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<p>I came across a problem which reads: </p>
<blockquote>
<p>The speed distribution function of a group of <em>N</em> particles is given by:<br>
$dN_v = kv\; dv\; (V>v>0)$<br>
$dN_v = 0 \; (v>V) $<br>
(a) Draw a graph of the distribution function.<br>
(b) Find the constant <em>k</em> in terms of <em>N</em> and <em>V</em>.<br>
(c) Compute the average speed, rms, speed and the most probable speed in terms of <em>V</em>. </p>
</blockquote>
<p>Can anyone please help me solve it?</p>
| 2,721 |
<p>I am reading Pekar's "Research in Electron Theory of Crystals" and I came across a passage I find a bit unclear:</p>
<blockquote>
<p>The theory developed below takes into account the dielectric
polarization of a an ionic crystal by the electric field of the
conduction electron. The local polarization that results from this is
related with the displacement of the ions and consequently is
inertial. It cannot follow the relatively rapidly moving electron and
therefore forms a potential well for the electron. The depth of this
potential well turns out to be sufficient for discrete energy levels
of the electron to exist in it. The electron, being in a local state
on one of these levels, can maintain with it sown field the
aforementioned local polarization of the crystal. Because of their
inertia, the ions are sensitive not to the instantaneous value of the
electron field, but to the average field. The latter can be calculated
as the static field of the $|\psi|^2$ cloud of the electron; it
produces a static polarization potential well, which in turn maintains
the electron stationarily in a local state. Such states of the crystal
with the polarization potential well, which in turn maintains the
electron stationarily in the local state. Such states of the crystal
with a polarization potential well, in which the electron is
localized, were called by the author polarons</p>
</blockquote>
<p>Now, what exactly does he mean by local vs. conduction electrons? Are local electrons those that are not moving and are in the crystal? That doesn't seem right. What does it mean for an electron to be in a local state? (Also what does he mean by "inertial"?) IN fact, it would be nice if one explains this passage in understandable terms so that I can have some intuitive picture in mind. </p>
| 2,722 |
<p>My question is in two parts. </p>
<ol>
<li><p>What is the origin of the electric field from an electric charge and why electron can have so small mass? While on the other hand for a magnetic monopole to create a magnetic field needs to be so heavy? </p></li>
<li><p>And if the magnetic monopole is a hadron what are the constituent elementary particles? What is balancing these energies so that the charges do not explode? </p></li>
</ol>
<p>A simple undergrad level answer will do.</p>
| 2,723 |
<p>I've observed this behavior many times. When it rains, the rainwater will form vertical channels along a glass window. The flow of water is mostly confined within these vertical channels and the channels are (more or less) stable.</p>
<p>But sometimes - and I suspect this happens when the flow intensity in one of the channels increases - the channel will switch from a vertical configuration into a zig-zag configuration. The zig-zag is composed of short segments running horizontally that are connected by semicircular (vertical) segments. The zig-zag is unstable and lasts only for 0.1 second or so. Then the channel reverts to its vertical configuration.</p>
<p>I have made photographs of this behavior but I cannot find them now.</p>
<p>I have seen similar patterns in the book "The self made tapestry" by Philip Ball, page 145. This shows growth instabilities in glass cracks. Is says "at higher speeds the crack becomes oscilatorry with a constant wavelength". This is what I see in the water flow. It feels counterintuitive.</p>
<p>There must be a good explanation for this behavior. Can you point me to it?</p>
<p>EDIT Here is a <a href="http://www.youtube.com/watch?v=mBYc1yB5XVc" rel="nofollow">video</a> .</p>
| 2,724 |
<p>In Zurek's theory of quantum Darwinism, information about the pointer states of a system imprint themselves upon fragments of the environment carrying records about the state of the system. Multipartite entanglement between the system and the many fragments effectively become classical correlations whenever one doesn't have access to all the fragments due to the monogamy of entanglement.</p>
<p>So far, so good, but typically, the fragments are themselves in a superposition; a superposition of their locations, a superposition of the form of their encodings of their records, a superposition of existing and not existing, etc. This problem becomes especially acute whenever the density of record carrying fragments is very low, but still high enough to lead to decoherence. Even only two imprintings upon the environment are enough if the observer intercepts one of them while the other forever escapes him. Given this, how can one perform a proper quantum Darwinism analysis unless one already knew in advance where the record carrying fragments are and the form of their encoding? And to specify where the records are and how they are encoded, doesn't one have to resort to a decoherence analysis of the environment prior to that, and isn't that circular?</p>
| 2,725 |
<p>Reading Dirac's Principles of Quantum Mechanics, I encounter in § 36 (Properties of angular momentum) this fragment:</p>
<p><img src="http://i.stack.imgur.com/z9T4O.png" alt="enter image description here"></p>
<p>This is for a dynamical system with two angular momenta $\mathbf{m}_1$ and $\mathbf{m}_2$ that commute with one another, and $\mathbf{M}=\mathbf{m}_1+\mathbf{m}_2$. $k_1$ and $k_2$ are the magnitudes of $\mathbf{m}_1$ and $\mathbf{m}_2$, so the possible eigenvalues of $m_{1z}$ are $k_1$, $k_1-\hslash$, $k_1-2\hslash$, ..., $-k_1$, and similarly for $m_{2z}$ and $k_2$.</p>
<p>The question is about the two $2k_2+1$ terms shown in the second line of eq (46). Shouldn't the last one be $2k_2+2$?</p>
| 2,726 |
<p>I've come across this explanation that the "arrow of time" is a consequence of the second law of thermodynamics, which says that the entropy of an isolated system is always increasing. The argument is that the past looks different from the future because of this increase in entropy. However, this still doesn't make time vanish, since a hypothetical clock could still be ticking in a completely uniform universe, but only this time there is no change in entropy because it is already at a maximum. In this maximum entropy universe, the past would look just like the future, but that need not mean that time isn't still flowing. It is just that we $\it{associate}$ the flow of time with a change that is recognizable.</p>
<p>But after having watched a few episodes of Professor Brian Cox's Wonders of the Universe, I want to know the deeper reason behind why people make the entropy argument. I've heard Sean Carroll make a similar argument to a group of physicists, so I get the idea it is not just a sloppy popularization.</p>
| 2,727 |
<p>How Dielectrics as an Insulating materials transmit electric effect without Conducting Electricity ? How its Possible ??</p>
| 2,728 |
<p>OK I know that <strong>R= V/I</strong>. I also know that <strong>R = ρl / A</strong> But what I want to know is that what really causes resistance? Is resistance equivalent to force? or is it just a constant?</p>
<p>Also, what causes conductors to heat up overtime when current flows through them? I know that the electrons lose energy and that energy gets converted to heat, but what causes them to lose this energy? Electrons don't collide with atoms or other electrons.</p>
<p><strong>EDIT-1</strong></p>
<p>Also, how does this lost energy gets converted to heat?</p>
| 2,729 |
<p>What's the most fundamental definition of <a href="http://en.wikipedia.org/wiki/Temperature" rel="nofollow">temperature</a>? Is it the definition concern about average energy, number of micro states, or what?</p>
<p>By "fundamental", I mean "to be applied" in such general cases as Black Hole's Temperature, Accelerated Frame's Radiation,...</p>
| 2,730 |
<p>I have a wheel (free to spin around the $z-$axis) with four spokes that is connected by sliding contacts to a circuit with $U_0 = 0,72V$. Also, there is a B-Field parallel to the $z-$axis
<img src="http://i.imgur.com/aLF3N7S.jpg" alt="Imgur"></p>
<p>For the induced electric potential I have:
$$U_i = - \frac{1}{2}(R_{outer}^2 - R_{inner}^2)\omega B$$</p>
<p>(with $\omega$ = angular velocity)</p>
<p>I'm now asked to find out the constant $\omega_0$ after the system is in a stationary state (moves with constant speed). The assignment points out to look at one mesh (with one spoke) on the wheel and to determine if Kirchhoffs second rule applies and if there is a current flowing in a mesh.</p>
<p>The most obvious way I can think of would be (since $U_0$ should be equal in any spoke):
$$U_0 - U_i = 0$$
and to solve for $\omega$. But elsewhere I was told that Kirchhoffs rules don't apply in systems with changing magnetic fields. Also I'm not sure if there still would be an emf induced in stationary conditions since the flow wouldn't change anymore then.</p>
| 2,731 |
<p>In this picture the acceleration vector $\vec{a}$ points upward when the pendulum is halfway</p>
<p><a href="http://en.wikipedia.org/wiki/File:Oscillating_pendulum.gif" rel="nofollow">Click To see animated GIF</a></p>
<p>But according to this picture, the force acts tangentially:</p>
<p><img src="http://i.stack.imgur.com/qki27.png" alt="enter image description here"></p>
<p>Which means the acceleration should be tangential too, and never pointing upward?</p>
<p>So whats right?</p>
| 2,732 |
<p>I need to determine angular velocity of a disc when a man with given mass and speed whacks on the edge of it. </p>
<p>I calculated the total moment of inertia of disc and body, how do I calculate the angular velocity of the disc? ( radius and mass of the disc are also given ).</p>
| 55 |
<p>When physicists talk about the expanding universe they often say that the distant galaxies are not really "moving" away but instead the space itself between us and them is expanding. If this is true then the expansion should apply to every region of space proportionally. Coming from a different direction, we all know from particle physics that atoms are mostly empty space. So doesn't the expansion theory imply that the space inside the atoms is also expanding and, as a result, every single object (excluding the unusual dark stuff) in the universe?</p>
<p>If this is the case then how do measure the difference? It's not so obvious since our meter sticks (or any other apparatus we use to measure space) are also expanding. If the length of my car was 3 meters (say) when I bought it a few years ago it would be more now but I wouldn't be able to tell since the definition of a meter has now changed. Just for clarification, I am talking about the length when the car is at rest with respect to me so relativity doesn't come into equation.</p>
<p>However, there is a way. Measure the distance light travels in a given period of time (off course synchronize your clocks and all that). I am assuming that the speed of light is unaffected by the expansion of space because if this wasn't the case, we would be able to see the whole universe and there would be no such thing as the "observable universe".</p>
<p>So apparently we all are expanding over time but the speed of light is not. Shouldn't the relative speed of light (relative to our measuring techniques) decrease over time as a result? Shouldn't we measure a different speed of light now than a hundred years ago?</p>
| 56 |
<p>Do sound waves in a gas consist of phonons?</p>
<p>What about a glass? Or other non-crystalline materials such as quasicrystals?</p>
<p>How does the lack of translational symmetry affect the quantization of the displacement field?</p>
<p>All the answers so far have treated this question at a much more elementary level than I was expecting. I am already quite familiar with the properties of phonons in crystals. Therefore, do not explain the well-known derivations of the dispersion relation and second quantization of phonons in crystal lattices in your answer (and especially don't get them <strong>wrong</strong>!).</p>
| 2,733 |
<p>How to find velocity and displacement equations from a given force equation? For instance, it was given the following 1-D equation:</p>
<p>$$F = b_1(v_1-v) - b_2 v$$</p>
<p>$v_1$, $b_1$ and $b_2$ are constants.</p>
<p>I know that $F = ma = m\frac{\mathrm{d}v}{\mathrm{d}t}$, but I can't find how to integrate $F$. Is there any technique that can help me or my problem is just calculus?</p>
| 2,734 |
<p>Is there any good reference for conceptual problems for students which learn nuclear physics first time? I am not searching problems that involve difficult calculations. Quite the converse, they should be computational rather simple but conceptually difficult. </p>
| 2,735 |
<p>According to the reports, the shutdown procedures at all the Fukushima reactors were successful, and all the control rods were fully inserted.</p>
<p>So - if there was a meltdown, would the control rods also melt and blend into the resulting material (corium)? If so, would that have the effect of "diluting" the corium in radioactive terms and stabilising it to some extent? (I guess it would depend on the relative melting points of the fuel and the control rods: if the rods are of boron, the melting point is a lot higher than that of uranium.)</p>
| 2,736 |
<p>I've seen the claim that solar eclipses are more common in the southern hemisphere than the northern hemisphere and would like to understand why and if that is the case? Does it relate more to the position of the moon relative to the earth or more to how the earth rotates the sun or is this just hogwash?</p>
<blockquote>
<p><a href="http://science.slashdot.org/story/12/09/17/1152238/curiosity-rover-sees-solar-eclipse-on-mars" rel="nofollow">http://science.slashdot.org/story/12/09/17/1152238/curiosity-rover-sees-solar-eclipse-on-mars</a></p>
</blockquote>
| 2,737 |
<p>Turns out there's <a href="http://en.wikipedia.org/wiki/Tritium_illumination" rel="nofollow">tritium illumination</a> - a tiny very strong plastic tube will be covered in phosphor and filled with tritium. Tritium will undergo beta decay and a flow of electrons will cause the phosphor to glow.</p>
<p>This gives enough light for illuminating hours marks on a wristwatch dial and the hands of the wristwatch for many years and is claimed to not pose health hazard.</p>
<p>Now how it is possible to have energetic enough radioactive decay and no health hazard at the same time?</p>
| 2,738 |
<p>With Hawking radiation, one half of virtual pair falls into horizon and this particle has negative energy.</p>
<p>What would an observer inside horizon observe when seeing negative particles ?
How do these negative particles interact with ordinary matter ?</p>
| 2,739 |
<p>Space looks like time depending on the motion of the observer so I was going to ask if space expansion was the same as the unfolding of time, but this was asked on physics.stackexchange <a href="http://physics.stackexchange.com/questions/32494/the-expansion-of-space-time-est-and-the-one-directional-flow-of-time">before</a> and the answer was that in GR time does not flow - there is no more a flow of time than there is a flow of space.</p>
<p>So instead I'll ask: is space expansion the same as time dilation ?</p>
| 26 |
<p><img src="http://i.stack.imgur.com/Bt418.png" alt="enter image description here"></p>
<p>I wonder how can I prove the fulfillment of the third principle of Nernst of a body that obeys the next expression.</p>
| 2,740 |
<p>I think, the answer is probably yes, but it can be answered by somebody who knows GR much better than I do.</p>
<p>In case of a positive answer, can we say that gravitational radiation will be bent around graviting bodies exactly as light?</p>
| 2,741 |
<p>As far as I know, most of an atom is vacuum. </p>
<p>Therefore, in theory, would it be possible for me to throw a tiny stone through my window without breaking it because no matter actually collides?</p>
| 2,742 |
<p>What does change in magnetic flux mean? How can you change magnetic flux? How does a change in magnetic flux influence a current of electrons (electricity)? </p>
| 2,743 |
<p>Let's say that an observer is moving with the speed of light relatively to an atom that he wants to look into. He has equipment that precise that he can observe the atom and what is inside.</p>
<p>From Einstein's theory we know that for light particles, everything else that moves with velocity smaller than the speed of light, 'looks like frozen, no move'. How would the elements inside the atom look?</p>
| 2,744 |
<p>In a basic friction problem with Block A sliding on top of Block B, the direction of the friction force is usually explained as being simply the opposite of the direction of motion. So if Block A is sliding to the right, the friction force is pointing to the left. But this reasoning implicitly assumes that we are calculating friction force from the reference frame of Block B. What if we instead look at the problem from the reference frame of Block A? To Block A, it looks as if Block B is sliding to the left, so an observer on Block A would say that there is a friction force which, to oppose the direction of motion, points to the right.</p>
<p>It seems counterintuitive and probably wrong for the direction of friction force to depend on reference frame like this. Where is the flaw in the reasoning above? Are the two reference frames described above not exactly equivalent in a way that leads to the force changing directions?</p>
| 2,745 |
<p>The <a href="http://en.wikipedia.org/wiki/Large_Underground_Xenon_Detector">Large Underground Xenon Detector</a> (LUX) recently released results<sup>1</sup> that they have found no signs of dark matter<sup>2</sup> after a ~3 month search this spring and summer. The LUX group plans to spend all of 2014 looking for dark matter interactions with the liquid xenon. (I thought I read somewhere that they were planning on doubling the amount of xenon, but cannot find a link that confirms this).</p>
<p>Early last year, researchers from Chile reported that there was no significant amount of dark matter in the solar vicinity<sup>3</sup>. They studied<sup>4</sup> the motions of about 400 stars within 13,000 lightyears radius from the sun, and all the matter is accounted for in what we see: gas, dust, star, etc., and there's little room for dark matter.</p>
<p><strong>Does it make sense to continue searching for dark matter via direct detection method when research suggests there's nothing to find in our solar vicinity?</strong></p>
<p><strong>Would it make more sense to build more sensitive space-based detectors?</strong></p>
<hr>
<p><sup>1</sup> preprint, <a href="http://lux.brown.edu/papers/LUX_First_Results_2013.pdf">Akerib et al 2013</a></p>
<p><sup>2</sup> article, <a href="http://www.symmetrymagazine.org/article/october-2013/first-lux-result-negates-previous-possible-dark-matter-sighting">K Jepsen, Symmetry Magazine, 2013</a></p>
<p><sup>3</sup> article, <a href="http://phys.org/news/2012-04-dark-theories-mysterious-lack-sun.html">ESO, Phys.Org, 2012</a></p>
<p><sup>4</sup> preprint, <a href="http://arxiv.org/abs/1204.3924">Mono Bidin et al 2012</a></p>
| 2,746 |
<p>I need some books to learn the basis of linear operator theory and the spectral theory with, if it's possible, physics application to quantum mechanics. Can somebody help me?</p>
| 2,747 |
<p>I read Arnold's book <strong>Mathematical Methods of Classical Mechanics</strong> and come across with <a href="http://books.google.com.hk/books?id=Pd8-s6rOt_cC&pg=PA229&lpg=PA229&dq=be+simple+%28multiplicity+1%29+eigenvalues+of+a+symplectic+transformation&source=bl&ots=uKsjzFCKMv&sig=hZCx5PXi5gw6kWt2ZUnxwKtKoDM&hl=zh-CN&sa=X&ei=ikpSU8SrJYLliAeHvIHYBA&ved=0CC4Q6AEwAA#v=onepage&q=be%20simple%20%28multiplicity%201%29%20eigenvalues%20of%20a%20symplectic%20transformation&f=false" rel="nofollow">three problems in page 229</a>.</p>
<blockquote>
<p>1.Let $\lambda$ and $\bar{\lambda}$ be simple (multiplicity 1) eigenvalues of a symplectic transformation $S$ with $|\lambda|=1$. Show that the two-dimensional invariant plane $\pi_\lambda$ corresponding to $\lambda,\bar{\lambda}$ is nonnull.</p>
<p>2.Let $\xi$ be a real vector of plane $\pi_\lambda$, where $Im~\lambda > 0$ and $|\lambda| = 1$. The eigenvalue $\lambda$ is called positive if $[S\xi,\xi] > 0$. Show that this definition does not depend on the choice of $\xi \neq 0$ in the plane $\pi_\lambda$.</p>
<p>3.Show that $S$ is strong stable if and only if all the eigenvalues $\lambda$ lie on the unit circle and are of definite sign.</p>
</blockquote>
<p>In my opinion, it will be difficult to deal with these question with the knowledge in this book.</p>
| 2,748 |
<ol>
<li><p>What's the motivation behind the action principle?</p></li>
<li><p>Why does the action principle lead to Newtonian law? </p></li>
<li><p>If Newton's law of motion is more fundamental so why doesn't one derive Lagrangians and Hamilton principle from it? </p></li>
<li><p>Also does all Lagrangians obey $L=T-V$? </p></li>
<li><p>I think that it's related to the fact that the kinetic energy of the particle at all points on the path or it's travel time is as small as possible? </p></li>
<li><p>If so, How can we derive the principle of least action from this fact in detail?</p></li>
</ol>
| 2,749 |
<p>I can't understand the electrolytic capacitors, when a capacitor has a capacitance of 100 microfarads, does that mean that when it is charged with 100 volts will the charge of the plate be 0.01 coulomb? If there is a part of the plate with no isolation, then I touch it, I will be shocked with a charge of 0.01 coulomb and 100 volts?</p>
| 2,750 |
<p>Is it true that $\left(H^\dagger H\right)^2$ is invariant under $U\left(1\right) \times SU\left(2\right)$ where $H$ is the Higgs field $(1,2,1/2)$?</p>
<p>Does this invariance imply that its hypercharge is invariant under $U\left(1\right)$ and its spin is invariant under $SU\left(2\right)$? . </p>
<p>$$H = [H_+, H_0]$$</p>
<p>$$H_+ = [H_-]$$</p>
<p>but </p>
<p>$$H_0 = [?]$$</p>
<p>$$H^\dagger H = [H_-][H_+] + [?][H_0]$$</p>
| 2,751 |
<p>A few closely related questions regarding the physical interpretation of the S-matrix in QFT: I am interested in both heuristic and mathematically precise answers.</p>
<p>Given a quantum field theory when can you define an S-matrix? Given an S-matrix when can you define a quantum field theory from it? (e.g. I have heard conformal field theories do not have S-matrices, is there a simple heuristic way to understand this? Also, I have heard that it is not possible to define a traditional S-matrix in AdS space.)</p>
<p>How does one, in principle, completely specify the S-matrix of a physical theory and what information is encoded in it? (Do I have to give you both a list of all the stable bound states and single-particle states, as well as the probability amplitudes for scattering from initial and final states? or can I get a way with just telling you some single particle states and from poles in the scattering amplitudes deduce the existence of additional bound states?) </p>
<p>Can two inequivalent QFT's give rise to the same S-matrix? E.g., from the S-matrix of the standard model can one, in principle, read off energy levels of the hydrogen atom and other atoms? </p>
| 2,752 |
<p>Assuming we have a sufficiently small and massive object such that it's escape velocity is greater than the speed of light, isn't this a black hole? It has an event horizon that light cannot escape, time freezes at this event horizon, etc. However this object is not a singularity.</p>
<p>If a large star's mass were compressed to the size of, say, a proton, it would certainly have these properties but it would still not be a singularity as a proton does have volume.</p>
<p>The reason "physics breaks down" at singularities is because we cannot divide by zero, but as long as the proton-sized object has volume, physics won't "break down", yet we still have an event horizon and an object that is invisible (but not undetectable) from the outside.</p>
<p>I have read the answers to <a href="http://physics.stackexchange.com/q/18981/2451">this</a> related question. I'm not sure if they don't address my specific question or if I don't understand the answers.</p>
| 2,753 |
<p>In condensed matter literature, at many places, the phrase 'deep lattice limit' is used. Please tell what is the <a href="http://www.google.com/search?q=%22deep+lattice+limit%22" rel="nofollow">deep lattice limit</a> and the <a href="http://www.google.com/search?q=%22shallow+lattice+limit%22" rel="nofollow">shallow lattice limit</a>?</p>
| 2,754 |
<p>In a well known Maxwell paper he uses the units of wavelength which he calls the Fraunhofer Measure. He states it for the Fraunhofer D and F bands as</p>
<p>$$\lambda_D = 2175 \text{ crazy units} = 589nm$$</p>
<p>$$\lambda_F = 1794 \text{ crazy units} = 486nm$$</p>
<p>So the conversion is:</p>
<p>$$1nm \approx 3.69\text{ crazy units}$$
$$1 \text{ crazy unit} \approx 0.270nm$$</p>
<p>But what is the motivation for this?</p>
| 2,755 |
<p>It is often quoted that the number of atoms in the universe is 10$^{70}$ or 10$^{80}$.</p>
<p>How do scientists determine this number? </p>
<p>And how <em>accurate</em> is it (how strong is the supporting evidences for it)?</p>
<p>Is it more likely (logically >50% chance) that the numbers are right, or is it more likely that the numbers are wrong?</p>
| 846 |
<p>As suggested by one of the commentators on my <a href="http://physics.stackexchange.com/questions/47713/the-story-since-bohr">last question</a>, I am going through Bohr's Nobel prize lecture in order to understand how quantum mechanics was developed. </p>
<p>The lecture describes Planck's observations on radiations. I'd like to know how it was concluded from these observations that energy can only change in discrete amounts and also the derivation of Planck's formula. </p>
<p>The lecture then goes on to Einstein's idea about the restricting condition for vibrational energies of atoms and the specific heats of crystals. Can anyone describe exactly what Einstein's idea was about the specific heats of crystal, how that accentuated the concept of discrete energy variation and how it led to further development of QM?</p>
| 2,756 |
<p>In <a href="http://profmattstrassler.com/2012/12/21/its-not-the-end-of-the-world/" rel="nofollow">this</a> end of the year article, Prof. Strassler mentioned that hidden valley sectors could lead to some still open loopholes concerning the experimental discovery of supersymmetry and other BSM physics at the LHC such as certain kinds of extra dimensions for example. He only explains that these hidden valley sectors are some kind of an extension of minimal supersymmetric models and he does not explain this further when I ask him in the comments.</p>
<p>So I want to ask here:</p>
<p>What exactly are these hidden valley sectors, and how are they related to some kinds of minimal supersymmetric models, such as the MSSM for example? Are they rather ad hoc additions to the minimal models or are they embeded in some theories valid at higher energies?</p>
| 2,757 |
<p>I'm and undergraduate student and I'm doing a report on Quantum computing. As a conclusion of my report I'd like to highlight the latest experimental advances in Quantum Computing, especially in methods like Ion trap and photon polarization. Most of the study I've made is on papers and documents dated 2000 or earlier, so I can't relay on them for this part. I've tried looking to the newest papers i could find online, but they're to specific and detailed and I'm not able to extrapolate something meaningful from them, given the small time I have. I just need to know how far have we come with coherence time, size of networks, number of gates applied et cetera.</p>
| 2,758 |
<p>I'm looking at the 1927 paper of Thomas, The Kinematics of an Electron with an Axis, where he shows that the instantaneous co-moving frame of an accelerating electron rotates and moves with some infinitesimal velocity. He states:</p>
<blockquote>
<p>At $t=t_0$ let the electron have position $\mathbf{r}_0$ and velocity $\mathbf{v}_0$, with $\beta_0=(1-{\mathbf{v}_0}^2/c^2)^{-\frac 1 2}$, in $(\mathbf{r}, t)$. Then, by (2.1), that definite system of coordinates $(\mathbf{R}_0, T_0)$ in which the electron is instantaneously at rest at the origin and which is obtained from $(\mathbf{r},t)$ by a translation and a Lorentz transformation without rotation is gven by $$\begin{align*}\mathbf{R}_0 &= \mathbf{r} - \mathbf{r}_0 + (\beta_0 - 1)\frac{ (\mathbf{r}-\mathbf{r}_0)\cdot \mathbf{v}_0}{{\mathbf{v}_0}^2}\mathbf{v}_0-\beta_0 \mathbf{v}_0(t-t_0)\tag{3.1a}\\ T_0 &= \beta_0\left( t - t_0 - \frac {(\mathbf{r} - \mathbf{r}_0)\cdot \mathbf{v}_0}{c^2}\right)\tag{3.1b}\end{align*}$$</p>
<p>By eliminating $(\mathbf{r},t)$ from equations (3.1) and the similar equations for $(\mathbf{R}_1, T_1)$,$$\begin{align*}\mathbf{R}_1 &= \mathbf{R}_0 + \frac{(\beta_0 - 1)} {{\mathbf{v}_0}^2}(\mathbf{R}_0\times (\mathbf{v}_0\times \mathbf{dv}_0)) - \beta_0 T_0(\mathbf{dv}_0 + (\beta_0 - 1)\frac{(\mathbf{v}_0\cdot \mathbf{dv}_0)}{{\mathbf{v}_0}^2}\mathbf{v}_0)\tag{a}\\ T_1 &= T_0 - \frac {\beta_0} c^2((\mathbf{R}_0\cdot(\mathbf{dv}_0 + (\beta_0 - 1)\frac{(\mathbf{v}_0\cdot \mathbf{dv}_0)}{{\mathbf{v}_0}^2}\mathbf{v}_0))) - d\tau_0\tag{3.3b} \end{align*}$$</p>
</blockquote>
<p>What are the steps to get from (3.1) to (3.3)?</p>
| 2,759 |
<p>Where can one find old Russian scientific papers in physics, say, in the Proceedings of the Russian Academy of Sciences or Zhurnal Eksperimentalnoy i Teoreticheskoy Fiziki? Can they be found online somewhere?</p>
| 2,760 |
<p>According to relativity,nothing can break light barrier.But a recent <a href="http://arxiv.org/abs/1101.1840" rel="nofollow">preprint</a> shows energy transmission of commercial electric power (f=60Hz) is faster than light. (It is not the drift velocity of electrons because energy transport depends on the electromagnetic field instead of charged particles). Moreover, the speed increases as its frequency decreases so the value is infinity for a direct current (f=0).That is action at a distance (instantaneous interaction)!</p>
<p>My question is whether it is possible to design a circuit to compare this speed with c in lab? For example,time-delay of an electromagnetic signal through a free space distance of 3m is $10^{-8}\text{ s}$. As to direct current along a copper wire, however, there should be no delay. Is the difference detectable? I'm interested to the experiment because it is of substantial significance to measure the rate of electric power for electrical engineering not matter the result can exceed c or not.</p>
| 2,761 |
<p>This is a thought I had a while ago, and I was wondering if it was satisfactory as a physicist's proof of the positive mass theorem.</p>
<p>The positive mass theorem was proven by Schoen and Yau using complicated methods that don't work in 8 dimensions or more, and by Witten using other complicated methods that don't work for non-spin manifolds. Recently Choquet-Bruhat published a proof for all dimensions, which I did not read in detail.</p>
<p>To see that you can't get zero mass or negative mass, view the space-time in the ADM rest frame, and consider viewing the spacetime from a slowly accelerated frame going to the right. This introduces a Rindler horizon somewhere far to the left. As you continue accelerating, the whole thing falls into your horizon. If you like, you can imagine that the horizon is an enormous black hole far, far away from everything else.</p>
<p>The horizon starts out flat and far away before the thing falls in, and ends up flat and far away after. If the total mass is negative, it is easy to see that the total geodesic flow on the outer boundary brings area in, meaning that the horizon scrunched up a little bit. This is even easier to see if you have a black hole far away, it just gets smaller because it absorbed the negative mass. But this contradicts the area theorem.</p>
<p>There is an argument for the positive mass theorem in a recent paper by Penrose which is similar.</p>
<p>Questions:</p>
<ol>
<li>Does this argument prove positive mass?</li>
<li>Does this mean that the positive mass theorem holds assuming only the weak energy condition?</li>
</ol>
| 2,762 |
<p>A tennis player has a tennis ball container with a single ball in it (it normally holds three). He shakes the tennis ball horizontally back and forth, so that the ball bounces between the two ends. We model the tennis ball as a quantum particle in a box.</p>
<p>The questions: what is the quantum number n for this ball? If the ball were to absorb a photon and jump to the next energy level, what should the energy (in eV) of that photon be?</p>
<p>For both of these questions, I am confused about how to apply quantum mechanical principles to the tennis ball. For the former, I suppose that a quantum number of n would make sense...if we model it as a particle in the box, the probability distribution across the container would match that of a particle at the n=2 energy level (remember--we are moving back and forth, and therefore the particle would be most likely to be at one of the ends and not in the middle). Would this be the correct reasoning? Is there something else I'm missing? For the latter question, I would use</p>
<p>$$E_n=\frac{n^2\hbar^2\pi^2}{2ma^2}$$</p>
<p>where m is the mass of the tennis ball and a is the length of our container. Say that we are now in the $n=2$ energy level. To go to $n=3$, we have to apply an energy of $\Delta E=E_3-E_2$ to make that jump. Is this the correct procedure for both of these questions? I'm just having a hard time applying quantum mechanical thinking to these macroscopic objects.</p>
<p>Thank you in advance. </p>
| 2,763 |
<p>One way to normalize the free particle wave function </p>
<blockquote>
<p>"is to replace the the boundary condition $\psi(\pm{\frac{a}{2}}) = 0$ [for the infinite well] by periodic boundary conditions expressed in the form $\psi(x)=\psi(x+a)$"
-- <em>Quantum Physics</em>, S. Gasiorowicz</p>
</blockquote>
<p>How does this work? What does this mean physically? Or more precisely, why does this approximation suffice? </p>
<p>I understand that this makes the wavefunction square-integrable (when integrated from $x=0$ to $x=a$) hence normalizable.</p>
<p>Thanks.</p>
| 2,764 |
<p>The edge of a fractional quantum Hall state is an example of a chiral Luttinger liquid. Take, for the sake of simplicity, the edge of the Laughlin state. The Hamiltonian is:</p>
<p>$$H = \frac{2\pi}{\nu}\frac{v_c}{2} \int_{\textrm{edge}} dx \rho(x)^2 $$</p>
<p>Here $\nu$ is the filling fraction, which is constant, $v_c$ is the velocity of the edge mode and $\rho$ is the charge density operator. You can think of this Hamiltonian as a delta-function interaction $V(x,x') = \delta(x-x')$. </p>
<p>Together with this Hamiltonian there is also the commutation relation of the field $\rho$:</p>
<p>$$ [\rho(x),\rho(x')] = i\frac{\nu}{2\pi} \partial_x \delta(x-x')$$</p>
<p>I haven't gone through the exercise myself, but I presume this is derived by going to momentum space, obtaining the canonical momenta through Hamilton's equation of motion and performing a canonical quantization. These equal-time commutation relations together with the Heisenberg equations of motion lead to:</p>
<p>$$\partial_t \rho(x,t) = i[H,\rho(x,t)] = v_c \partial_x\rho(x,t) $$</p>
<p>This demonstrates that the edge is chiral, since $(\partial_t - v_c\partial_x)\rho(x,t) = 0$ and therefore the correlator involving $\rho(x,t)$ (or any other correlator) is a function of $t+x/v_c$ alone (hence the name "chiral" and "left-moving"). </p>
<p>There are also particle excitations (e.g. the electron) which are generated through vertex operator $\Psi(x,t)$ (these can be motivated through bosonization and/or conformal field theory, but I won't go into that). In any case these field operators have the following equal-time commutation relations with the current operator:</p>
<p>$$[\rho(x),\Psi(x')] = Q \Psi(x')\delta(x-x')$$</p>
<p>Here $Q$ is the charge of the operator $\Psi$ with respect to the charge density operator $\rho$. This charge is then of course the electric charge.</p>
<p>My question is now: how do you generalize the commutation relations to non-equal time? What is:</p>
<p>$$[\rho(x,t),\rho(x',t')] = \ldots $$
$$[\rho(x,t),\Psi(x',t')] = \ldots $$</p>
<p>?</p>
| 2,765 |
<p>So I am studying for a final and can't seem to solve this. There is a log floating in water and I need to find its weight. The question I have is what parts of the volume of the log count when summing the forces in the Y axis.</p>
<p><img src="http://i.stack.imgur.com/108N2.png" alt="enter image description here"></p>
<p>What i have now for AREA alone is $r^2 - .25\pi r^2$ pushes down
and $.5\pi r^2 + r^2$ pushes up. however this does not take into account the air above the log in the upper right quadrant. is the force pushing up taking into account the half circle below the water and also the $2r^2$ above the horizontal of the log?</p>
<p>The actual question for this image says:
A log is stuck against a dam as shown in the diagram. given the radius of the log of 1.4 m and the length of the log into the page, 10 m find the weight of the log in kN.</p>
| 2,766 |
<p>I am seeking an algorithm to generate a random wavefunction = $\sum {c_i |\varphi _i\rangle }$ from a thermal ensemble, whose density matrix $\rho \sim e^{-\beta H}$, without the need to diagonalize the Hamiltonian. One possible method is to generate a random number for each basis and compare it with $e^{-\beta \langle\varphi _i|H|\varphi _i \rangle }$ and if it is lower we assign the corresponding $c_i$ to complex number with norm = 1 and totally random phase and otherwise make it just zero. Another possible algorithm to assign all $c_i$ to random complex numbers of norm one and then evaluate $e^{- \frac{\beta}{2} H}|\psi \rangle$. Are there other algorithms?</p>
<p>Edit:
I now tried the second method with evaluating $e^{- \frac{\beta}{2} H}|\psi \rangle$ by propagating the wavefunction in imaginary time and it works fine! So I recommend this one.</p>
| 2,767 |
<p>When one is doing zeta-function regularization of the heat-kernel for QFT then one is doing these following steps,</p>
<ul>
<li>the integral over the imaginary time</li>
<li>taking the trace of the heat-kernel or the short-distance limit </li>
<li>the space-time volume integral</li>
</ul>
<p>I would like to know as to what justifies the sequence in which these steps need to be done.
I have generally seen it being done in the order as listed above but its more or less clear from working with examples that the answer clearly depends on which order on does it. </p>
<p>Or is the art of regularization about being able to choose the "right" sequence depending on the situation?
But is there an argument as to why there should be only one particular sequence which will generate a finite answer? </p>
<p>Also in some examples it seems that the order needs to be changed whether one is regularizing the zero-modes of the theory or not. But that doesn't seem consistent! That would effectively mean doing a different regularization for different terms of the same expression! </p>
| 2,768 |
<p>I'm a first year physics student and the main source for our Physics I course is "Berkeley Physics Course - Volume I."
I'm having a hard time understanding this book because it assumes a pretty high level of previous knowledge, and the mathematical level is also advanced. </p>
<p>Is anyone familiar with a site that assists with this book in particular, or some kind of accompanying source?</p>
| 2,769 |
<p>Magnetic fields are obvious distortions.. of.. something, but what exactly are they distortions of? Massive objects produce curvatures/gradients in space-time resulting in what we observe as gravity.. what is the equivalent explanation for magnetic/electric fields?</p>
| 2,770 |
<p>I require only a simple answer. One sentence is enough... (It's for high school physics)</p>
| 2,771 |
<p>Seeing an interesting BBC article today at <a href="http://www.bbc.co.uk/news/science-environment-23514521" rel="nofollow">http://www.bbc.co.uk/news/science-environment-23514521</a> about the Longitude Problem, I wondered if it could have been solved, in a way practical at the time (the 18th century), by any means other than the solution eventually found.</p>
<p>So if fanciful, but possibly entertaining and instructive, questions are allowed here, suppose you were transported back to the early 18th century and forbidden from disclosing any fundamental physics unknown at the time, explicitly or otherwise. Would you, knowing what we do today about classical physics and astronomy etc, have any ideas for bagging that prize money, aside from building a sufficiently accurate clock?</p>
| 2,772 |
<p>I learned electrodynamics.
According to the vector potential determination,
$$
\mathbf B = [\nabla \times \mathbf A ],
$$
Coulomb gauge,
$$
\nabla \mathbf A = 0,
$$
and one of Maxwell's equations,
$$
[\nabla \times \mathbf B ] = \frac{1}{c}4\pi \mathbf j,
$$</p>
<p>I can assume, that</p>
<p>$$
[\nabla \times \mathbf B ] = \nabla (\nabla \mathbf A) - \Delta \mathbf A = -\Delta \mathbf A = \frac{1}{c}4 \pi \mathbf j.
$$
How to prove that the one of the solutions of this equation is solution like newtonian potential,
$$
\mathbf A = \frac{1}{c}\int \limits_{V} \frac{\mathbf j (r) d^{3}\mathbf r}{|\mathbf r - \mathbf r_{0}|}?
$$</p>
| 2,773 |
<p>I am a postgraduate in mathematics. I studied physics during my B.Sc.studies.I want to go for further studies in physics particularly in theoretical physics. I am in a job and cant afford regular classroom teaching. Could anyone tell me something about some distance education programs? or are there programs for mathematics graduates to work in theoretical physics areas like string theory? </p>
| 2,774 |
<p>The theory of an anti-reflective coating is that the reflected light off the coating and the reflected light off the substrate is 180 degrees out of phase, causing destructive interference and subsequently no light is 'reflected'. But how does this process allow more light to pass through the substrate. Because although the reflected light is causing destructive interference, before the light leaves the coating, it is still reflected, meaning that light has still been lost.</p>
| 2,775 |
<p>Why is the force required to slide a magnet off a steel plate A LOT less than the force required to directly pull it off?</p>
<p>The force required to pull the magnet can be: 20lb
While the force required to slide the magnet can be: 1lb more/less.</p>
<p>Why is that?</p>
| 2,776 |
<p>I refer to the time-domain version of the Poyinting theorem in electro-magnetism:</p>
<p>$- \displaystyle \oint_S (\mathbf{E} \times \mathbf{H}) \cdot d\mathbf{S} - \int_V \mathbf{E} \cdot \mathbf{J}_i \ dV = \int_V \frac{\partial}{\partial t} \frac{\mu |\mathbf{H}|^2}{2} \ dV + \int_V \frac{\partial}{\partial t} \frac{\epsilon |\mathbf{E}|^2}{2} \ dV + \int_V \sigma |\mathbf{E}|^2 dV$</p>
<p>where $S$ is the boundary surface of the integration volume $V$. With $\mathbf{J}_i$ I mean impressed currents (imposed by some field source, like antennas) and with $\mathbf{J}$ I mean induced currents (induced on some conductor, if present, into $V$).</p>
<p>The product $\mathbf{E} \cdot \mathbf{J}_i$ must be negative if $\mathbf{J}_i$ is the current that generates $\mathbf{E}$. But if some current $\mathbf{J}_i$ generates power into $V$, some power should enter $V$ to feed $\mathbf{J}_i$.</p>
<p>If there is a Poynting vector entering $V$ and providing power to $\mathbf{J}_i$, can we consider both (the Poynting vector and the current $\mathbf{J}_i$) as increasing the power into $V$, and so both negative? Should not the Poynting vector entering $V$ be considered the only source of power in $V$?</p>
<p>As an example we can consider a volume $V$ enclosing an antenna. There will be a term $\mathbf{E} \cdot \mathbf{J}_i$ due to the radiation; there will be a Poynting vector <em>exiting</em> from the volume (radiated power); but what about the Poyting vector related to the feed line of the antenna? It is <em>entering</em> the volume and it has a different form than the previous one, because it is the Poyting vector of a transmission line and not of a radiated field. How is it represented in the above equation?</p>
<p>Thank you anyway!</p>
| 2,777 |
<p>I have calculated a tree level amplitude for Compton scattering (${e\left(p\right)+\gamma\left(k\right)\to e\left(p\prime\right)+\gamma\left(k\prime\right)}$):</p>
<p>$${
i\mathcal{M}=M_{\mu\nu}\epsilon^{*\mu}\left(k\prime\right)\epsilon^{\nu}\left(k\right)\textrm{.}
}$$</p>
<p>How should I go about trying to verify that it is gauge invariant?</p>
| 2,778 |
<p>I get water to my home from a nearby Tank A at a certain height above ground level.
I have a 1" pipe through which I get this water to my home.. I leave this water into my well by connecting a 1" tube to this pipe. </p>
<p>Reason for question: I have seen water pressure vary(lower- more flow) depending upon the height I hold my pipe(on the outlet side) when I empty my fish tank, keeping how deep the pipe is immersed on the other side a constant. </p>
<p>Now, if I elongate and leave the pipe from Tank A at deeper level below ground level should the flow rate increase?(will i get more water in the same time) as apposed to a shorter pipe which still goes into my well.</p>
<p>or simply:
Will I empty my overhead tank on 2nd floor quicker if I use the tap on the ground floor instead of the tap on the second floor. The taps being same size.</p>
| 2,779 |
<p>Can we get high energy from laser like fusion and fission reactions ? what is highest energy we can get from laser ?</p>
| 2,780 |
<p>Title says it all.</p>
<p>Have they been seen in experiment or are they just theoretical things?</p>
<p>Do quarks really exist?</p>
| 2,781 |
<p>I was wondering whether there is an equation that enables me to calculate the reflection, transmission, absorption and polarization, when the electric field everywhere is given?</p>
<p>Consider this: You have solved the full Mie scattering process, so incident field, the field in the sphere and the scattered field are known. How can one calculate those quantities then?</p>
| 2,782 |
<p>Even on a current new 2012 car, when the green LED clock inside the car is quite bright, but when the car's headlight is turned on, the clock dims down to only about 1/4 of its brightness, which makes the time hard to see.</p>
<p>I thought the clock requires merely a watt or even less for its brightness, and the car stereo which output at least 30 watt of music (if comparing a 30 watt speaker for the PC to the car stereo), won't be less loud when the headlight is turned on.</p>
<p>Why does the clock dim down so much? Is it explained by Ohm's law? Also, can't it be "parallel" instead of "in series" with the headlight, so that the brightness is not affected?</p>
| 2,783 |
<p><strong>The situation</strong></p>
<p>An inclined conveyor belt with topmost point $h$ height above the ground receives sand at a constant rate $X$ from a container at a negligible height above the lowermost point of the conveyor belt. There is sufficient friction on the conveyor belt so that the sand stops almost immediately after coming in contact with the belt.</p>
<p><strong>The question</strong></p>
<p>On trying to find the minimum force required to maintain this situation, miraculously (after making some appropriate assumptions) the force needed at the bottom most point for the sand to start moving and the force required to maintain the motion of the sand on the conveyor belt above that point have to be same for the total force exerted by the conveyor belt to be minimum.
Mathematically it is easy to reach to this conclusion but I can't understand why this happens physically. </p>
| 2,784 |
<p>EDIT: I think I can pinpoint my confusion a bit better. Here comes my updated question (I'm not sure what the standard way of doing things is - please let me know if I should delete the old version). The major change is that I removed focus from the third question which probably is a purely mathematical question (in the notation below, it asks what properties of (M,T) together with (M,T) being consistent, forces (M,T) to be unique.).</p>
<p>Say that a pair (M, T) is <em>consistent</em> if it satisfies the Einstein field equations. Here M is a manifold with a metric g (from which one can define its Ricci tensor among other things) and T is a map from M to tensors living in the same space of tensors as the Ricci tensor (I ignore units for now). I put absolutely no other restrictions on (M, T).</p>
<p>Now relativity makes perfect sense to me as a mathematical statement: it distinguishes some pairs (M, T) as 'consistent'.</p>
<p>Therefore, if we had a way to map "our world" to a pair (M,T) at least we could theoretically check whether (M,T) is consistent or not. My problem is that I do not at all understand how to do this. </p>
<p>To begin with, which set do I choose for M?</p>
<p>I think I can answer this question myself. I take this set to be the set of intuitive descriptions(that I can make intuitive sense of) of events in the world. For example, E := "(a particular point in) Stockholm on 08:00, Jan 24, 2013". This description I could understand intuitively, and at least theoretically (if time permits) I could go there to check the theory if it makes a statement about E. Another kind of description, given already another description F, could be G:="the event I get to by using rocket R, travelling for time T according to this watch I bring with me, from G", where R and T are intuitive descriptions. Please let me know if this choice of set is inappropriate.</p>
<p>In this case I have no problem of turning the set M into a manifold, not yet with a metric.</p>
<p>Finally (and here is my confusion): I am at a point p (constructed as above). What (intuitively described) experiments do I perform to find the metric tensor at p, respectively the stress-energy tensor at p?
I cannot come up with two different answers for these two tensors - and in this case the theory is not a very interesting one, since then it just predicts that two identical (in the intuitive sense) experiments are the same.</p>
<p>If I try to get an answer to this from e.g. Wikipedia I get lost in a deep tree of coordinate-dependent definitions which in some places appear to assume I already have intuitive sense for both mass and metric, and that I have intuitive sense for these being the related as relativity predicts they should be. I'm hoping there are two distinct intuitively described experiments I could perform, which relativity predicts should have the same result.</p>
<p>FINAL EDIT: I have received many useful comments, and the answer by Ron Maimon answers my initial question, which was "what is a suitable set to choose for M when trying to map 'our world' to a pair (M,T)?". It seems a definition such as I suggest above "should work", as should that described by Ron in his answer. Furthermore, Ron points out(I think) that it is an assumption of the theory that any such labeling should give the same results.</p>
<p>Since my initial question is answered I accept Ron's answer and will possibly come back with my further question "how to intuitively understand the metric and stress energy tensors in terms of experiments any person with sufficient degree of common sense and superhuman abilities (by which I just mean, can reach high accelerations, is not so heavy as to affect the stress-energy tensor in significant ways et.c. Equivalently, superhuman abilities would not be needed in case the speed of light was something like 10 meters per second) could perform?" if I am able to formulate it in a precise way.</p>
<p>OLD VERSION (not needed for the question):
As far as I understand, <a href="http://en.wikipedia.org/wiki/General_relativity" rel="nofollow">general relativity</a> states that </p>
<p><em>the world is a manifold M, and M is completely described by the Einstein field equations.</em></p>
<p>This already appears as an incomplete statement, and I'll explain why I think so. Before that:</p>
<ul>
<li>what is a complete statement of general relativity, possibly including undefined terms (so in my attempt above, the "is" in "the world is a manifold" and "Einstein field equations" are undefined terms)?</li>
</ul>
<p>Now to why this does not make sense to me. The Einstein field equations state that two tensors (it is not necessary to define tensor for my confusion to arise) agree <em>at every point</em>.</p>
<p>This seems to presuppose that the set of points making up the manifold is already given. Thus:</p>
<ul>
<li>what is a good description of the set of points of M?</li>
</ul>
<p>For clarity, my definition of manifold M says for one thing that M is a <em>set</em>.</p>
<p>For the first question, it appears to me that there need to be some extra assumptions, since one could conceivably think of a 'world' without matter which should be completely 'flat', and also of our world which is not. These cases should clearly be different.</p>
<ul>
<li>Exactly what data determines a 'theory'? (meaning that M is completely determined from this data - again I would like to have complete description but am happy with undefined terms as long as it is clear that they are such)</li>
</ul>
<p>Ideally, the second and third questions should be answered by any answer to the first question, but I added the latter questions to indicate what confuses me particularly.</p>
| 2,785 |
<p>I've been wondering about the porosity of materials, I know that, for example the air comes out of tires/balloons because (besides having huge gaps on the rim contact area/knot) they are made of a porous material, but it has nothing to do with molecules, because the porosity appears in a much larger scale.</p>
<p>Now, let's say we have a flask made of a solid material, and let's say it's "perfect", I mean, the molecules are perfectly aligned, and it has a normal thickness like 1mm or so, if we fill this flask with a gas and put it in a vacuum chamber*, will the gas come out over time? I don't know if all elements have "alignable" molecules, but you have the idea.</p>
<p>*-let's say it's an inert chamber, no gravity, radiation and stuff.</p>
<p>I have a few possibilities I could think of:</p>
<ul>
<li>It depends on the size of the gas molecule and the gaps between the molecules on the solid material. If it fits in, then yes.</li>
<li>It isn't possible because the forces keeping the molecules on the solid material together would also keep the gas molecules from transpassing it.</li>
<li>If the above is correct, after some time the flask itself would disintegrate (?) depending on how strong is the force keeping the molecules together. I know that in normal conditions, objects are always "losing" molecules, but will it happen in this hypothetical chamber also?</li>
</ul>
| 2,786 |
<p>Consider a solid ball of radius $r$ and mass $m$ rolling without slipping in a hemispherical bowl of radius $R$ (simple back and forth motion). Now, I assume the oscillations are small and so the small angle approximation holds. I wish to find the period of oscillation and I analyze the motion in two ways, first using conservation of energy and secondly using dynamics. However, I receive two inconsistent answers. One or both of the solutions must be wrong, but I cannot figure out which one and more importantly, I cannot figure out why. </p>
<p><strong>Method 1</strong>: We write the energy conservation equation for the ball</p>
<p>$mgh + \frac{1}{2}mv^2 + \frac{1}{2}I\omega^2 = Constant$</p>
<p>from the center of mass, we take the height as $h = R-(R-r)cos\theta$ where $\theta$ is the angle from the vertical. Applying the no slip condition $v = r\omega$ and taking the moment of inertia for a solid sphere $I = \frac{2}{5}mr^2$ we can write the energy equation as</p>
<p>$mg(R-(R-r)cos\theta) + \frac{7}{10}mr^2\omega^2 = Constant$</p>
<p>Differentiating with respect to time:</p>
<p>$mg(R-r)sin\theta\cdot\omega + \frac{7}{5}mr^2\omega\cdot\alpha = 0$</p>
<p>taking the small angle approximation $sin\theta = \theta$ we get</p>
<p>$g(R-r)\theta + \frac{7}{5}r^2\alpha=0$</p>
<p>$-\frac{5g(R-r)}{7r^2}\theta = \alpha$</p>
<p>from which we can get $T = 2\pi\sqrt{\frac{7r^2}{5g(R-r)}}$</p>
<p><strong>Method 2</strong>: The only torque acting on the ball at any point in its motion is the friction force $f$. So we can write</p>
<p>$\tau = I\alpha = fr$</p>
<p>again using the rolling condition $a = r\alpha$ and the moment of inertia for a solid sphere,</p>
<p>$\frac{2}{5}ma = f$</p>
<p>The net force acting on the system is the tangential component of gravity and the force of friction, so</p>
<p>$F = ma = mgsin\theta - f$</p>
<p>$\frac{7}{5}a = gsin\theta$</p>
<p>taking the small angle approximation and converting $a$ to $\alpha$ we get</p>
<p>$\alpha = \frac{5g}{7r}\theta$</p>
<p>and a corresponding period of $T = 2\pi\sqrt{\frac{7r}{5g}}$</p>
<p>Now the solutions are very different and I would appreciate it if someone would point out where I went wrong.</p>
| 2,787 |
<p>What is the relationship of <a href="http://en.wikipedia.org/wiki/General_relativity" rel="nofollow">General Relativity</a> and <a href="http://en.wikipedia.org/wiki/Newton%27s_law_of_universal_gravitation" rel="nofollow">Newtonian</a> <a href="http://en.wikipedia.org/wiki/Newton%27s_laws_of_motion" rel="nofollow">Mechanics</a>? Namely, which laws does GR replace of Newtonian Mechanics, and which laws of Newtonian Mechanics are incorporated into it. Or is GR a complete replacement and overhaul?</p>
| 2,788 |
<p>Consider a system of particles where the kinetic energy of the system is varying with time. I'd like to know the significance (or meaning) of the time derivative of the kinetic energy being zero at a point. What is the significance of time instances where the kinetic energy has maxima and minima ?</p>
| 2,789 |
<p>Someone once incorrectly told me that, given the speed of light is the speed limit of the universe, aliens would have to live for hundreds of years if they are to travel distances of hundreds of light years to reach Earth.</p>
<p>In a "special relativistic" and non-expanding universe however, this is not the case. As velocity approaches the speed of light, say $v = 0.999c$, then we have </p>
<p>$\gamma = \frac{1}{\sqrt{1-\frac{(0.999c)^2}{c^2}}} = \frac{1}{\sqrt{1-\frac{0.998001c^2}{c^2}}} = 22.37$ </p>
<p>Let us assume that an alien wishes to travel 100 light years from his planet to Earth. If the alien is travelling at $v = 0.999c$, he will observe the distance between his planet and the Earth to contract, and will measure the contracted distance to be:</p>
<p>$Distance = \frac{100ly}{\gamma} = \frac{100ly}{22.37} = 4.47$ Light years.</p>
<p>The Alien will be able to travel this distance in a time of :</p>
<p>$Time = distance/speed = 4.47/0.999 = 4.47 years$</p>
<p>It is easy to show that as the alien's speed increases, the time taken to travel the 100 light year distance approaches 0. It can thus be shown that thanks to length contraction and time dilation of special relativity, all parts of a special relativistic universe are accessible to an observer with a finite life time.</p>
<p>We however don't live in a purely special relativistic universe. We live in an expanding universe. Given the universe is expanding, are some parts of the universe no longer theoretically accessible to observers with finite life times? </p>
| 2,790 |
<p>Notation: The magnetic field $\mathbf{B}$ generated by a point charge $e$ moving with velocity $\mathbf{v}$ is given by <a href="http://en.wikipedia.org/wiki/Biot%E2%80%93Savart_law" rel="nofollow">Biot-Savart's law</a></p>
<p>$$\mathbf{B} = \frac{\mu_0 e\ \mathbf{v} \wedge \mathbf{r}}{4\pi r^3}$$ where $\mathbf{r}$ is the vector from the charge to the point at which the field is measured, $r = \left| \mathbf{r} \right|$, and $\wedge$ denotes vector product. </p>
<p>Question: According to my book: Since $\mathbf{r}\, / \, r^3 = - \,\textrm{grad} \left(1\, /\, r \right)$, we have $$\textrm{div} \left( \mathbf{v} \wedge \frac{\mathbf{r}}{r}\right) = \mathbf{v} \wedge \textrm{curl} \left( \textrm{grad} \frac{1}{r}\right) = 0.$$</p>
<p>What I have is $$\textrm{div} \left( \mathbf{v} \wedge \frac{\mathbf{r}}{r}\right) = \mathbf{v} \, . \, \textrm{curl} \left( \textrm{grad} \frac{1}{r}\right) - \left( \textrm{grad} \frac{1}{r} \right) \, . \, \textrm{curl} \ \mathbf{v},$$ so I think there is a typo in the book ($ \, \wedge$ should be $\, . \,)$. However, I still don't know how to go from my equation to the correct one. Is it because $\textrm{curl} \ \mathbf{v} = 0$? If so, why? I understand that the curl of a gradient vanishes identically.</p>
| 2,791 |
<p>Some time ago I asked a question about gravity on a hemispherical planet.</p>
<p><a href="http://physics.stackexchange.com/questions/29707/what-would-gravity-be-like-on-a-hemispherical-planet">What would gravity be like on a hemispherical planet?</a></p>
<p>Would the water all boil away at first, quickly cooling the core of the planet? Would the ocean boil for centuries?</p>
| 2,792 |
<p>I'm trying to model a flexible stick with a partial differential equation. I want one of the ends to be fixed and the other end to swing. </p>
<p>Do you guys know of any good models I can use? Any references would be appreciated. </p>
| 2,793 |
<p>Just what the title states with the qualification that the change must be affected without using other celestial bodies as mentioned in the Clarke/Baxter SF 'Sunstorm'.</p>
<p>Obviously given the momentum of Earth it would require a major something to break the inertia. But something like the way an ice-skater whilst spinning on their own axis can apply a touch of heel/toe at the correct point to change the way they spin. For instance, change the rate at which our oceans move with the spin of Earth ... </p>
<p>This is a 'curiosity' question rather than a real-life problem so please feel free to vote to close.</p>
| 2,794 |
<blockquote>
<p><em>One charge density surface is distributed uniformly in one infinity tape of length with $2a$ width from distance $d$. Determine the Electric Field in the point perpendicular from the distance $d$ of the centre of tape.</em></p>
</blockquote>
<p>Answer: </p>
<blockquote>
<p>$\frac{\rho_s}{\pi\epsilon_0}\tan^{-1}(a/d)$</p>
</blockquote>
<p>PS.: I tried every ways (Coumlomb Law and Gauss Theorem)</p>
<p>Gauss Theorem (I guess closer)</p>
<p>Consider cylindrical surface:</p>
<p>$Q = \int_v \rho_v dv = \rho_s.2a.L$ (Call L as infinity length)</p>
<p>$Q = \oint_s \vec{D}.d\vec{S} = D_r . 2\pi.d.L$</p>
<p>$\Rightarrow E = \large\frac{\rho_s}{\pi\epsilon_0}\frac{a}{d}$</p>
<p>Coulomb</p>
<p><a href="http://i.stack.imgur.com/Ks4gC.jpg" rel="nofollow">http://i.stack.imgur.com/Ks4gC.jpg</a></p>
<p>The image woth more than thousand words.</p>
<p>Please I'd like some advise to solve this problem. </p>
<p><a href="http://i.stack.imgur.com/Ks4gC.jpg" rel="nofollow">http://i.stack.imgur.com/Ks4gC.jpg</a></p>
| 2,795 |
<p>I have been told all my physics life that potential energy between two mass/charge has no meaning and only their difference has meaning. The same goes for electric potential, only the difference matter.</p>
<p>Perhaps I am not understanding it correctly, but before I talk about masses, let's talk about potential energy/potential associated with two charges. </p>
<p>I am not sure where had I seen it, but a long time ago I was presented with a problem like this. Let's say I have a +Q and a -Q. What is the potential energy between them?</p>
<p>The change in potential energy is the negative work done by the conservative force namely (vector sign and dot product got rid of, since the cosine 1)</p>
<p>$\Delta U = -\int_{a}^{b} k(Q)(-Q) \frac{1}{r^2} = -k(Q)(-Q) \left. \frac{-1}{r} \right |_{a}^{b} = -k(Q)(-Q) \left (\frac{1}{b} - \frac{1}{a} \right) $</p>
<p>Now I assume that I brought it from infinitely far, so that 1/a = 0</p>
<p>In that case I am left with $\delta U = \frac{kQQ}{b}$</p>
<p>Here are my questions</p>
<p>1) A long time ago, I saw a formula looking EXACTLY like what I just did there, but it doesn't concern with the <em>change</em>, it's just gives me the potential energy. Now the formula I remember was $U = -\frac{kQq}{r}$ where there is a negative. I thought this formula already takes care of the signs? Or am I wrong? </p>
<p>2) Kinda the same concept. If I tell you some charge (not telling you the sign) has a electric field and you have another charge (which is the test particle, not telling you the sign again even though it is conventional to use + charge ) somewhere in that field. I tell you that the electric potential at that point (not the difference) is K (where K is positive number). What can you conclude, if anything? What if it were negative? </p>
<p>Suppose I tell you suddenly that the charges are the same signs, and I give you a location in which the electric potential is positive (I think it has to be). What does it mean? </p>
<p>EDIT: Let me also just clarify a bit that I was taught that electric potential (not difference, I stress again) is the work that someone does to bring a charge from infinity to some point whereever. In my book however, it's defined as $V = \int_{R}^{\infty} \vec{E} \cdot \vec{ds}$</p>
| 2,796 |
<p>Consider an ensemble of electrons which all experienced a collision at time $t=0$. Let $n(t)$ denote the number of electrons in this ensemble. </p>
<p>Assume that the number of electrons $\mathrm{d}n$ from this ensemble experiencing collisions in a time $\mathrm{d}t$ is proportional to $n$, i.e. $$\mathrm d n = -an(t) \mathrm d t,$$
for some consant of proportionality $a$.</p>
<p><strong>Edit.</strong> Also assume that at $t=0$ an electric field is switched off.</p>
<p>Why is the relative change in drift velocity $\frac{\mathrm d |\langle \mathbf v \rangle|}{|\langle \mathbf v \rangle|}$ equal to the relative change in the number of electrons which have not yet experienced a collision$-\frac{\mathrm d n}{n}$?</p>
<p><strong>Edit.</strong> Noting that the thermal drift velocity is always zero, the contribution of an electron, which experience a collision after $t=0$, to the average velocity will vanish as soon as it experiences a collision. Because then it loses the drift velocity that was induced by the electric field.</p>
| 2,797 |
<p>Conductivity is noted in S.cm-1 in this <a href="http://pubs.acs.org/doi/abs/10.1021/ja502765n" rel="nofollow">http://pubs.acs.org/doi/abs/10.1021/ja502765n</a></p>
<p>i wanted to compare it to the conductivity values listed on wikipedia for common materials.</p>
<p>i could not find information on what the difference was through google's broken search engine.</p>
| 2,798 |
<p>My problem gives me a Carnot cycle heat engine with water as its working fluid, with $T_H$, $T_L$, and the fact that it starts from saturated liquid to saturated vapor in the heating process.</p>
<p>I need to find the net work output of this engine. So my solution goes like this:</p>
<p>$$\eta_{HE} = 1 - \frac {T_L}{T_H}$$</p>
<p>So I get $\eta_{HE}$. And then I also know that</p>
<p>$$\eta_{HE} = \frac {W_{HE}}{Q_H}$$</p>
<p>Since my goal is $W_{HE}$, I know I'll need to solve for $Q_H$ first. Since I have the state and temperatures of water at both states, I can get $h_H$ and $h_L$. I know that $h_L - h_H$ is some quantity of energy, and it must be either $Q_H$ or $Q_L$. The problem is, I don't know which it is. And I assume it is $h_L - h_H$ because it is heated first and then cooled. I hope this is correct.</p>
<p>I know that the change in enthalpy is the energy either released or absorbed by the system. In this case, since the temperature moves from higher to lower, it seems to me that the system is absorbing energy and hence this must be $Q_H$.</p>
<p>But it also makes sense to me to say that $h_L - h_H$ is the energy released by the system (as in an exothermic reaction), so it can be $Q_L$ too, because that is the heat rejected by the system.</p>
<p>So my question is, for the general case, which is it? Or is it situational? Does its being $Q_H$ or $Q_L$ depend on the resulting sign when I do my calculations? For this problem, the sign of $h_L - h_H$ that I computed is positive. Then this looks like heat entering the system and so it is $Q_H$. Am I correct?</p>
<p>Or, am I completely on the wrong track and should be chasing down another solution?</p>
| 2,799 |
<p>I was watching a whip crack in slow motion and I noticed that the motion of the whip could be described using two different circular descriptions.</p>
<p>1) the user circles the whip around over his head, creating a rotation with a period.</p>
<p>2) next, he jerks the whip, causing a different and faster movement of the whip.</p>
<p>the new movement appears to travel down the whip (which is already moving) until it reaches the tip. At this point, the tip creates a loud crack, which is associated with a supersonic movement.</p>
<p>In my mind, the two different motions cause an visual effect similar to a (constructive?) interference pattern. Can the cracking of a whip be described as the interference of two waves? If so, then what is going on? </p>
| 2,800 |
<p>In this <a href="http://www.mso.anu.edu.au/~charley/papers/LineweaverDavisSciAm.pdf" rel="nofollow">article</a>, the authors make the claim (pg <strong>44</strong>) that "Expansion by itself—that is, a coasting expansion neither accelerating nor decelerating—produces no force."</p>
<p>I'm having a hard time convincing myself of this. I think about two bonded atoms and the space between them expanding. While I don't doubt that the structure remains intact, it seems to me that the attracting force will always have to play "catch-up" against the expansion which is pushing the particles apart. Where am I going wrong in thinking of expansion as a force which acts counter to the attraction? Does anyone have a metaphor handy?</p>
<p>Another way of stating my question: with large enough (but not accelerating) rate of expansion, would we get to a point where molecules broke apart?</p>
<p>EDIT: In <a href="http://physics.stackexchange.com/questions/2110/why-does-space-expansion-not-expand-matter">this</a> related question, the agreed-upon answer seems to be that the expansion of space manifests itself as a force.</p>
| 2,801 |
<p>I apologize if this question is dumb, but I've looked all over for a straightforward answer and either I can't find one or the terms are too complex for me to understand. I have only a rudimentary knowledge of Mechanics, but I do understand basic Linear Algebra.</p>
<p>So torque, mathematically, is the cross product of the radial distance vector and a force vector. This cross product gives another vector that is orthogonal to both vectors and it points either outside or towards the "page" (in the context of a two dimensional diagram). </p>
<p>Assuming this is correct, I do not understand what it pointing in or out means. Does it even have a phyisical, intuitive meaning? </p>
<p>The best answer I've been able to come up with is that it's just a mathematical convention with no actual phyisical meaning, meant to provide a framework within which operations between torque vectors, such as addition and substraction, make sense.</p>
<p>Am I correct or way off the mark here?</p>
| 413 |
<p>I am studying the <a href="http://en.wikipedia.org/wiki/M%C3%B8ller_scattering" rel="nofollow">Møller scattering</a>, but I don't know how to get the twisted diagram from the S-matrix. Has anybody a good explanation?</p>
| 2,802 |
<p>If you unfold a tesseract into 3D space you get a cross shape (basically). <a href="http://www.youtube.com/watch?v=249AxWw-RbE" rel="nofollow">Animated</a>, it looks like the bottom most cube becomes inverted from it's 4D orientation. Would that mean that the pull of gravity within that cell would be opposite of the other cells when in 4D?</p>
| 2,803 |
<p>In the following circuit, I'd like to calculate the potential difference $V_{BA}$.</p>
<p>One way is to solve the circuit, by calculating all the currents $I_1, I_2, I_3$. The system of equations is:</p>
<p>$\{I_1 + I_2+I_3 = 0, 6 - 2 I_2 +2 I_1=0, 12 - 2I_3 + 2I_2 = 0\}$.</p>
<p>The solution is $(I_1, I_2, I_3) = (-4, -1, 5) mA$. Then $V_{BA} = 2 I_3 = 2 \times 5 = 10V.$</p>
<p>I'd like to solve the same problem via a different route. I put the GND at the negative pole of $-6V$ source. Then for point A, I write:</p>
<p>$\frac{0-V_A}{2} + \frac{V_A - 6}{2} + \frac{18-V_A}{2} = 0$, giving me $V_A = 12V$. Then $V_{BA} = V_B - V_A = 18 - 12 = 6V$, that is clearly wrong. Where is my mistake ?</p>
<p><img src="http://i.stack.imgur.com/Y5oPS.png" alt="enter image description here"></p>
| 2,804 |
<blockquote>
<p><strong>Possible Duplicate:</strong><br>
<a href="http://physics.stackexchange.com/questions/30824/can-a-photon-be-made-to-orbit-a-known-or-undiscovered-theoretical-body">Can a photon be made to orbit a known (or undiscovered theoretical) body?</a> </p>
</blockquote>
<p>How massive would a black hole have to be for light to orbit it at 1km away from the singularity? Given that Gravitational lensing occurs, I assume that it should be possible to bend light in a full circle. How would you calculate, using minimal advanced general relativity, show the minimum mass of that black hole?
What would be the orbital period according to different reference frames?</p>
| 57 |
<p>Just as the title asks,</p>
<p>How far away can, say, a satellite be and still be in "orbit" ?</p>
<p>How about for a given velocity?</p>
<p><em>Fun Facts</em></p>
<p>200 miles (320 km) up is about the minimum to avoid atmospheric interference. The Hubble space telescope orbits at an altitude of 380 miles (600 km) or so.</p>
<p><em>potentially helpful numbers</em></p>
<p>mass of Earth = 5.97219 × 1024 kilograms</p>
<p>mass of the Moon = 7.34767309 × 1022 kilograms</p>
<p>distance (earth, moon) = 238,900 miles (384,400 km)</p>
| 2,805 |
<p>The force carrier for magnetic fields and electric fields are supposedly <a href="http://physics.stackexchange.com/questions/3134/is-the-force-carrier-of-the-magnetism-in-a-common-household-magnet-a-photon">photons</a>. I don't get it:</p>
<p>1) Wouldn't that mean that a charged particle (e.g. an electron or even a polarized H<sub>2</sub>O molecule) would constantly be losing endergy from sending out photons?</p>
<p>2) Wouldn't that mean that an electric field is inseparable from a magnetic field, as photons have both - and that one can't have one without the other?</p>
<p>3) Would it be possible, then, to determine the wavelength of magnetic-field-mediating photons? If so, what is the wavelength - is it random or constant?</p>
<p>4) How can a photon (which has momentum) from one electrically charged particle to an oppositely charged particle cause these particles to <em>be pulled toward each other</em> - or how can a magnetic field cause an electrically charged moving particle to experience a force <em>perpendicular to</em> the source of the magnetic field if a particle with a non-zero mass moving between the two is the mediator of that force?</p>
<p>If <a href="http://en.wikipedia.org/wiki/Virtual_particle#Virtual_particles_in_Feynman_diagrams" rel="nofollow">"virtual photons"</a> are involved, please explain why they work differently from regular photons.</p>
| 2,806 |
<p>I've have got some vertical and horizontal distances for a projectile-like motion.</p>
<p>In order to work out the trajectory, why is it better to plot on the x-axis, "horizontal distance^2", and on the y axis, "vertical distance"?</p>
| 2,807 |
<p>I am studying to return to school in physics and would like to start spending as much time as possible on that task. Most of my small amount of free time, however, I am either doing house work or commuting to work. While it is difficult or impossible to read while doing these chores, I think I could get great benefit out of listening to educational physics material. I know that there are textbook reading services for the blind, but I have not been able to locate audio versions of physics texts available to the public. I know that several schools put their lecture material on YouTube, but I would love to get something that is specifically oriented to an audio only audience.</p>
<p>Are there any good resources to find educational material on physics in the form of audio?</p>
| 522 |
<p>I'm currently learning what electromotive force is and while reading my book's description of an ideal source of emf, I had difficulty understanding what these sentences mean:</p>
<blockquote>
<p>The nonelectrostatic force maintains the potential difference between the terminals. If it were not present, charge would flow between the terminals until the potential difference was zero.</p>
</blockquote>
<p>I don't quite get what it means by this. How does the nonelectrostatic force "maintain" the potential difference between the terminals? If it wasn't present and only the electric force remained, why would the potential difference decrease to zero?</p>
<p>The only thing I could think of was that the electric force from the E field inside the source of emf would still be exerting forces on charges from high potential to low potential, turning its electric potential energy into kinetic energy by doing work on the charges. I still don't know how that would reduce the voltage difference across both of its terminals to zero though.</p>
<p>Regarding the ideal source of emf, the book assumes there is a positive and a negative terminal with the positive terminal at a higher potential and the nonelectrostatic force going from low to high potential while the electric force goes from high to low, just in case that helps clear any ambiguity.</p>
| 2,808 |
<p>I have a problem with the argument of a finite square well.</p>
<p><img src="http://i.stack.imgur.com/HVL3H.png" alt="enter image description here">
<img src="http://i.stack.imgur.com/O1rSN.png" alt="enter image description here"></p>
<p>The stuff I read has mentioned that the Curvature " second derivative " is opposite sign of the wave function only when the E larger than V where E = energy of the particle V = potential.This is how we obtained oscillatory solution (when E is larger than V) ( I understood this part )</p>
<p>And For E smaller than V ,it is true that we obtain exponential solutions, but can we use the same argument I used above? Is it true that as u = ( exp(-ikx ) decays the curvature has the same sign, so the negative gradient starts getting to be more positive but less and less positive until it tails down to infinity? since now second derivative u depends on the value of u and the difference between E and V.</p>
<p>Is it a correct way of interpreting this phenomena?</p>
<p>Appreciate any idea or help from every one.</p>
| 2,809 |
<p>So here is my homework question: </p>
<blockquote>
<p><em>Two long cylindrical shells of metal (radii $r_1$ and $r_2$, $r_2 > r_1$) are arranged coaxially. The plates are maintained at the potential difference $\Delta\phi$. The region between the shells is filled with a medium of conductivity $g$. Use Ohm's law, $J = gE$, to calculate the electric current between unit lengths of the shells.</em> </p>
</blockquote>
<p>So I understand how to go from the current density to the actual current, but I need to find the electric field $E$ in order to find the current density $J$. I am not given the charges on each cylinder. How do I calculate the $E$ field when I am only given a potential difference? I know $\Delta\phi = \int E\,\mathrm{d}\ell$ but I feel like that doesn't help me much. </p>
| 2,810 |
<p>What does it mean by an infinite square well being <strong>transparent</strong>?
I have been doing the calculation of the infinite square well and I came up with an answer
$T = 1$ where
$T$ for Transmission coefficient.
But I can't really tell what it actually means in terms of physics.
I would imagine a particle to be trapped in a infinite square well to be the inner electron very close to a Big nucleus, So what does it mean by transparent in this context? Does it mean No other wave function can interact with this electron? </p>
<p>If there is an infinite potential, why would wavefunction still be able to pass through it but not getting bounce off the edges? of the well?</p>
<p><img src="http://i.stack.imgur.com/DgX2U.png" alt="enter image description here">
<img src="http://i.stack.imgur.com/3Ha97.png" alt="enter image description here"></p>
| 2,811 |
<p>I have a pretty basic pulley problem where I lack the right start.</p>
<p>A child sits on a seat which is held by a rope going to a cable roll (attached to a tree) and back into the kid's hands.</p>
<p><img src="http://wstaw.org/m/2011/11/08/m7.png" alt="Sketch"></p>
<p>When it sits still, I believe that the force on either side of the rope must be equal to keep is static, therefore each rope holds $\frac{1}{2}mg$, the cable roll has to carry the full $mg$.</p>
<p>Now, the kid wants go up with $\frac{1}{5}g$. For the whole system to accelerate up, the cable roll has to support another $\frac{1}{5}mg$ resulting in $\frac{6}{5}mg$ of force.</p>
<p>The question that I cannot answer is:</p>
<blockquote>
<p>How much force does the kid need to apply onto the rope in its hands?</p>
</blockquote>
<p>As I said before, $F_k$ (kid) and $F_s$ (seat) have to be $\frac{6}{5}mg$. So I get this:</p>
<p>$$F_k + F_s = \frac{6}{5}mg $$</p>
<p>In order to solve for either one, I would need another equation. The forces cannot be equal, otherwise there would be no movement of the rope. So I just invented the condition, that the difference of the forces has to be the acceleration:</p>
<p>$$F_k - F_s = \frac{1}{5}mg $$</p>
<p>I can solve this giving me $F_s = \frac{5}{10}mg$ and $F_k = \frac{7}{10}mg$ which will sum up to the total force.</p>
<p>But is this the right approach at all?</p>
| 502 |
<p>Did Einstein completely prove Newton wrong? If so, why we apply Newtonian mechanics even today? Because Newton said that time is absolute and Einstein suggested it <a href="http://en.wikipedia.org/wiki/Theory_of_relativity" rel="nofollow">relative</a>? </p>
<p>So, if fundamentals are conflicting, how can both of them be true at a time?</p>
| 2,812 |
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