarts Law</p> https://physics.stackexchange.com/q/219740 0 Back EMF in Motor Manzoor Shah Khalil https://physics.stackexchange.com/users/99197 2015-11-21T03:25:02Z 2019-08-13T13:02:15Z <p>Why does <a href="https://en.wikipedia.org/wiki/Counter-electromotive_force" rel="nofollow noreferrer">back EMF</a> tend to decrease as the rate of doing work increases. When load increases it reduces the angular speed of motor as a result induce current due to back emf also decreases because the flux changes at a slower rate than before.</p> https://physics.stackexchange.com/q/496531 0 Are the electrons' orbitals the same for all atoms? Matrix https://physics.stackexchange.com/users/238963 2019-08-13T04:29:45Z 2019-08-13T12:49:46Z <p>Are the electronic orbitals of an atom always quantified in the same way (i.e. the same energy required to reach the next level), or does each atom have its own values for each level?</p> <p><img src="https://i.stack.imgur.com/9gfmm.jpg" width="450"></p> <p>If the quantification is universal, then the creation of photons (due to the deexcitation of the electrons) at the wavelength / color corresponding to the transition should be more abundant in the universe than all the other frequency. Except one detects no more photon of a given wavelength than of another.</p> <p>So where is my reasoning error?</p>