Q stringlengths 18 13.7k | A stringlengths 1 16.1k | meta dict |
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Can we find a vector if its dot product and cross product with another vector is given? If I have two vectors $\vec{b}$ and $\vec{v}$, and I know that
$$
\vec{b} \times \vec{v} = \vec{c}
$$
and
$$
\vec{b}\cdot\vec{v} = \lambda
$$
can I find the $\vec{v}$ vector in terms of the $\vec{c}$ vector, $\vec{b}$ vector, and $\... | Notice, we have $\vec b\times \vec v=\vec c$ or $ \vec v\times \vec b=-\vec c$ & $\vec b\cdot \vec v= \lambda$
now,
$$\vec b\times \vec c=-\vec b\times(\vec v\times \vec b )$$$$\vec b\times \vec c=-\vec v(\vec b\cdot \vec b)+\vec b(\vec b\cdot \vec v)$$
$$|\vec b|^2\vec v=\lambda\vec b-\vec b\times \vec c$$
$$\vec v=... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/221174",
"timestamp": "2023-03-29T00:00:00",
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Does voltage always cause current? I'm wondering if the following statement is fully correct:
Voltage causes current through a closed circuit, but through an
inductor it is the change in current that causes a voltage.
Obviously there is no current without voltage. In a simple DC circuit there's no doubt that voltag... | The magic here is Jefimenko's equation (of causity). It is charge, and moving charges that produce and respond to a field.
Let's suppose you have a voltage field. These can exist, but if the charge is fixed, then little current flows. This is what a resistor does. On the other hand, if the field can cause a displac... | {
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What are good references for learning about Biophysics at graduate level? I am graduating this year on both Physics and Mathematics and I want to pursue a career in research, more concretely I want to study Biophysics.
I've been recommended Boal's Mechanics of the Cell and I think that it is a good book after giving it... | Quantitative Human Physiology: An Introduction By Joseph Feher (link to google books)
Although the content is (obviously) designed towards physiology rather then biophysics, his mathematical treatment of the some of the main concepts in biophysics (e.g. the Nernst equation) is the best that I have come across. The down... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/221417",
"timestamp": "2023-03-29T00:00:00",
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How should I interpret a Chi-Squared Result? I've got a Model A with a reduced chi-square of 1.28. I've got a Model B with a reduced chi-square of 0.70. Which is a better model? The model closest to 1 or the model closest to zero?
(Yes, I know this is probably better on the math site, but I got no answer there. Bes... | The one closest to zero is the best fit, but depending on the conditions you can't rule out the model with 1.28. Most often you cannot rule out anything where Chi-squared is closer than 1 to the value of your best fit - but it does depend in reality on a bunch of things including the number of variables you used for yo... | {
"language": "en",
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Induced EMF dependent on terminal wire connection? Figure(a):
When a conductor moving inside magnetic field, of a given length at a certain velocity the induced EMF is:
$$\epsilon = vBL$$
However, what if we changed the position where the bottom wire is connected to the wire like so:
Is the induced EMF now:
$$\epsil... | You need to look at the rate of change of flux through the circuit, including the flux being added by the slanted section of wire (stretchable?). A more realistic (and simpler) arrangement would be to have a rod sliding on parallel rails which can be moved closer together.
| {
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How do we find the number of bounded states in this potential? for the potential
$$V(x)=-\frac{1}{1+\frac{x^2}{m^2}}$$
we can approximate the wave function and bounded state accurately for $x << m$ as simple harmonic oscillator, so what are we gonna do if $x$ is large compared to $m$? Is it the number of bounded state ... | You can get an estimate that is correct (up to order one) from WKB. Given the Hamiltonian $$H = \frac{p^2}{2m} - \frac{1}{1+x^2/x_0^2}$$
the $n$-th level is characterized by
$$\frac{1}h \oint_{H= E_n} p\,dx = (n+\tfrac12). $$
The last bound state is at $E=0$, so the number of levels $N$ is given by
$$N = \frac{1}h \oin... | {
"language": "en",
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Why should gluons move at a speed determined by $\mu_0$ and $\varepsilon_0$? I understand that the speed of light can be derived from Maxwell's equations, giving $c=\frac{1}{\sqrt{\mu_0\varepsilon_0}}$
I furthermore understand how the principle of invariance of laws w.r.t. inertial reference frames gives rise to specia... | I suggest that you write Maxwell's equations in (the physicists') Gaussian units, rather than (engineers') SI:
$$\nabla \cdot \mathbf{E} = 4\pi\rho$$
$$\nabla \cdot \mathbf{B} = 0$$
$$\nabla \times \mathbf{E} = -\frac{1}{c}\frac{\partial \mathbf{B}} {\partial t}$$
$$\nabla \times \mathbf{H} = \frac{4\pi}{c}\mathbf{J}_\... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/222345",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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For the transition metals, how does counting the number of up-spins and down-spins still give you a non-integer magnetic moment? The transition metals like Fe, Co and Ni have magnetic moments of 2.2, 1.7 and 0.6 Bohr magnetons, respectively.
The band theory says that you get this when you calculate the density-of-state... | When the Fermi level cuts through some bands, only the fraction of the Brillouin zone for which the band is below the Fermi level counts toward occupancy of that spin.
Those fractional occupancy values are averages. It's not that an individual electron will flip spins instantly and change bands, but out of many unit c... | {
"language": "en",
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Operators and addition of angular momenta Consider a two particle system with one particle having spin 1/2 and the other spin 1.
One state of the system is $||\frac{3}{2},\frac{3}{2}\rangle\rangle$ where a double ket means this is in the coupled basis. So $S=\frac{3}{2}\text{ and } m_s=\frac{3}{2}$. This state can als... | It doesn't matter on which side $S^2$ acts. It should be equivalent shouldn't it?
here is the math.
$$\hat{S}=\hat{S_1}+\hat{S_2}$$
$$\implies \hat{S^2}=\hat{S_1^2}+\hat{S_2^2}+2\hat{S_1}.\hat{S_2}$$
$$S_1=S_x^1 \hat{i}+S_y^1 \hat{j}+S_z^1 \hat{k}$$
$$S_2=S_x^2 \hat{i}+S_y^2 \hat{j}+S_z^2 \hat{k}$$
$$\hat{S_1}.\hat{S_2... | {
"language": "en",
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Velocity of a leak in a closed water tank Bernoulli's equation states
$P_1+{1\over2}\rho v_1^2+\rho g h_1 = P_2+{1\over2}\rho v_2^2+\rho g h_2$
In a classic "water tank with an open top and a leak" scenario, "point 1" is the surface water in the tank, and "point 2" is the leak. The equation could be rewritten for $v_2$... | Depends on your assumptions. In the extreme case, with vaccum on the top of the fluid you can set $P_1=0$. This yields $$v_2=\sqrt{2g\Delta h-\frac{p_{\infty}}{\rho}}$$ with $p_{\infty}$ as ambient pressure. Be aware that $v_2$ is only an approximation since in reality $\Delta h$ changes as fluid leaves the tank.
| {
"language": "en",
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"source": "stackexchange",
"question_score": "3",
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What is the purpose of taking coefficients as 1 in numerical solutions? How can we recover the real solution after getting a solution by solving with parameters set to 1?
For example, on my case to solve the Shrödinger equation via finite difference method, the author took the coefficients like $h$ and $2m$ as 1, and g... | Another way to think of it is that you're dividing the equation by $\frac{\hbar}{2m}$. Any solution to
$$ \hat{H} \psi = 0 $$
is a solution to
$$ \frac{2 m \hat{H}}{\hbar} \psi = 0 .$$
Since the second equation is just the first multiplied by something on both sides. You are interested in finding the space of solutio... | {
"language": "en",
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Supersymmetry as a solution of hierarchy problem Hierarchy problem is the statement of why the weak force is much stronger than gravity.
In terms of coupling constant, weak force (Fermi coupling) is much larger than gravity (Newton's constant).
I want to know how supersymmetry can be a solution to Hierarchy problem. ... | It is all about appropriate cancellations in the expansions when calculating the Feynman diagrams:
The hierarchy problem
Supersymmetry close to the electroweak scale ameliorates the hierarchy problem that afflicts the Standard Model. In the Standard Model, the electroweak scale receives enormous Planck-scale quantum c... | {
"language": "en",
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What's the difference between charge density wave and charge ordering for superconductors So far, my understanding is that they are the same. Charge ordering is a phase transition and the material will have charge density waves once it's in a charge ordered state...? This sounds too simple though... And a similar quest... | I agree with Meng Cheng, charge ordering is a broader notion than CDW. My understanding is that CDW means charge ordering with a non-zero value for the wavevector $q$ : if your order parameter is some $\Phi(q)$, you develop a nonzero expectation value for $<\Phi(q)>$ with $q \neq 0$.
On the other hand, you could also ... | {
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Is it feasible to lift a human off the ground with a suit of fans?
So, we live in a world that is technologically developed enough where it is reasonably within reach to attach small rockets to someone/something to lift it off the ground.
One serious problem we encounter with this is damage to the surrounding environ... | lift is achieved when you push down on the air with a force equal to(hovering) or greater than your weight this means that you can In theory create the system of fans that you want in fact these machines have already been created tested and they do work but the main problem is flight time and a system of fans addresses... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/223190",
"timestamp": "2023-03-29T00:00:00",
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Laser-induced electrical discharge Attracting lightning with an ion beam has been done in a lab but how strong of a laser is needed to reach the clouds to redirect the lightning bolt?
| I can talk about the discharge experiment since I am not aware of any experiment to trigger real lightning with lasers. Note Discharge in lab is different than the lightning however the effort of all experiments is towards taming the lightning.
Laser filaments are low density plasma channels (order is $10^{16}cm^{-3}$)... | {
"language": "en",
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What is a state in physics? What is a state in physics? While reading physics, I have heard many a times a "___" system is in "____" state but the definition of a state was never provided (and googling brings me totally unrelated topic of solid state physics), but was loosely told that it has every information of the s... | Our physics prof once put it informally that way:
A state is a set of variables describing a system which does not include anything about its history.
The set of variables (position, velocity vector) describes the state of a point mass in classical mechanics, while the path how the point mass got from point $A$ to po... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/223564",
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What is a quasi-probability distribution? What is quasi-probability distribution? Why is it important in quantum mechanics? What does "quasi" mean?
| A quasi probability distribution relaxes an axiom of probabilty. In the context of Quantum Mechanics,it is specificly the axiom of probability that requires $p_{i} \geq 0$. So the sum of the distribution can include negative terms!
Quantum mechanics allows for events with a negative expectation values, to acount for p... | {
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Polarized light in single mode fiber In single mode fiber the light propagates in two orthogonal planes. Input will be linearly polarized light, which state of polarization will be on output and why? And if there will be some different state of polarizatin on output what will happen?
| In standard single-mode fiber, the polarization will tend to drift as the signal propagates (due to slight and varying birefringence of the glass, possibly stress-induced, coupling one polarization to the other).
For short lenths (1 m or so) polarization is typically maintained fairly well. For long distances (1 km or... | {
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What parts of a string stretch most when a wave passes through it? So there's a (transverse) traveling wave on an (ideal) string under tension. Why does the stretching occur around zero displacement? Why not at the crests?
| When a string is pulled tight to allow a transverse wave to pass, there will be some tension everywhere, not just in the bits near the crests or the zeros. However, if you consider a sine wave as a distorted straight line, then you can see that the amount of distortion (stretching) will depend on the gradient of the li... | {
"language": "en",
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Is it always possible to determine whether or not one is accelerating? Consider the following two situations: | You wake up in an elevator that is in free fall in a gravitational field.
B: You wake up in an elevator that is floating in a vacuum.
Is it possible to distinguish between these two situations?
It seems to me that Newton's second law formulated in a local coordinate system would look the same whether or not situation A... | {
"language": "en",
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Globally defined solutions in bc CFT system Consider $bc$-system which is 2-dimensional CFT of fermions:
$S = \int_\Sigma d^2 z \ b \bar{\partial} c + h.c. $
where $\Sigma$ - 2-dimensional manifold of genus $p$, fields $b, c$ have dimensions $(\lambda, 0)$ and $(1-\lambda, 0)$ respectively.
The question is to find n... | Comments to the question (v2):
*
*Given a manifold $M$, the word locally is associated with an open neighborhood $U\subseteq M$, while the word globally refers to the whole manifold $M$.
*If $E\to M$ is a fiber bundle, let $E_{|U}\to U$ denote the restriction of the bundle $E\to M$ to the neighborhood $U\subseteq ... | {
"language": "en",
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In most physical cases, the elements of a group can be represented by unitary matrices. Why no time-reversal? In Dresselhaus's group theory page 19, a theorem writes:
Every representation (of a Hamitonian's group) with matrices having non-vanishing
determinants can be brought into unitary form by an similarity
tr... | I think this passage is not very good (By the way, here is an online version with slightly different paging: http://web.mit.edu/course/6/6.734j/www/group-full02.pdf).
If you have a look at the proof, what they actually does is the following:
Theorem: Every representation of a finite group with matrices having non-vanis... | {
"language": "en",
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Why quantum fluctuation existed before big bang? I read somewhere that quantum fluctuation can give rise to a big bang and thus the creation of a universe which we know today, where do these quantum fluctuations come from if space is only created after big bang?
| The Big Bang is a purely classical concept. If we make a couple of assumptions about the distribution of matter in the universe then Einstein's equation tells us how the scale factor of the universe evolves with time. We can take our current universe and evolve it backwards in time, and if we do so we find the geometry... | {
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Why are the jets of the "light saber" star slightly curved? Why don't the jets of the HH-24 object follow a straight line?
In the image below, notice how they bend towards left from the expected straight line.
Is it an optical distortion, or some nearby massive object exerting a gravitational field?
| Pretty picture, but your reference is full of misnomers and errors with a reference to "Star wars" to capture attention.
"Beams of light at supersonic speeds"???, light speed is 'pretty' constant.
Young stars do not emit beams of light, they emit light in all directions. Some or most of the light, (or any other EM ene... | {
"language": "en",
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Elliptical orbit changing as a star's mass increases I'm studying Kepler's Laws, specifically the orbit of the Earth around the Sun. I know that if the Earth was more massive, the orbit would not be significantly affected. If the Sun was more massive, I know the velocity of Earth's orbit around the Sun would increase, ... | Kepler's laws are not correct:
No area law, no elliptical orbits, nor period. Starting with Newton's mechanical laws, Kepler's area law does not exist. Newton's universal attraction force is radial. $F=F_r$. A side force component, a perpendicular force does not exist $F_p=\frac {m dV_p} {dt}=0$. Then when integrated ... | {
"language": "en",
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Are orbitals observable physical quantities in a many-electron setting? Orbitals, both in their atomic and molecular incarnations, are immensely useful tools for analysing and understanding the electronic structure of atoms and molecules, and they provide the basis for a large part of chemistry and in particular of che... | The general answer is that when there is electron correlation the picture of each electron occupying an orbital is no longer adequate. In this case a single Slater determinant is no longer sufficient.
The Hartree-Fock or selfconsistent field approach to atomic and molecular problems approximates the many electron wave ... | {
"language": "en",
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How many fixed points does a Kelvin scale have? I have a book that says:
In the absolute Kelvin scale, the triple point of water is assigned the value of 273.16 K. The absolute zero is taken as the other fixed point.
But, then another section in the same book says:
On the Kelvin scale, the lower fixed point is taken... | The Kelvin scale is based on the Celsius scale in which 0 °C and 100 °C were defined to be the freezing and boiling points of water.
When the absolute minimum temperature was discovered to be -273 °C, scientists began simplifying matters by simply adding 273 and using the Kelvin scale in which 0 °C becomes 273 K. By de... | {
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Magnetic field due to stationary electric dipole As we know from Maxwell's 3rd equation the magnetic field is given as
$$\nabla \times \mathbf{E} = - \frac {\partial \mathbf{B}}{\partial t}$$
Now, if we consider an electric dipole which is stationary, there will be electric field lines
like this:
I want to know what w... | It would be interesting if you wrote our each vector component of the curl-E equation, and equate each of them to zero. Try to intuit what the derivative of each E-field component means with respect to your drawing.
| {
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Change in acceleration due to gravity because of rotation of earth
The formula above is the equation for acceleration due to gravity when earth rotates. G is the original acceleration.
Can someone explain how this formula came?
| In the above formula $g'$ is the component (directed towards centre of earth) of the net acceleration due to centrifugal force which is due to rotation of earth and acceleration due gravitational force of earth.
i.e. $g'=g-R\omega^2\cos^2\lambda$ where $R\omega^2\cos^2\lambda$ is the component of centrifugal force away... | {
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If you lift something does the internal energy increase or remain unchanged? So change in internal energy $\Delta U=Q+W$; so in lifting an object you do work on it, thus increasing its internal energy. Is this correct?
Sorry if this is a stupid question.
| Not a silly question! Although your formula is the way that we often memorize the First Law, the true First Law is actually
$$
\Delta (U + KE + PE) = Q + W_\text{non-grav}
$$
where $KE$ and $PE$ are, respectively, the kinetic and potential energy and $W_\text{non-grav}$ is the work done by all forces except gravity. W... | {
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Conservation of angular momentum in a collision Suppose I have a stick hinged to a pivot and it is released from its horizontal position and just after it becomes completely vertical, it strikes a ball completely stationary as in the given figure below.
The collision is completely elastic.
QUESTION: Will angular momen... | Angular momentum of an isolated system is always conserved. But it does require you to define what you consider part of your system - the hinge will provide a reaction force on the stick at the moment of collision, and that means there is an "external force" (that is, external to the stick and ball) to be taken into ac... | {
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Current from Middle Battery in a Two-looped Circuit
With this question, as with many tutorials of similar questions I’ve found online, my textbook only mentions three currents: $I_1$, which flows through the left loop from and to the 19 V battery, $I_2$, which flows through the right loop from and to the 19 V battery,... | The labelling of the voltages and currents does not matter as long as you stick to a convention.
If you had used the passive sign convention you might have labelled the voltages and currents as shown in the circuit diagram below.
In this case using Kirchhoff's current law one gets these relationships between the cu... | {
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Which elementary particles are behind magnetic field, similar as photons behind radio waves? I see, there are photons behind radio waves.
As Wave–particle duality said: the radio waves are waves and at the same time are fluxes of particles called Photons.
I'm wondering, what is behind magnetic fields?
Means, magnetic... | A particle must contain some amount of energy. Otherwise it wouldn't exist. There is no energy transfer with a steady-state magnetic (or electric) field, so there are no particles involved in transferring energy. Only when a magnetic field changes (the producer of that field moves) can there be energy transferred. In t... | {
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Exact meaning of "pi/2 pulse" In studying Mach-Zehnder and Ramsey interferometers, I came across the expression "$\pi/2$ pulse". What does it mean exactly? I am working with a Bloch vector representation $(u,v,w)$ of a 2 state system. We have a Rabi frequency $\Omega_0$ and a detuning parameter $\delta$ to the $|1\rang... | $\frac{π}{2}$ pulse means that all the particles in the system have gone to the higher level. $π$ pulse excites all particles in the first half time and de-exites in the second, so all particles are in lower level.
| {
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Closing a switch in series with a capacitor Suppose we have the following circuit:
Such that for $t<0$ the switch M was open. If we close the switch at $t=0$ what will the voltage on the capacitor, $V_C$, be at $t=0^+$? What about $\dot V_C$ at $t=0^+$? Will there be a current passing through $R$ the moment the switch... | You cannot solve the problem presented.
An ideal battery connected to a capacitor will have an initial current equal to infinity, which is obviously not possible. To make the problem solvable, you need to know the internal resistance of the battery.
Once you add the resistor in series with the battery, you will simply ... | {
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How are the protons for collisions in the LHC made? I heard that the LHC smashes two protons together to research the universe.
But how does it create the protons for collision? If we strip off the electrons won't there be neutrons along with protons?
A "Duoplasmatron source" is used by the LHC, it ionises atoms into n... | See this article on the LHC proton source.
Hydrogen gas is ionised using a strong electric field, and the resulting protons are accelerated and focused then injected into a linear accelerator.
| {
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Dirac equation, $\alpha_i$, $\beta$ hermitian The argument I've seen is the one given here: http://epx.phys.tohoku.ac.jp/~yhitoshi/particleweb/ptest-3.pdf under (3.10):
$$H=\vec{\alpha}\cdot(-i\vec{\nabla})+\beta m$$
$H$ is hermitian, $-i\vec{\nabla}$ is hermitian, so $\vec{\alpha},\beta$ are hermitian.
This is not con... | The Hilbert space in which the Dirac equation acts is a product of the infinite-dimensional space corresponding to position (or momentum) and a finite-dimensional spinor space, in which the matrices $\alpha_{j}$ and $\beta$ act. We know the momentum operator is Hermitian, so we may look at a subspace for fixed $\vec{p... | {
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Description of transparency of a Faraday cage to different frequencies? A Faraday cage within a static electric field leaves an internal electric field equal to $\vec{0}$ (as long as there are enough mobile electrons in the conductor to counteract the external $\vec{E}$).
It could be said as "a Faraday cage is fully op... | According to What is the relationship between Faraday cage mesh size and attenuation of cell phone reception signals? for a Faraday cage with a characteristic mesh size of $l$, then the cut-off frequency $f_c$ corresponds to a wavelength of $2l$, i.e. $f_c = c/2l$. In these circumstances, the wavevector
$$k = \frac{2 \... | {
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What will a glass look like in 500 years? The glass is in a metastable state. It is changing constantly. So what will a piece of glass look like in 500 years in room temperature?
| It's a common misconception that glass flows appreciably over time. So the answer is that your glass will have exactly the same shape as it does now, to within under a wavelength.
You can debunk the myth of flowing glass with simple experiment / observation. There are on Earth several very large refracting telescopes o... | {
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Why is it always foggy on new years eve? I live in Hamburg in northern Germany and a few years ago I started to notice this: It is always foggy on new years eve. Yesterday there even was a sight distance of about 10 meters at some point. This doesn't happen usually in the city.
I have some basic meteorology knowledge a... | Because of the extensive fireworks on new years eve a wide variety of particles enter the lower part of the atmosphere (boundary layer). Among those are trace gases but also black carbon [1]. Black carbon acts as a strong cloud condensation nuclei [2] which enhances condensation and therefor fogginess.
Also, "SO2 is a... | {
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Does quantum randomness measurably affect macro-sized objects? I understand that while it is believed that there is no true randomness on the macro scale, there is true randomness on the quantum scale. A previous theory that quantum processes could be determined through "hidden variables" has been disproven (through po... | There is no randomness on the quantum scale, there is only uncertainty, which describes the information that is available to a macroscopic observer. An easy way to see that quantum processes are not random is by looking at starlight. That light has been coming to us from up to billions of lightyears away, but it doesn'... | {
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Sliding along a circular hoop: work done by friction
Assume a point object of mass $m$ slides along a hoop of radius $R$, starting from a position which makes 90 degrees with the line of radius connecting the center and the ground. Let the coefficient of kinetic friction between the hoop and the object be $\mu$. Assum... | For people interested in this problem, you can also define a differential equation for the frctional work itself. Just express the differential work as a function of the angle, apply again energy conservation for the kinetic energy and then solve the one-degree differential equation that appears. Details can be found i... | {
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How is $ \left(1-\frac{p^2}{2mE}\right)^{3N/2-2} =\; \exp\left(-\frac{3N}{2}\frac{p^2}{2mE}\right)\;?$ How is
$$ \left(1-\frac{p^2}{2mE}\right)^{3N/2-2} = \exp\left(-\frac{3N}{2}\frac{p^2}{2mE}\right)$$
(Karder, Statistical Physics of Particles, Page 107)
in the large $E$ limit. Here $N$ is particle, of the order of $... | Add a comment needs 50 reputation, and I got only 46 now. So I write my opinion here.
I have read the textbook, the original formula is
$$p(\vec{p_1})=(1-{{\vec{p_1}^2}\over {2mE}})^{3N/2-2}\cdots\cdots$$
So $\vec{p_1}$ is the momentum of only one particle in the ensemble. Considering the system has very large $N$, tha... | {
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Minimum Power Required to Maintain a Population Inversion According to many sources, the minimum power required to maintain a population N in the upper level of a two level laser system is $$P_{min}=fA_{21}Nh\nu$$ where $f$ accounts for the lack of 100% efficiency, $A_{21}$ is the Einstein A coefficient and $\nu$ is th... | It is not possible to have a population inversion in a system with just two states.
The trick with any laser is that you need three possible states - let's call them 1, 2 and 3 (in increasing order of energy - see image from wikipedia):
If we can make it so that the 2->1 transition is much slower than the 3->2 transi... | {
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Do free-electron lasers actually lase? Free-electron lasers are devices which use the motion of highly energetic electron beams to produce bright, coherent radiation in the x-ray regime. More specifically, they start with a high-energy electron beam and feed it into an undulator, which is an array of alternating magnet... | FELs produce a coherent, monochromatic, intense light beam that can be collimated with an iris (basically a hole in a large lead block).
An optical cavity can be arranged by putting two mirrors around the undulators, spaced so each pass of the electrons constructively interferes (go here and click Watch a Movie on How ... | {
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Symmetry of the Polyakov action? Let us look at the Polyakov action for a string moving in a spacetime with metric $g_{\mu \nu}(X)$:$$S_P = -{1\over{4\pi \alpha'}} \int d^2 \sigma \sqrt{-\gamma} \gamma^{ab} \partial_a X^\mu \partial_b X^\nu g_{\mu\nu}(X) \tag{1}$$ and suppose there exists a Killing vector $k_\mu$ in sp... | Killing vector fields correspond to infinitesimal isometry generators of the spacetime manifold and any physical action including the Polyakov action should be preserved under it. In fact, any physical action should be invariant under the (infinitely) larger group of diffeomorphisms of a manifold. Isomotry transformati... | {
"language": "en",
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Why is the Fourier transform more useful than the Hartley transform in physics? The Hartley transform is defined as
$$
H(\omega) = \frac{1}{\sqrt{2\pi}}\int_{-\infty}^\infty
f(t) \, \mbox{cas}(\omega t) \mathrm{d}t,
$$
with $\mbox{cas}(\omega t) = \cos(\omega t) + \sin(\omega t)$.
The Fourier transform on the other ha... | Short answer: The Hartley transform is a subset of the results given by Fourier transforms, which is only the real part (assuming your signal is real, which is almost always the case in physics).
Long answer: Practically, you need the amplitude and phase of the signal, and the Fourier transform gives you both amplitude... | {
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Would a mass of bare iron nuclei be visible? As I understand it most of how objects look is because of how photons interact with electrons and photons emitted when excited electrons fall to lower energy levels producing photons.
So if one traps a completely ionized mass of say iron or nickel and drew off the associated... | It is extremely hard to reach any kind of density of "plasma" of just nuclei - the thought experiment of "drawing off" the electrons would be surprisingly hard in practice, as the net charge gets larger and larger so the energy required to remove one more electron gets astronomical very quickly.
Thus you would have a v... | {
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Why is chemical potential, μ=0 when calculating critical temperature of BECs? How do we justify taking the chemical potential, $\mu$ as $0$ when calculating the critical temperature of Bose-Einstein Condensates (BECs)?
I apologise as I do not how to use LaTeX, for if I did the elegance of mathematics would’ve allowed m... | You can think of the chemical potential as the amount of free energy needed to add one additional particle to the system. Because the ground state of a BEC is degenerate and can hold an infinite number of particles, there's no energy cost to add another particle to that state. So, $\mu = 0$.
| {
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Why is the speed of sound lower at higher altitudes? At sea level the speed of sound is 760mph, but at altitudes like the Concorde would fly at (55,000ft) the sound barrier is at 660mph, so 1000th slower. Does it have to do with lower pressure?
| A sound wave moving through a gas requires a small scale bulk movement of gas molecules back and forth as pressure at any locations builds or falls. Therefore, the sound wave can not possibly move through the gas at a speed greater than that of the individual molecules themselves, and in fact must move at a lower speed... | {
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Hamiltonian of a quantum harmonic oscillator On page 286-287 of Nielsen Chuang's Quantum Information and Quantum Computation (10th edition) book, the Hamiltonian for a quantum harmonic oscillator is approximated as $H=a^\dagger a.$ What are the assumptions involved in such an approximation and why is this approximation... | I have a lot of experience with this particular book, but unfortunately it is in my office right now so I can't reference the exact page you're on.
In QIQC, and this book in particular, you're going to be doing a lot of manipulating the Hamiltonian of the QSHO using commutators. Since constants always commute, the con... | {
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visible light spectrum Why do we see black objects? Colors of objects are formed when the spectrum of that color is reflected. Example Green objects are green because they reflect the green spectrum of light, red objects are red because they reflect red spectrum of the visible light and white objects because they refle... | We don't actually see light itself. We see objects which emit, reflect, absorb or refract light. Where the light strikes our retina and which cone is triggered allows the brain to create images because of contrast. This visual representation of reality is what we see. Because we have binocular vision this image appears... | {
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Acceleration of log moving without slipping with/under a plank So I have this image:
I know how to solve the accompanying physics problem once I have determined the relative accelerations of the logs and the plank. According to my physics textbook, the cm of each log will move half the distance that the log will and ... | The point where the log touches the ground is the point where the log has zero velocity. If you now draw a small displacement, you see (from equal triangles) that if the center of the log moves $x$ the top moves $2x$ .
| {
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Electron-Positron Annihilation in a Gravitational Field When an electron and positron annihilate what happens to any gravitational energy they have?
In a way the energy is 'shared' between these two particles and all the matter in space. It must take a finite time for it to vanish. I realise of course that the gravita... | We all learned in school that gravity is associated with mass. For example if we have two bodies with masses $m$ and $M$ then Newton's law tells us that the gravitational force between them is:
$$ F = \frac{GmM}{d^2} $$
So if either object has zero mass the force goes to zero. And since photons are massless it's entire... | {
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Heisenberg's uncertainity principle In the Heisenberg uncertainty principle,
$$\Delta x \cdot \Delta p \geq \frac{h}{4\pi}$$
The values of $\Delta x$ and $\Delta p$ are the standard deviations which we get from the probability distribution function of the particle and I heard that it has nothing to do with the measurin... | These are standard deviations of a probability distribution indeed. The probability distribution is that of getting a particular value while the system is in the state prior to measurement. So we imagine measuring a state - it collapses to some value, and then somehow resetting time back before measurement and measurin... | {
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What's the reason double-slit experiment can't be explained by edge effects rather than quantum interference? Say we had exactly this...
But instead, it was a PING PONG GUN (imagine as table tennis players use to train),
throwing out PING PONG BALLS. The two slits are say 20 cm wide, and the observing screen is say 5... | Your explanation has a tennis ball that is a body and you are influencing it with forces , but in reality particles like electrons , photons even complete atoms show this behavior because everything behaves like a wave of some wavelength , it is just that as the particles become macroscopic , the effect is minimized .
... | {
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What would be the view like from inside a black hole looking towards the event horizon? Ignoring the fact that we would be torn apart by gravitational gradient and assuming we get some time to make some observations before hitting singularity, what would we see looking towards the event horizon or in any other directio... | To answer this question we have to raytrace the lightrays hitting the observer, for rotating black holes the coordinates of choice are Doran raindrop coordinates which make it possible to calculate the view from both outside as well as inside. The first image shows the outside perspective of an observer at a latitude o... | {
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Why is the sound channel in the ocean especially good for low frequency sound? Why does not the high frequency sound propagate as far?
The dispersion curve $\omega(k)$ is almost linear, right?
| The basic phenomenon is that high frequency sound is more strongly attenuated than low frequency sound. The mechanism for sound attenuation is viscous damping. The absorption coefficient is
$$
\gamma= \frac{\omega^2}{2\rho c^3}\left[ \frac{4}{3}\eta + \zeta
+ \kappa\left(\frac{1}{c_v}-\frac{1}{c_p}\right) \right],
$$... | {
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Given a current velocity and a fixed input energy, how much faster will a relativistic particle be? The relativistic kinetic energy of a particle with mass $m$ and velocity $v_0$ is $$m c^2 (\gamma_0 - 1) \textrm{ where } \gamma_0 = \frac{1}{\sqrt{1 - \frac{v_0^2}{c^2}}}$$
I would like to know how quickly the particle ... | You do not need the kinetic energy. Working with the total energy $\gamma m c^2$ produces the same result.
Assuming both the total initial energy $\bar E_0 = \gamma_0 m c^2$ and the additional energy $E_i$ are known, write $\gamma_1 mc^2 = \frac{mc^2}{\sqrt{1-\beta_1^2}} = \bar E_0 +E_i$ for $\beta_1 = \frac{v_1}{c}$,... | {
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Does momentum space have a speed limit? In ordinary $xyz$ space, the maximum velocity of propagation for mass-energy and/or information is $c$.
So, my question: Is there also a maximum velocity of propagation in momentum ${p_x}{p_y}{p_z}$ space, one that would for example place a maximum limit (not necessarily approach... | For a transition like electron-hole recombination, its probability is linear with time with some characteristic time scale that depends on the system: the probability of having a transition between $0$ and $dt$ is $\frac{dt}{\tau}$. So there is a non-vanishing transition probability at arbitrarily small times.
In momen... | {
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Newtons third law with two charged particles Imagine we have two charged particles, $q$ and $Q$.
$q$ is at rest at a point and $Q$ is moving with a velocity. Now $q$ is exerting an electrostatic force on $Q$ and $Q$ makes a magnetic field but because $q$ is at rest there is no force from $Q$ to $q$.
So, is the third l... | $Q $ doesn't generate just a magnetic Field, but also an electric field: Just because $Q $ moves, that doesn't mean that it doesn't generate a field, this field just has to satisfy the Maxwell equations. $\mathbf{\nabla\cdot E} = \rho$ still has to hold, and also the magnetic field that is created is time dependent, so... | {
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Understanding of dipole moment and its vector property I have a trouble understanding the electric dipole moment.
The electric dipole moment formula is
$${\bf p}= \int {\bf r}' \rho({\bf r}')d\tau '$$
I'm interested in the coordinate, the origin of which is changed into $\bf a$.
$${\bf r}' = {\bar {\bf r}}' + {\bf a}$$... | I think you are confused with the new coordinates system.
You sould correct the above equations like this:
\begin{align}
\bar{\mathbf p} &= \int \bar{\mathbf r} \bar\rho(\bar{\mathbf r})d\bar\tau \\
&=\int ({\mathbf r}-\mathbf a) \rho(\mathbf r)d\tau\\
&=\mathbf p - \mathbf a\int\rho(\mathbf r)d\tau = \mathbf p - Q\mat... | {
"language": "en",
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Identifying an ideal gas I'm pretty confused. So I've been told that the equation of state for $n$ moles of some type of gas is $P(V-b) = nRT$. That's not quite like an ideal gas. But then the relations $C_p - C_v = R$, and $\gamma = \frac{C_p}{C_v} = 5/3$ hold for this gas, and at the very least the last equation is d... | The gas you are describing is not precisely an ideal gas, but is pretty close. In an ideal gas, the molecules are dots, they don't have volume ; moreover, threr are no interactions except for the elastic collisions that allows the gas to thermalize.
The gas you describe is is a gas with no interactions, but with molecu... | {
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Do we know why there is a speed limit in our universe? This question is about why we have a universal speed limit (the speed of light in vacuum). Is there a more fundamental law that tells us why this is?
I'm not asking why the speed limit is equal to $c$ and not something else, but why there is a limit at all.
EDIT: A... | Why is there a speed limit in our universe? This might have something to do with the principle of locality in physics. Note that in Fredkin 's universe as a cellular automaton , there always is a speed limit, for any emerging pattern (just an example). So the existence of a speed limit in our universe is an endorsemen... | {
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Does a trumpet play at a tritone lower without lip vibration? My trumpet teacher noticed that if you blow into a trumpet for warm-up, without any lip vibration, there is still a slightly audible pitch which is a tritone lower than "expected" in the following sense:
For example, if none of the vents are pressed on a Bb ... | There are three points to be noticed:
*
*If you just blow without closing the lips, you would change the boundary condition.
*The trumpet waveguide is not "nicely predictible", the approximation of an open tube does not work cause the bore variations $S(x)$. You need to solve this kind of beasts for reasonable 1D p... | {
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Can one write down a Hamiltonian in the absence of a Lagrangian? How can I define the Hamiltonian independent of the Lagrangian? For instance, let's assume that i have a set of field equations that cannot be integrated to an action. Is there any prescription to construct the Hamiltonian of a such system starting from t... | Comments to the question (v2):
*
*First of all, let us stress that OP is correct, that a given set of equations of motion does not necessarily have a variational/action principle, cf. e.g. this Phys.SE post and links therein.
*On one hand, if there exists a Lagrangian formulation, then one may in principle obtain a... | {
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Perturbative QCD application in FAIR In FAIR CBM scenario i.e at high density will be perturbative QCD applicable?
| PQCD is only applicable at really high energy and FAIR CBM experiment will have quite low energy and finite baryonic density.
As it is said on the official doc :
http://www.fair-center.eu/fileadmin/fair/publications_FAIR/FAIR_BTR_3a.pdf
Low energy model will be available to compare data, but in my opinion, lattice QCD... | {
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When sunlight bounces off the Earth, why isn't the entire spectrum reflected rather than just the infrared portion? I've read that greenhouse gases absorb and reemit sunlight, and that the infrared portion is what bounces off Earth back to space. When sunlight bounces off the Earth, why isn't the entire spectrum reflec... | It does. Consider this: you can see the Earth from space. Therefore, not just infrared light gets reflected but also light on the visible spectrum.
Here's a graph (by NASA) of various planet's radio emissions. The ways that Earth can release radio waves is a bit limited. Because of that, it is safe to assume that at l... | {
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What does a zero topological S matrix element mean? I realize that for nonabelian anyons, their S matrix elements could be zero (eg. the Ising anyons). I'm confused by the meaning of a zero S matrix element. Does it mean that the corresponding braiding process results in a zero amplitude?
| Let us consider the S matrix of Ising anyons as an example: $S_{\sigma\sigma}=0$. To be more precise, suppose we have four $\sigma$'s, labeled as $1,2,3,4$. We assume $1$ and $2$ are in a definite fusion channel. Then we braid $3$ around $1$ (or $2$, no difference). Then the state of $1$ and $2$ must be orthogonal to ... | {
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What is the minimum force required to move this block Please don't report. It's not a homework question. Yesterday on my physics test there was this question. there is a block of mass $m$ connected to a spring as shown in the figure. the spring constant is $k$ and the friction coefficient between the block and the floo... | F(x) = kx, according to Hooke's Law. This means that your friend is incorrect, and you got the question correct.
Note: the potential energy of the spring is (kx^2)/2, so your friend confused potential energy with force. A bit of dimensional analysis would greatly decrease the chance of mixing the units in this way.
| {
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Quantum computing, NP complexity Hi I have a very limited knowledge of quantum physics and its bothering me trying to understand quantum computing.
I want understand how a qubit can return usable data faster then a regular bit, how is the NP complexity not an obstacle?
| The best way to understand this is to work through an example. Here is how you factor the number 15 using Shor's algorithm. (If you prefer, view the problem not as factoring 15 but as solving $2^r=1 \hbox(mod 15)$, and skip Step Seven). As you work through this, imagine replacing 15 with a much larger composite numb... | {
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How do two metal balls of radius $r$ kept at a large distance form a capacitor? So this is something really new to me. I have learnt of plate capacitors, cylindrical capacitors, single spherical capacitors, etc. but that to, of finite distance between them. Also please explain if the distance is not very large and comp... | Here is how:
And the expression is (from wikipedia):
$$2\pi \varepsilon a\sum_{n=1}^{\infty }\frac{\sinh \left( \ln \left( D+\sqrt{D^2-1}\right) \right) }{\sinh \left( n\ln \left( D+\sqrt{ D^2-1}\right) \right) } $$
| {
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Charge inside a charged spherical shell
*
*If I were to put a negative charge inside a negatively charged spherical shell, will it move to the center?
*Electric field inside the shell due to the shell is zero (Gauss's Law), would that mean the charge inside the sphere faces no force?
But, that doesn't make intuitiv... |
If I were to put a negative charge inside a negatively charged spherical shell, will it move to the center?
Electric field inside the shell due to the shell is zero (Gauss's Law), would that mean the charge inside the sphere faces no force?
The answer depends upon whether the spherical shell is conductive, and if n... | {
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Does matter stacks up as it approaches Black hole? When something approaches Black hole it'll experience time dilation with respect to a frame away from the black hole.
So to an observer away from the hole the object would seem to slow down until it finally appears to have stopped .
Would that mean all the matter th... | Yes and no. Remember in special relativity whenever someone asks a question, they always are told to draw a spacetime diagram. The same thing happens in general relativity. If you want to see what is possible, consider drawing a Carter-Penrose diagram.
For a black hole you can draw the event of a test particle crossing... | {
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Symmetry and group theory book I would like to start learning about symmetries in physics and how they affect physical quantities. As far as I know, the mathematical language that describes symmetries is the Group Theory. So, I think the best start would be getting deep in this theory. Although there are many books on ... | opinion based question, so it may be closed.
The author Vincent (family name) has a very good introduction to group theory for molecules.
I like this book as it has questions for you to answer as you go along so you really learn it as you read.
If you are interested in solid state then you will have to go further to sp... | {
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Does light interact with electric fields? We know that light is an electromagnetic wave and it does interact with charges.
It contains magnetic field and electric field oscillating perpendicularly but when we apply an electric or magnetic field in any direction to the wave the applied electric field or magnetic field v... | An applied electric or magnetic field doesn't alter the field of an electromagnetic field because, as you said, the superposition principle holds. This principle is a principle of linearity, and comes from the linearity of electromagnetic equations : there is no interaction between photons at low energies.
You can see ... | {
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Does potential difference or electric field change with distance between parallel plates? Say you have a set of parallel plates, one is positive and one is negative, if you change the distance between them would electric field strength change or potential difference, given the equation
$E=dV/dx$
From pure intuition, ... | $C={kA\over d}$. When $d$ increases, $C$ decreases.
$Q=CV$. $C$ stands for capacitance, and $V$ stands for potential difference. $C$ decreases, $V$ increases. That's why the potential difference increases.
| {
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Why is meteor speed what it appears to be? Is the speed of a meteor through our sky because of the speed of the earth's axis rotation, or because the meteor is speeding towards us at that speed?
| All speed is relative. But an object that starts from rest at infinity will reach a velocity of about 11 km/s when it hits Earth, if Earth is the only thing pulling on it. At the same time, Earth is moving with an orbital speed of about 30 km/s. Their relative importance will depend on the direction from which the mete... | {
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Why do materials show plastic behaviour for large stress? As the stress is increased, the strain increases proportionally up to elastic limit and the material regains its original dimension within elastic limit. When the stress is increased further the material shows a plastic behaviour. What change in the internal str... |
What change in the internal structure causes the transformation from elastic to plastic behavior?
It depends on the material. For metals, small elastic strains are just the result of very small changes in the interatomic spacings. When more stress is applied, pre-existing dislocations in the metal start to move, caus... | {
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Balancing Utensils: Center of Mass If you have a cork piece on top of a nail, it is extremely hard to keep it stable, and the slightest action will make the cork fall off. However, when you balance it on top of a nail but put forks into it, apparently it becomes extremely easy to keep stable. I looked in my textbook an... | The experiment involves sticking the tines of the forks into the cork so that the long heavy handles of the forks extend downward. Take a look at the photo in this link: https://www.kecksci.claremont.edu/physics/demo/corkfork.htm.
Now, the cork and the forks are bound together as one object, and the center of mass of ... | {
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Why is thermal energy not a state variable? It is written on Wikipedia: (https://en.wikipedia.org/wiki/Thermal_energy)
The thermal energy of a system scales with its size and is therefore an extensive property. It is not a state function of the system unless the system has been constructed so that all changes in intern... | An example you asked for :
Consider a system of an ideal gas where volume of the gas is constant (call it system A) and one where the pressure is constant (System B). Because the internal energy of the system is a state variable, same change in temperature would cause same change in internal energy. Now, $$ \Delta U = ... | {
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Coefficient of friction and practical experience of sliding The classical model of friction has a coefficient of friction depend only on the materials, but not area, and the force proportional to the normal force and coefficient of friction. So a given object on the same surface has the same friction whether it is supp... | Going faster on a dry playground slide if you lie down seems not to be well-documented, so I shall discount the effect of posture. The amount of friction depends on your weight, which is the same lying down as it is sitting up.
If there is any difference on a dry slide it is probably due to the reduced coefficient of ... | {
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Variant of the Sokhotski–Plemelj theorem I am aware of the Sokhotski–Plemelj theorem (I have also heard people referring to it as the "Dirac identity") which states that in the limit $\eta\rightarrow 0^+$
$$\frac{1}{x\pm i\eta}=\mathcal P\frac{1}{x}\mp i\pi\delta(x) \, .$$
Now, I am reading the book "Solid State Physic... | I don't think we need Sokhotski-Plemelj for this.
Think of $E_j - E_i$ as a fixed value $E$.
Then the formula is re-written as
$$\frac{\hbar \omega}{E - \hbar \omega - i \eta}\, .$$
Now let $x \equiv \hbar \omega$ and you get
$$\frac{x}{E -x - i \eta} \, .$$
This integral is dominated by the part where $x \approx E$ so... | {
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Why are the closed and open ends of an organ pipe nodes and anti-nodes? Here is a diagram of a wave in an organ pipe you'll find in most physics books
*Waves in air are longitudinal (not traversal), so what do the curves represent?
*Why are the open ends always anti nodes and the closed ends always nodes?
| Sound waves are made of alternation of compression (higher density) and rarefaction (lower density) regions in the air. However, this can be somewhat difficult to visualize. Because of this, textbooks often show the wave like it's a string in the organ pipe. Really what the curves are showing you in the amplitude of... | {
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Why does a laser beam stay collimated? I am looking for a simple way of explaining the collimation of a laser beam. The typical discussion of the two slit experiment of quantum theory relies heavily on the Huygens principle. Its application to a laser beam would tend to predict spreading. From a purely electromagnetic ... | Just as Jon Custer wrote in his comment, even a perfectly collimated laser beam with a planar wavefront will diverge. The way it happens is determined by the Huygens principle, and depends on the beam profile:
When the light intensity is abruptly cut by a sharp flat obstacle, the light will indeed diffract in almost al... | {
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Why is amorphous classified solid? Because it does not have a crystal structure, it is hard to find physical similarities with a solid. Why isn't it then another state other than solid?
The physics of amorphous is also quite different from crystal solid.
|
"Because it does not have a crystal structure, it is hard to find physical similarities with a solid"
simply proves that you're using the wrong definition of "solid". Relatively few solids have crystalline structure, so a good definition of solid simply can't depend on that.
Let me see if I can offer a better defini... | {
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Non-Euclidean mechanics; is it useful? Special relativity has the following single-particle Lagrangian:
$$S = \int_{t_0}^{t_f}\sqrt {\langle \mathrm d\vec{s},\mathrm d\vec{s}\rangle}.$$
Clearly it is based on Euclidean norms; it is in Minkowski or Riemannian-geometry norm, but both norms are only a generalization of th... | OP's proposal (v2) is a special case of Finsler geometry with $n=3$. The main idea is to replace the quadratic metric tensor $g^{(2)}_{\mu_1\mu_2}$ for pseudo-Riemannian manifolds, which defines (infinitesimal, possibly imaginary) distance on the manifold via
$$ds ~=~ \sqrt[2]{g^{(2)}_{\mu_1\mu_2}dx^{\mu_1}dx^{\mu_2}},... | {
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Would the Moon be able to take water from Earth? I know that if you add mass to the moon, it would get closer to the Earth. We all know that the moon causes the tides because it's gravity pulls the water. So, my question is: If the moon gained more mass and got closer to the Earth, could it have enough pull on the wate... | Gravity acts on all matter, not just water (it just so happens that water flows with less resistance than rock) which is why we get noticeable water tides but not very noticeable earth tides. However, if you were to bring a very large gravitating body too close to earth, you would find that the earth isn't quite as sol... | {
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Why is the Pythagorean Theorem used for error calculation? They say that if $A = X \times Y$, with $X$ statistically independent of $Y$, then
$$\frac{\Delta{A}}{A}=\sqrt{ \left(\frac{\Delta{X}}{X}\right)^2 + \left(\frac{\Delta{Y}}{Y}\right)^2 }$$
I can't understand why that is so geometrically.
If $X$ and $Y$ are inter... | The square root is there as a better estimator of the error than just adding the errors together. If you add the errors together you are finding the maximum possible error which will happen when both quantities are a maximum(or minimum) together. This is an unlikely event compared with all the other domination of err... | {
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Deriving Wave Function for Scattering States with Delta-Function Potential I am following the Griffiths Book on Quantum Mechanics, and am following the derivation for the wave function for Delta-Function Potentials.
$$V(x) = -\alpha \delta(x)$$
In the scattering states, where $E > 0$, when solving the Schrodinger Equat... | Neither one of the terms blow up because of the complex exponential. This exponential is real for the bound state case.
| {
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Can the linear momentum of a system be constant, even though its centre accelerates? My instructor says if the velocity of center or mass is constant, it means that the linear momentum of a body is conserved. So if no external force acts on a body, there is no change in the linear momentum of the system.
*
*Now, if... | It's not difficult to show that the total linear momentum of a system can be found by multiplying the velocity of the center of mass by the total mass. If the momentum is constant (in the absence of a net external force), then the velocity of the center of mass is constant. But be careful with your statements. The ce... | {
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How far do we need to be removed from the earth to show the curvature with a viewing angle between 42 and 48 degrees? I have seen already a couple of answers but none of them give an exact number of what should be the minimum height where we would be able to record the curvature of the earth
All I could find is minimum... | In order to see the curvature, you need a 60 degree field of view and a cloud free day. From what I've read, you need to be about 35,000 feet above the surface. Find more information in this article here: http://www.howitworksdaily.com/how-high-do-you-have-to-go-to-see-the-curvature-of-the-earth/
| {
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Scattering amplitude Green's function integral On page 208 of Weinberg's QM book, he calculates the following integral
\begin{align}
G_k (\vec{x}-\vec{y})
=& \int \frac{d^3 q}{(2\pi \hbar)^3} \frac{e^{i\vec{q} \cdot (\vec{x}-\vec{y})}} {E(k)-E(q)+i\epsilon} \\
=& \frac{4\pi}{(2\pi)^3}\int_0^{\infty} q^2 dq \frac{\sin(q... | Write $d^3 q = dq q^2 d\theta d\phi \sin\theta$ and integrate over the angular variables. The only angular dependence in the integrand is in $e^{i \vec{q} \cdot ( \vec{x}-\vec{y}) } = e^{i q r \cos\theta}$ where I've defined $r = | \vec{x} - \vec{y} |$. Then, we have
$$
\int_0^{2\pi} d\phi \int_0^\pi d\theta \sin\theta... | {
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What is the electric field exactly on the surface of a conducting sphere? Within a conducting sphere, the electric field is 0, but is the electric field still 0 exactly on the surface?
| The point about the E-field being zero inside is a conductor is that you must be writing about electrostatics, the study of charges when they are not moving.
In the ideal world every bit of metal inside your surface (an infinitely thin shell) has no E-field within it.
In the real world when the surface is particular in... | {
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Determine resultant couple moment by summing moments The question states:
Determine the resultant couple moment by (a) summing moments about point $O$ and (b) summing the moments about point $A$.
I used scalar analysis for solving this question, wherein
$$M=\sum{F_xd_y}+\sum{F_yd_x}$$
When completing part (a), I fou... | The net force acting on the beam is zero but there is a couple acting on the system. A couple has the nice property that the moment about any point is the same.
So you should have found the same answer for both parts.
So find the vertical component of the two forces on the left which will equal the magnitude of the ve... | {
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How can a product of Bra and Ket be a scalar if they are matrices? I am trying to teach myself Quantum Mechanics and am currently on Complex Vector Space Arithmetic. According to Wikipedia, product of a Bra and Ket is a scalar (which, I think, means a complex number). But then, on the same page, it also says that both ... | This is just the dot product of two vectors. If you want to get more into dot products I would suggest migrating to the math site.
| {
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Are isentropic closed rigid thermodynamic systems also isolated? $\newcommand{\d}{\, \mathrm d}$Currently it seems to me that isentropic closed rigid thermodynamic systems have to be also isolated. Is this correct?
The reason why it seems to me like this is the following.
The energy-based fundamental equation is: $$\d... | No it doesnt necessarily mean that. In general, the internal energy is of the form,$$d U = Td S - Pd V + \sum \mu_{i} d n_{i} + J.dx$$
where $J$ refers to a generalised force and $dx$ to a generalised displacement, and even $-P.dV$ can be written as product of a generalised force and displacement with pressure serving ... | {
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Navier Stokes: what about angular momentum? I play with CFD for a while, and suddenly, a transcendantal question raises: :-)
Navier Stokes is basically Newton applied on a continuum in Eulerian.
For solids, we would consider linear, but also angular momentum.
Why don't we have to do that for fluids ?
Conversely, you ca... | For the exact equation, that's almost true (one should look at a derivation of the NS equation from the more fundamental Boltzmann equation, where the conservation laws are build into the particle-particle interactions -- but the closure in the approximation of the continuity and NS equations might spoil this if not do... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/235117",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
"answer_count": 2,
"answer_id": 1
} |
Relation of conformal symmetry and traceless energy momentum tensor In usual string theory, or conformal field theory textbook, they states
traceless energy momentum tensor $T_{a}^{\phantom{a}a}=0$ implies (Here energy momentum tensor is usual one which is symmetric and follows conservation law) conformal theory. (i.... | Note that under an infinitesimal change in the metric of the form $g \to g + \delta g$ the action changes to
$$
\delta S = \int T^{ab} \delta g_{ab}
$$
Now, under Weyl transformations we have
$$
g_{ab} \to e^{2\omega} g_{ab} \qquad \implies \qquad \delta g_{ab} = 2 \omega g_{ab}
$$
For Weyl transformations $\omega$ is... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/235246",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "6",
"answer_count": 1,
"answer_id": 0
} |
Effect of paint on drag force Aerospace engineering as well as automobile engineering gives a particular significance to the shape of a vehicle to enable proper and more effective transportation.What I want to know, is, about the impact that the protective covering aka the paint on an automobile etc. has on the drag fo... | Teflon has a low surface tension. What counts in viscous drag is the mechanical roughness of the surface. If the "peaks" of this roughness stick out into the boundary layer, they decelerate the flow more than a smooth surface would.
Normally, the drag coefficient drops with increasing Reynolds number. The Reynolds numb... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/235314",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
"answer_count": 1,
"answer_id": 0
} |
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