Q stringlengths 18 13.7k | A stringlengths 1 16.1k | meta dict |
|---|---|---|
If an earthquake can destroy buildings why it cant kill us according to physics? Most earthquakes with magnitude 5.5 and higher can damage or destroy buildings. However, according to my knowledge and experience, I have never seen someone dying from an earthquake itself. Rather, they die from an associated tsunami, dama... | There are several differences between humans and buildings:
*
*Anchoring Suppose I were to push you backward. Just on reflex, one of your feet will move backward to catch yourself. A building, on the other hand, is anchored in place. When the ground moves, the bottom of the building has to move with it. But a human ... | {
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Is there a difference between topological defects and topological soliton? Is there a difference between topological defects and topological soliton? Or are these objects the same thing? I ask this because it very common find some papers whose the authors itself refer, for example, the domain wall's, monopoles, cosmic ... | Yes, there is. In static situations, both are strictly the same thing. But, when analyze the dynamic of these structures, we see that they are differents.
| {
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Why would entropy of a system be fixed if it can exchange energy with its environment? Entropy maximization and energy minimization are equivalent statements of the same thing, as I understand it. If the internal energy is fixed, entropy is maximized because of statiatical reasons. If the entropy is fixed, and the syst... | I think you are misunderstanding a few things. Both the entropy maximization principle and energy minimization principle are due to statistical reasons. Suppose we have some parameter of the system $X$ (e.g. volume, particle number, etc.) that is free to vary, and the energy is fixed at $U_0$. The system will evolve to... | {
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Why don't (can't) astronomers take advantage of interferometry to the extreme? Reading and watching from various sources (e.g: APOD, ESO videos, or Wiki), whenever interferometry is mentioned, it is also usually explained like this:
An astronomical interferometer consists of two or more separate telescopes that combin... | ELT is an optical telescope. The short wavelengths of light necessitate extreme precision and stability of construction.
| {
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Two-photon interference inside Mach-Zehnder interferometer Imagine there's a strong laser beam, not just an attenuated stream of single photons, entering a balanced Mach-Zehnder interferometer.
One-photon picture: Each photon interferes with itself on the second beam splitter. As a result, all photons leave out of the ... | A MZ interferometer is very carefully setup, you can think of the path distance in 1 arm to be close to a perfect distance of n wavelengths of light and the other arm to be a n+1/2 wavelengths of light. Single photons entering the MZ interferometer will have the highest probability of transmission in the n arm and alm... | {
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On proving that charge is linearly proportional to potential for a conductor In Mr. Purcell's Electricity and Magnetism, page 103, it is stated,
An isolated conductor carrying a charge $Q$ has a certain potential $\phi _{0}$, with zero potential at infinity. $Q$ is proportional to $\phi _{0}$. The constant of proporti... | we know charge and potential have linear relation , as charge is directly proportional to potential. so if you draw charge versus potential graph you'll get straight line ( notice: the value you put on graph are experimental ) . now if you compare the equation y=mx and Q=CV means C(capacitance) represent slope which ... | {
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Sign-Conventions for Spinor Transformations In the literature one encounters a lot of different conventions for how left-handed spinor transforms (rotation angle $\phi$, rapidity $\beta$), among them
$M_L = M_{(\frac{1}{2}, 0)} = e^{-i \frac{1}{2} \vec{\theta} \cdot \vec{\sigma} - \frac{1}{2} \vec{\beta} \cdot \vec{\si... | A wrong assumption was made in the question asked.
An element $A\in SL(2,\mathbb{C})$ that induces the Lorentz transformation $X \rightarrow A X A^\dagger$ is a Spinor transformation for a right-handed Spinor (not left-handed, as claimed).
Rather, a left-handed spinor transformes with an element $A\to SL(2,\mathbb{C})$... | {
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Why don't we care about bound charges inside dielectric? I'm quoting Marek's answer from the question : Difference between electric field E and electric displacement field D
..materials have lots of internal charges you usually don't care about. You can get rid of them by introducing polarization P (which is the mater... | We cannot control the bound charges, but we can control the free charges. Therefore, it makes sense that we would want to refer to something that only depends on that which we can control. This is why we introduce the electric displacement
$$\mathbf D=\epsilon_0\mathbf E+\mathbf P$$
where the bound charge volume densit... | {
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$O(p,q)$ as transformations that conserve quadratic form Let us try to define $O(p,q)$ in two different ways, which I want to show their equivalence.
*
*Define the symmetric bilinear quadratic form $[\cdot ,\cdot]$ which is given by $$[x,y]=\langle x,gy\rangle$$ where $\langle \cdot,\cdot\rangle$ is the standard inn... | OP's two definitions of the indefinite orthogonal group$^1$ $O(p,q;\mathbb{F})$ are equivalent, which can be proven with the help of a polarization identity.
--
$^1$ Here $\mathbb{F}$ is a field with characteristic different from 2.
| {
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Some digital watches display digits in black on a white background and in the dark the backlight is reversed. How is this possible? Some digital watches display digits in black on a white background and in the dark the backlight is reversed, blue on a black background. How is this possible?
Here is an example:
https://... | The other way to invert an LCD so the digit segments and the background are "flipped" is to have extra LCD elements built into the background which can be switched on and off independently of the digit segments. When you want backlit segments against a black background, you de-energize the segments and energize the bac... | {
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Differences between charge quantity and electric charge As a senior middle school from China mainland, I am teaching physics about electric field. I work with my workmates, and we got a problem now. We cannot get an agreement. There are three viewpoints.
The first is that: electric charge is physical attribute and a ph... | I am not entirely sure of the nuances of meaning, but I hope this helps.
In English we can say "the object is charged", and we can say "the charge on an object is positive" and we can also say "the charge on the object is 3 Coulomb. I think the first and possibly the second treat charge as an attribute, and the third t... | {
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Factor of 3 in Photon Diffusion coefficient From definition of Diffusion coefficient:
$$D = c/3(\mu_a+\mu_s),$$
where $c$ is the speed of light front, $\mu_a$ is absorption coefficient and $\mu_s$ is scattering coefficient.
I wonder where does factor of $1/3$ comes from? I assume it is coming from dimensionality, but I... | Here is some information about this. The factor comes from an approximation and using spherical harmonics.
| {
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Gauge fixing of Polyakov Action In the Gauge fixing of Polyakov action we do general coordinate transformation where we take the transformation stated below
$$h_{\alpha\beta} = e^{\phi(\sigma)}\eta_{\alpha\beta}.$$
But here the left side has three free parameters (one less in the 2x2 h metric as it is symmetric in the ... | It is important to also keep track of the local symmetries present in each case. In the first case the dynamical metric $h_{\alpha\beta}$ has three gauge symmetries - two diffeomorphisms and a Weyl symmetry.
It is possible to choose the parametrisation in a particular way such that $h_{\alpha\beta} = e^{\phi(\sigma)}\e... | {
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Why doesn't stochastic resonance allow us to ignore noise? I don't know how to formulate the question better. This question is inspired from here where the author states that satellite communication is sometimes lost when radio noise from the sun makes the signal impossible to detect.
My understanding of stochastic res... | The signal is not "strengthened" by adding extra noise to it; instead the added extra noise $N_X$ and the received signal and noise $S+N$ are in different frequency bands; when the original $S+N$ is smaller than say a quantization step then adding the right amount extra noise can make that $S+N$ flip between levels and... | {
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Magnetic Field in Perfect Electric Conductor I know that one of Maxwell's equations states that the curl of the electric field is proportional to the time derivative of the magnetic field. We know that the electric field in a perfect electric conductor is 0, so why couldn't the magnetic field just be a constant instead... | Maxwell's equations give us the divergence and the curl of the magnetic field in this case:
$$\nabla\cdot\mathbf{B}=0$$
$$\nabla\times\mathbf{B}=\mu_0\mathbf{J}$$
For a conductor with current flowing, there is obviously a nonzero, non-constant (in space) magnetic field with a finite curl. I gather that this is not the ... | {
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Derivation of Conservation of Energy from Newton's Second Law Given Newtons's Second Law: $$ \frac {d}{dt} (m \boldsymbol{\dot r}) = \mathbf F $$
How is it possible to derive the conservation of energy equation with a constant mass?
That is how can you derive $ \mathbf F = - \nabla V(\mathbf r) $ where $V(\mathbf r)$ i... | As stated, the answer is: you cannot. There are force fields which are not conservatives, i.e. they cannot be written as the gradient of a scalar function. In such situations energy is not conserved. Such examples are quite common, consider for example friction.
Note that, by definition, a force is said to be conservat... | {
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Expectation value of operators with non-zero Hamiltonian commutators I'm a bit embarrassed because there seems to be an obvious thing that I'm missing, but I can't see what it is.
Consider $[\mathcal{H},A]=B$, where $A$ and $B$ are some operators and $\mathcal{H}$ is the Hamiltonian. Let's look at the expectation value... | $$\left\langle B\right\rangle =\left\langle \left[H,A\right]\right\rangle=E\left\langle A\right\rangle-\left\langle A\right\rangle E=0$$
| {
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Why do things cool down? What I've heard from books and other materials is that heat is nothing but the sum of the movement of molecules. So, as you all know, one common myth breaker was "Unlike in movies, you don't get frozen right away when you get thrown into space".
But the thing that bugs me is that things in the ... | Everything that is not 0 Kelvin radiates electromagnetic energy. In vacuum, this is the only relevant form of heat transfer. The hotter you are, the more energy you radiate (I believe the relevant equation is given here).
The question whether you cool off or heat up in space depends on whether you absorbs more electrom... | {
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Rotation of helium balloons A number of balloons are attached to a circular disk with string. Some balloons are
filled with air and some balloons are filled with helium. The disk is hung freely from
ceiling of a room and is disk is rotated about its center. Assuming that the disk
remains horizontal while rotating, desc... | Since the balloons are rotating, there must be a centripetal force that is keeping them going around the circle.
This resultant force is coming from a component of the tension in the string.
The centripetal force must point inwards towards the centre of rotation, so therefore the balloon must swing outwards so that par... | {
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What made Born interpret $|\psi|^2$ as a probability density? What was Born reasoning when he introduced the rule that $|\psi|^2$ could be interpreted as a probability density?
| You can consider the position basis, made of delta functions $\delta(x_i) \, \forall x_i \in \mathbb{R}$ (in $1$D).
You can write your wavefunction $\psi(x)$ in terms of that basis: $$ \psi(x) = \sum_i a_i \delta(x-i) = \int \mathrm{d}x_i\, a(x_i)\,\delta(x-x_i),$$
where $a_i$ is the probability amplitude of being at a... | {
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Is it really true that valence band is completely filled at zero temperature? Is it really true that valence band is completely filled at null temperature?
Indeed, I would think that if we apply an electric field, this would give some energy to the electrons from the valence band, so would they be prevented to leave th... | The temperature we're talking about here isn't the temperature of the room where you do the experiment, or even the temperature of the atoms in the material. It's the temperature of the ensemble of electrons in the material.
If you had a sample of semiconductor with its electrons at 0 K, and you did something to it (ap... | {
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Spring mass damper system: Distance from equilibrium after applying velocity to mass I have a spring fixed to a wall on one end and a mass object on the other end in its natural resting position. The question is how far does the spring stretch when a velocity $v_0$ is applied to it, assuming there is no friction.
My id... | Initially the mass has kinetic energy $\frac 1 2 mv^2$ and the spring has potential energy $E_{pot}=0$. So $E_{total} = \frac 1 2 mv^2$.
When the spring is fully extended, the velocity of the mass is $0$, so $E_{kin}=0$, and the potential energy is a function $f$ of the spring's maximum extension $x_{max}$. So $E_{tot... | {
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Peskin's treatment of Pions as Goldstone Bosons After restoring the mass terms in the Lagrangian
\begin{align}
\mathcal{L}=\bar{u} i \not D u+\bar{d i} \not D d-m_{u} \bar{u} u-m_{d} \bar{d} d,
\end{align}
one obtains equations of motion for the quark field
\begin{align}
Q=\left(\begin{array}{l}{u} \\ {d}\end{array}\... | The generator $\tau^a$ comes from the creation of the pion state. The calculation then decouples into the standard trace over all the color factors, that can be taken outside the expectation value, and an expectation value. The expectation value is an invariant for which they introduce the symbol $M$ ($M^2/2$ to be sp... | {
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Is 'Curl of magnetic field in electrostatic is zero' only empirical? I was looking up on the uniqueness of the displacement current.
About the uniqueness of the displacement current this question was exactly what I was looking for, but all the answers seem to go with 'empirically, when the electric field is constant an... | I think that the reason is that the Maxwell equation say so, and the Maxwell equations are empirically right. I can't think of a deeper reason
| {
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Non-holonomic constraints, degree of freedom and generalized coordinates If a system has $N$ coordinates and $M$ number of holonomic constraints then number of degree of freedom $=N-M$ and generalized coordinates $=N-M$ too. But if there are $k$ non-holonomic constraints then what will be no. of degree of freedom and ... | *
*Consider a classical point-mechanical system with $3N$ coordinates but only $n$ generalized coordinates $(q^1, \ldots,q^n)$, because of $3N-n$ holonomic constraints.
*Let us for simplicity assume that:
*
*All constraints are 2-sided, i.e. we do not allow 1-sided constraints (= inequalities).
*All non-holonomi... | {
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Pressure waves for sounds Is it possible to mechanically create a pressure wave, with correct amplitude, frequency, and other noise characteristics to recreate known sounds like train horns, chime bells, gun shot, etc.?
I am interested if a vibrating body, driven by a computer with controlled forces at various places i... | A device that does this is called a synthesizer. It can be programmed to emulate many types of sounds fairly well, but complicated sounds like the human voice are harder to synthesize.
| {
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What would be the potential due to a charge $Q$ at $Q$ itself? We know that the potential due to a point charge $Q$ at any distance is given by $V=\frac{kQ}{r}$, but what would the potential be at the charge itself?
| This question goes to the centre of the problem of self interaction, which is unsolved. So it is an excellent question. Often self interaction is ignored, but in quantum field theory it is prominent. There it leads to the infamous infinities or divergences. In QFT self energy is assumed to be incorporated into mass. Ho... | {
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Electron cloud and Quantum Physics Is it possible to detect the Electron Cloud? Also, it it possible for the Electron Cloud itself to contain any mass?
| It's always a danger to assign classical meaning to quantum objects, like electron clouds. One way to help clarify what's happening in atoms is to compare it with a another bound system: the nucleon.
Can we detect the quark-cloud in a proton? Yes, by elastic electron scattering. The angular/energy dependence cross sect... | {
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How are thermonuclear weapons possible? Given the fact that thermonuclear devices are a mix of fission through enriched uranium whose energy initiates the fusion in surrounding deuterium. Question is (how come) fission raises temperature so high that, instead of expansion of gases (possible at few hundred degree Celsiu... | This is possible because the fission reactions occur so fast that there is essentially no time for expansion to occur on the same time scale.
In addition, the X-ray-driven implosion reaction that is initiated by the radiation output of the initial fission process also happens so quickly that it too proceeds to completi... | {
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Why is the sky near the Earth limb warm-colored, even far from the sun? I've seen many sunset pictures with explanations. The sun is red, the areas adjacent to it is orange, then yellow... because redder lights bend less, and the air is thick at that angle. Far enough from the setting sun, the sky returns to its usual ... | The Belt of Venus happens before sunrise or after sunset, when the sun is below the horizon. As you know, the bluish or violet light by the sun gets scattered more than the red one, therefore when the sun is below the horizon, some blue light may be scattered and arrive to us, that's why Belts of Venus appear Violet.
... | {
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Eigenstructure of the Dicke Model I am beginning a study of the Dicke model and found a very interesting publication: "The Dicke model in quantum optics: Dicke model revisited" by Barry M Garraway in Phil. Trans. R. Soc. A (2011).
I would like to understand how he developed the eigenstates in section 2 (for the 2-atom ... |
First, what is he calling the number of excitations for the 2-atom system?
There are two atoms coupled to a radiation mode, i.e. to a harmonic oscillator. The states $|n\rangle$ refer to the harmonic oscillator, the states $|S, m_s\rangle$ refer to the two atoms. (Each atom is assumed to have only two energy levels a... | {
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Why isn't this anomaly in the CMB taken more seriously? Almost every time I try to find more information about the Axis of Evil, I end up with people trying to ignore the phenomena.
The video The (Cosmological) Axis of Evil explains it.
However, it's no doubt that this discovery leads directly to earth-centered univers... | The reason it is not taken too seriously, although it is still a legitimate avenue of research is that assuming we have a special place in the universe has always proved to be incorrect in the past, plus there are possibilities that remain to be explored that might explain the "anomaly". Further, it is stretching credi... | {
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Why is the triple point of water defined as 0.01 degrees Celsius and not 0? This was stated in my thermodynamics lecture today and I tried to ask my lecturer why it was not just defined as 0 since 0.01 seems weirdly specific. She was mentioning something about the order in which the Celsius and Kelvin scales came about... | At very low pressures (less than 1/1000 of an atmosphere) water goes directly from a solid to a gas phase as temperature increases. At about 0.006 atmospheres, the pressure of the triple point, the pressure allows for a liquid phase to exist at intermediate temperatures between solid and gas.
The temperature at whic... | {
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The right hand rule confusion?
I have a question regarding this problem. By using the right hand rule, I thought the answer would be A, but the answer key says it's B.
Doesn't the current come from the + side, so you wrap your fingers towards yourself(?) so that the thumb points to the left?
| The question is referring to the lines of force outside the coil. The lines of force go from the north pole to the south pole outside the magnet. The direction is the opposite inside from south to north.
Hence if you use the right hand rule correctly, you will see that the lines of force so from y to x outside the coi... | {
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Work done by friction in a complicated path
A block of mass $M$ is taken from point $A$ to point $B$ in a complex path by a force $F$ which is always tangential to the path. We also have coefficient of friction as $K$. What will be the work done by force $F$ when it reaches point $B$ from point $A$? Given that the ve... | The fact that no details on path are given implies that any path should give the same answer. Take a straight line from A to B or move horizontally and then vertically. Either way you get kmgl for the work done by friction. The work done by force F is just Fl + Fh = kmgl + mgh. (This assumes F changes and produces no... | {
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Why is work equal to force times displacement? This is how I think of what work is.I am sure I am wrong somewhere because I shouldn't be coming to the conclusion that I am coming to.It would be helpful if you would point out where this conceptual misunderstanding is.
Work is just change in the energy of an object.The o... | Let me not answer this question but only provide you with a hint. You are already close to what you are looking for.
I don't think that your approach is flawed. There are just a few gaps that you have overlooked. You are right in concluding that the work $W$ should depend on the mass $m$ and the velocity $\vec{v}$. How... | {
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How to interpret negative time in Lorentz transformation? I am somewhat confused about how to interpret negative time in Lorentz transformation. In the usual case of two reference systems S and S' where the distance X (the one that measures S) to an event, is very large with respect to the distance between S and S' (a... | According to Marco's answer and comments, I tried some numbers playing with http://www.trell.org/div/minkowski.html, and now I can answer my own question.
We have two events, event $A$ in $x=x'=0$ ; $t=t'=0$ and event $B:$ $x=11$ and $t=7.5$ with $v=0.8$ ($t' = -2.1666$, $x'=8.333$)
Lorentz transformation gives you the... | {
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What is the time derivative of resistance? Is there a unit for $\frac{\Omega}{sec}$? I have tried looking it up, but I can’t find anything
| Resistors are usually a constant value. They may vary with temperature but you'd need to know the material the resistor is composed of. If you just search on resistors you should be able to find technical sheets for different resistors that will have information as I described. The resistors should be constant in time ... | {
"language": "en",
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Are photons locked in time, and does this explain the "delayed choice quantum eraser" experiment? I'm trying to wrap my head around the "Delayed Choice Quantum Eraser" experiment and how events in the future affect light in the past.
I'm sure I'm wrong but to me this seems to indicate that photons experience no time. S... | The apparent retrocausality in delayed choice quantum eraser experiment is another confirmation of the theory of relativity. Because the photons travel at the maximum velocity possible, no time passes for them. So both photons hit a target, or are detected, simultaneously, as far as they are concerned. Anyone not movin... | {
"language": "en",
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The potential at a point According to my book, 'The potential at a point is said to be 1 volt when 1 joule of work is done in bringing 1 coulomb charge from infinity to that point.' But I wonder how it is possible. As the charge is being brought from infinity, the work done = force * infinity, thus, the work done would... | Loosely speaking, at great distance the force required gets infinitely tiny, so the two infinities largely cancel out.
| {
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How to interpret the wave function for non point-like objects The accepted interpretation of a single-particle wave function is that it represents (among other things) the probability of finding the particle at any point. The wave function is normalised so that the probability sums to 1 over space.
In principle, how... | Simply, you cannot talk about a wave function for a non point particle. A non point particle is a body, composed of many particles, and you have to write down the wave function for the coordinates of each particle composing the body. Of course, as in classical mechanics, you can make approximation, like idealizing the ... | {
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Understanding simple LC circuits I'm trying understand the physics of simple inductor-capacitor circuits such that there is just an inductor L and a cacpacitor C and a switch.
Imagine first that the capacitor is fully charged and the switch is then closed.
I do not understand why the current increases from an initial l... | An inductor "resists" changes in the current through the energy required to build up the magnetic field. Much like a capacitor "resists" changes in voltage through the energy stored in the electric field between the plates.
If you connect an inductor and a resistor in series, you will get a charge/discharge curve for... | {
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What is the difference in the way a single rope and a double rope would behave under dynamic load? Suppose I have a single rope attached to a fixed point via a load cell, which gives a number (in kN) based on the load it's experiencing. I take a weight (x) and attach it to the rope at a fixed point and raise it up to a... | Allowing for a tidier knot than you have drawn, so the knot itself has no effect on load (i.e. the knot doesn't have any 'give' in it), then things will be as follows:
*
*While the weights are falling freely the load cells in both systems
will record zero load (for simplicity I am assuming a weightless
rope).
*When... | {
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Hamiltonian capable of quantum computation Suppose we have a 1D spin chain evolving in time according to some Hamiltonian $H_t(p_0, p_1, p_2 \ldots)$, where $p_i$ are classical parameters ``set by the lab equipment". Divide time into discrete intervals of some length $\Delta t$: we are allowed to change the $p_i$ every... | Many Hamiltonians will be good. In particular, if you have control over the individual couplings, any interaction, together with a local terms in two directions, will suffice.
As an example, the Ising model with two fields,
$$
\sum p_is_z^is_z^{i+1} + \sum p_i' s_z^i + \sum p_i'' s_x^i
$$
will do: The local terms allo... | {
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Confusion about circular motion So today in class, I learnt that the angular quantities are related to the linear quantities by
$$s = r\theta \qquad \qquad v = r\omega \qquad \qquad a = r\alpha$$
where it is assumed that the object travels in a perfect circle.
My teacher then went on to derive the formula
$$a = \frac{v... | As the other answers and comments suggest, you are mixing up different properties by accidentally giving them the same labels.
The actual formulas are:
$$a_\perp = \frac{v^2}r$$
$$a_\parallel = r\alpha$$
A parallel $_\parallel$ acceleration is along with the circular path (also called tangential).
A perpendicular $_\p... | {
"language": "en",
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Why does water boil harder when you push a ladle to the bottom of the pot? I noticed this today while cooking. When I push a ladle to the bottom of my pot on my stove top, the boiling sound gets louder, and the bubbles rise to the top more aggressively. Can someone explain?
| I see this effect on my electric stovetop. The bottoms of my pots are no longer quite flat, and pushing downward on the pot improves the thermal contact between the pot and the heating element. The effect is present whether I push down on the bottom of the pot with a ladle, or whether I push down on the handles on th... | {
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Can someone explain what is the force the ball will exert? If a ball is falling under free fall then the force exerted by the ball on the ground would be $mg$. But that's not the case in real life ball would hit with more force. But when i draw free body diagram there is only one force that is acting on it $mg$
Can som... | Interesting question. Ball force affecting ground is $$ F_c = \frac{\Delta p}{t_i} = \frac{mv}{t_i} $$, because end speed is zero.
Now let's assume ball started to fall from some altitude, so it reached it's "contacting" speed $v$ according to :
$$ v = v_0 + a \space t = g \space t_f $$
Plunging this into formula abov... | {
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Would an infinitely (or very long) diffraction grating produce a diffraction pattern? Take a typical science lab diffraction grating which is producing a pattern on a screen.
Let's consider the location of say the first maximum on the right side.
Let's draw straight lines from the slits to the first maximum and think i... | All secondary peaks of the pattern are going to become dimmer and dimmer until they disappear completely as the number of slits is increased. But the central peak will become more and more bright and sharp, since light from each slit interferes constructively at the center of the pattern
| {
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Why do the expressions for an object rolling down an incline not depend on the coefficient of static friction? In my physics course, we are doing an experiment rolling disks and spheres down an incline (assuming there is no slipping). In doing the derivations (assuming a moment of inertia of $\frac25mR^2$ for sphere an... | The coefficient of static friction predicts the maximum possible value of static friction. Static friction can have any value below that. If the required value exceeds the maximum, the the friction becomes kinetic (usually smaller).
| {
"language": "en",
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Why is Jupiter's ring system so faint? Planetary ring systems are formed when asteroids, comets, or any other large objects pass too close to the planet and are torn apart by the planet's gravity [1]. Jupiter is often called the "punching bag" of our solar system. Because of it's massive gravity, it is impacted more of... |
So I would expect Jupiter to have a more prominent ring system than Saturn. Why is Jupiter's ring system not as spectacular as Saturn's?
The rings of Jupiter likely formed due to very different processes than that of Saturn. It is thought that Saturn's rings formed from the collapse of a large, icy body (e.g., somet... | {
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Physical Interpretation of an Elementary Inequality in Kinematics I recently came across the following question: suppose a point mass moves a distance $d_1$ for $t_1$ seconds at a velocity $v_1$, then accelerates instantaneously to a velocity $v_2$ and travels a distance $d_2$ for $t_2$ seconds at this velocity. Show t... |
You can view it pictorally. For when the second velocity is very high, the LHS tends to the second velocity. However the RHS tends to the average of the two velocities.
| {
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Why is the top surface of a ceiling fan more dusty than the bottom?
Top surface of a ceiling fan ( that hasn't been cleaned for a long time)
The bottom surface
The top surface seems to be way more dusty than the bottom. I reason that it doesn't have anything to do with gravity, as I've seen pretty much the same res... | That are many factors at play here.
Let us consider the case when the fan is rotating.Since there is a suction of air towards the bottom in the top surface of the fan the dust particle which move along the air flow collides with the top surface of the fan.On the contrary the dust particles get pushed away from the bott... | {
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Taking the speed of light into account during $n$-body simulation Currently, I compute the force between two gravitational interacting particles in a simulation with $n$ bodies according to
$$F = G\frac{m_1m_2}{r^2}.$$
Doing this, however, assumes that all bodies in the simulation interact instantly with each other mea... | You could use the Einstein-Infeld-Hoffman equations, derivable from General Relativity, which have Newton’s inverse square force as their dominant term but also include first-order relativistic corrections.
| {
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To lift an object, do we need a force equal to its weight, or greater than its weight? We have all heard people saying that to lift an object of mass $m$, you have to apply a force $F$ equal to its weight $mg$. But isn't it getting the force equal to its weight from the surface to which it is attached to (normal force)... | As has been mentioned in @Adrian's answer in the real world there is nothing rigid, neither the support where the mass m is resting on be it a table or cement bench nor the mass itself.
So there is always a certain amount of energy reserved in the support due to its deflection/settlement under the weight of the mass.
T... | {
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Does the wavelength of a particle depend on the relative motion of the particle and the observer? The de Broglie wave equation states:
$$\lambda = \frac{h}{p},$$
where $\lambda$ is the wavelength of the “particle”, $h$ is Plank's constant, and $p$ is the momentum of the particle.
Momentum is usually written $\,p=mv$, w... |
So does this mean that the wavelength of a particle depends upon the relative motion between the particle and the observer?
Yes.
The second statement is more or less equivalent to the first.
Side note: The strange thing about this relationship is that it means that, e.g., wave train seen by one observer as consistin... | {
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Question about changing mass under conservation of momentum In class today, my professor was teaching conservation of momentum. One example she used was an open cart rolling on a frictionless track while in the rain. As the cart collects water, the mass increases; and due to conservation of momentum the velocity must d... | The net force on the cart is not $0$. The cart is interacting with the rain in the cart, giving up some of it's momentum to the rain so that it travels the same velocity as the cart.
The net force of the cart and rain system is $0$. Any force the rain puts on the cart is directly opposed by the force of the cart on t... | {
"language": "en",
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Velocity not affecting heat produced by impact
A bolt of mass 0.3 kg falls from the ceiling of an elevator moving down with an uniform speed of 7 $\text{m s}^{–1}$. It hits the floor of the elevator (length of the elevator = 3 m) and does not rebound. What is the heat produced by the impact? Would your answer be diffe... | I do not have the full answer, but here is what I found out so far:
If we take the elevator as a frame of reference, it is clear that everything would be identical and thus the heat produced from the impact would be the same for a stationary elevator. However, if we consider the ground as a reference frame, it would be... | {
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Where do we see centrifugal acceleration? A body in circular motion always possesses centripetal acceleration which is felt by a person sitting at the center of mass. It will not be felt by a person viewing the motion from the ground frame. Then where do we feel the centrifugal acceleration? We cannot be anywhere on th... | Centrifugal force is a misnomer. The force that makes a body move on a curve is centripetal. The fact that you 'feel' a force is exactly analogous to feeling you are being forced back in your seat if you are in an accelerating car. There is no force pushing you back in your seat- the force is accelerating forwards.
| {
"language": "en",
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Why does a chain or rope move the way it does when suspended and rotated on a vertical axis? I have always been interested in why objects like chains, ropes, etc. move the way they do when "rotated" around a vertical axis while being held only where it is suspended. It forms a shape if you will, resemblant of a "C" or ... | Not a real answer but I'd like to note the model used while studying these phenomena. The shape of rotating chains is modeled by the Bessel functions. Precisely speaking, the radial displacement function $x$ is given as:
$$ r(x) = J_o ( \frac{2 \omega \sqrt{x}}{\sqrt{g}})$$
Where, $\omega_o$ is the angular frequency at... | {
"language": "en",
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What do we see when we observe a molecular orbital? My understanding is that when two hydrogen atoms bond (for example) the wavefunctions describing each atom combine into a single molecular wavefunction. Assuming the Copenhagen interpretation, does the wavefunction collapse into two particles whenever we look at the m... | The states of the hydrogen molecule come from the molecular Hamiltonian, not a combination of the atomic states. Molecular orbital theory uses the Born-Oppenheimer approximation and the atomic orbitals to get approximate electronic states (for H2).
The states are not necessarily entangled, except in the trivial antisy... | {
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Quantization of the Nambu bracket The most simple quantum mechanical system consists of a canonical pair of operators $\{P, Q\}$ satisfying
$$ P Q - Q P = i \hbar. $$
It is well known that there is a unique (modulo unitary maps) irreducible representation of this algebra (actually, of the Weyl algebra generated by $P, ... | A narrow reiteration of eqn (49) in Nambu's original paper, in response to your limited
for example, an explicit realization of $P,Q,R$ would already be a very helpful answer (even with the details of how to obtain this realization missing).
You just consider the Casimir-normalized generators of so(3),
$$
P=\left(\f... | {
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Pendulum attached to a cart. What have I done wrong?
A bob of mass $m$ is attached to the base of a cart via a thread of length $l$. The cart is accelerating with a non-uniform acceleration with magnitude $a$. The positive x-direction is towards the right and the positive y-direction is downwards. A simple diagram of ... | Your first approach is correct.
For the second approach, You have not taken into account centripetal acceleration $m\omega^2l$ which is the term you are missing in your second equation.
| {
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Poynting vector interpretation I am trying to calculate the dynamics of the power density of light in vacuum. The absorption per unit volume defined in terms of the Poynting vector is given by:
\begin{equation}
\text{Absorption} = -0.5 \nabla\cdot\vec{S}.
\end{equation}
Using $E = E_0\cos(k_yy-\omega t)\hat{z}$ and $H ... | The divergence of the Poynting vector is a measure of the rate at which energy is arriving or departing from a given region. As a sinusoidal plane wave propagates along the $y$ axis, wave crests wash over any given point, arriving and departing. This doesn't mean that energy is being absorbed. Absorption would be occur... | {
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Equations of motion in curved spacetime I'm trying to understand how to use covariant actions to derive equations of motion. A simple example would be the free scalar field
$$
S = \int\;d^4x\; \sqrt{-g} \left( -\frac{1}{2}\nabla_\mu\phi\nabla^\mu\phi-\frac{1}{2}m^2\phi^2 \right)
$$
Now from classical mechanics we know ... | I think it's more straightforward to vary the action with respect to $\phi$ and cancel surface terms. Also, check this: Derivation of Klein-Gordon equation in General Relativity
| {
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Why doesn't string theory predict the existence of infinitely many elementary particles? I'm a physicist, but my knowledge of string theory is extremely minimal. My naive conceptual understanding is that the vacuum is modeled as a certain topology (and geometry?) for the spacetime, and fundamental particles are explain... | For simplicity take the bosonic string theory in 26 dimensions. When you quantise the open and closed string you find excitations (states) of the string at any level $N$ with masses
\begin{equation}
M^2_\mathrm{open}=\frac{1}{\alpha '}\left(N-1\right),\qquad M^2_\mathrm{closed}=\frac{4}{\alpha '}\left(N-1\right).
\end{... | {
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Time and distance in a photon's frame of reference Disclaimer, not a physicist.
When I look at the sky I can see the star Rho Cassiopeiae. In my frame of reference, the photon hitting my retina has traveled for 4000 years and 3.78x10^16 km. In the photon's frame of reference, there's no time elapsed and my retina and t... | The calculation you performed in your reply to John, which related to an object moving at 0.99999999999999999999999c (or thereabouts!), has given you the right idea about the effects of relative speed when distances and elapsed times are viewed from a moving reference frame.
What you might like to think about is the fa... | {
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How do I experimentally measure the surface area of a rock? I hope this is the right place to ask this question.
Suppose I found a small irregular shaped rock, and I wish to find the surface area of the rock experimentally. Unlike for volume, where I can simply use Archimedes principle, I cannot think of a way to find ... | You can put the rock in an MRI scanner and get a 3D profile of it (and therefore, the volume and surface area). If it doesn't have spins that are useful for NMR, you can dunk the rock in something that does (ie. water or mineral oil), and then image that, and the void will give you the 3D profile of the rock (which you... | {
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When the direction of a movement changes, is the object at rest at some time? The question I asked was disputed amongst XVIIe century physicists (at least before the invention of calculus).
Reference: Spinoza, Principles of Descartes' philosophy ( Part II: Descartes' Physics, Proposition XIX). Here, Spinoza, following... | To explain this, I shall use the same example of a ball bouncing on the ground. In a perfectly ideal world, the ball will never be at rest throughout the bounce. There will be a time $t$ when the ball is going downwards. At time $t+dt$, the ball will be going upwards. This assumes that the coefficient of elasticity of ... | {
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What determines whether we use a vector or scalar potential? I understand that electrostatic potential is scalar because the curl of the field is zero, and this implies the electrostatic field is the gradient of the scalar potential to satisfy this. Similarly the divergence of a magnetostatic field is zero so a magneto... | For some vector field $\mathbf F$, you can use a scalar potential (unique up to a constant) whenever $\nabla\times\mathbf F=0$, and you can use a vector potential (unique up to the gradient of a scalar field) whenever $\nabla\cdot\mathbf F=0$. These are purely mathematical ideas, but you can see how this (very usefully... | {
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Why do we feel weightlessness during free fall? An object in free fall accelerates towards the Earth at a acceleration equal to $g$ (the accleration due to gravity). Now if we ignore the air resistance, why do we feel weightlessness? I could not understand the reason that we could not feel the pulling force that the Ea... | It's because what you feel is distortions to your body's shape. When in free fall, when air resistance is low, every part of your body is accelerating very nearly the same amount. No difference in force between any parts of your body means your body doesn't have to exert any forces to keep its shape, so you don't feel ... | {
"language": "en",
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Is there a way to construct a Hamiltonian from a set of DE? Let's say I have a set of first-order differential equations for set of position $x_i$ and conjugate momenta $p_i$, which might be complicated and time-dependent
$$ \dot{x}_i = f_i(x_j,p_j,t)$$
$$ \dot{p}_i = g_i(x_j,p_j,t)$$
and I know that these equations or... | Assuming from the notation
$$ \dot{x}^i~=~f^i(x,p,t), \qquad \dot{p}_i~=~g_j(x,p,t), \tag{1}$$
that the symplectic structure is the standard canonical symplectic structure $$\omega = \sum_{i=1}^n\mathrm{d}p_i\wedge \mathrm{d}x^i,\tag{2}$$
we get that
$$\begin{align}\mathrm{d}H(x,p,t)- \frac{\partial H(x,p,t)}{\partia... | {
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What is the length of the yarn in a ball of yarn? The image https://commons.wikimedia.org/wiki/File:Ball_of_yarn_10.jpg shows a typical ball of yarn. Such a spherical ball of radius $R$ has a volume $4πR^3/3$. The radius of the yarn is $r$.
How long will the yarn be on average? The length will depend on the way the bal... | I agree with you that the question is tricky. To a first order approximation you might consider the packing density of the yarn to be equivalent to the hexagonal close packing of straight lengths of tube (that's the optimal) which is about 90%. However, if the yarn is wound at random you won't achieve that optimum dens... | {
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Do liquids continuously boil in a pressure cooker? First, I understand that the boiling point of water is increased as the pressure is increased. At 15 PSI, the boiling point is about 250F.
My question, which seems like nobody can answer with certainty, is this: Is there a continuous boil within the pressure cooker on... | The way my older pressure cooker works is that, once it reaches operating temperature, it boils all the time. It has a pressure relief valve that has a weight that is placed over a conical tube sticking up in the lid. The weight has different diameter holes drilled partway through it, so that as larger a hole is placed... | {
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Difference between joint eigenstate and a single eigenstate? In angular momentum, we define $m,l$ as a joint eigenstate for $J_{z}$ and $J^{2}.$ Why is there any need to introduce $2$ variables to define an eigenstate? What difference it makes if we use just a single eigenstate for $J_{z}$ and $J^{2}$. Will the expecta... | Since $J_z$ commutes with $J^2$, they share a common eigenbasis (an eigenstate in this case). But that does not neccesarily mean they have the same eigenvalues (for instance, they could differ in magnitude), so you use $m$ to refer to $J_z$ eigenvalues and $l$ to $J^2$ ones.
That's why you use $m,l$ (or $m,\lambda$ dep... | {
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Help understanding unit: Micromoles per square meter per second The context is light, illumnination, photons.
The units seem to suggest something different from the definitions I have found:
$$\frac{µmol}{m^2 s}$$
This, to me, says I have one millionth of a mole ($6.022×10^{17}$) in photons landing on a one meter squar... | Well, amounts measured by given a number times a unit, so the number is the amount divided by the unit. This is, if $x=n\frac {\mu mol}{m^2s}$, then $n = x \frac{m^2s}{\mu mol}$. That's similar to how, if something is five meters long, that means that its length divided by a meter is five.
| {
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Principle of stationary action vs Euler-Lagrange Equation I am a bit confused as to what I should use to derive the equations of motions from the lagrange equation.
Suppose I have a lagrange function:
$$L(x(t), \dot{x}(t)) = \frac{1}{2}m\dot{x}^2-\frac{1}{2}k(\sqrt{x^2+a^2}-a)$$
Method 1: Principle of least action
$$\d... | Granted appropriate boundary conditions, the stationary action principle and the Euler-Lagrange (EL) equations are both precisely the condition that the functional/variational derivative
$$\frac{\delta S}{\delta x^j (t)} \tag{1} $$
vanishes, so they better agree!
| {
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Why doesn't the block fall?
I came upon this question as I was going through the concepts of tension. Well according to Newton's third law- every action has an equal and opposite reaction. Here my question is that if the tension at point B balances the tension at point A then which force balances mg as it can't be bal... | There are two forces acting on the mass are gravity and tension from the rope. This is seen in your free body diagram on the right side of your image. The mass does not fall (or rise) because these forces are of equal magnitude and opposite direction, thus the net force acting on the mass is $0$.
Yes, if we look at the... | {
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Energy of a dielectric rod Let a dielectric rod kept in an electric field (initially in equilibrium) be rotated by an angle, and then released. Is some energy stored in it (the rod)? Why? What is the value of this energy? How can I come up with energy for dielectric of arbitrary shape?
| A dielectric consisting of polar molecules initially in random orientations when no electric field is applied will undergo some degree of polarization by orienting the dipole moments of the polar molecules to align them with an external electric field.
If either the rod of such a dielectric is rotated in a stationary ... | {
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Isotropic moments of inertia Explicit integration can show that the moment of inertia of a Platonic solid (i.e., tetrahedron, cube, octahedron, dodecahedron, or icosahedron) of uniform density is the same around any axis passing through its center. The axis need not pass through a vertex, or midpoint of an edge, or cen... | Start with any solid whatsoever. Choose a coordinate system $x,y,z$ in which its moment of inertia tensor is diagonal. The diagonal components are
\begin{align}
I_{xx} = I_0 - \sum_n m_n x_n^2
\\
I_{yy} = I_0 - \sum_n m_n y_n^2
\\
I_{zz} = I_0 - \sum_n m_n z_n^2
\end{align}
where the $I_0$ term is the same for all ... | {
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What's 'force per second'? For example, if a force of 10 N per second (10 N/s) is applied to an object, does this have a name or a definition? I'm not referring to impulse - which is Ns.
An airplane's engine thrust is simply given as a force, but this must be a force applied by the engines each second (N/s)?
Thanks! ... | As per second Newton law force is defined as momentum change over time :
$$ F = \dot p $$
If force is constant, then each second it will remain the same, thus defining "force per second" doesn't make much sense.
However force can be function of time too, i.e. $F=F(t)$, then one can calculate force change over time :
$$... | {
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What vector field property means “is the curl of another vector field?” I'm an undergraduate mathematics educator and I teach a lot of multivariable calculus. I posed this question on MSE over four years ago and I haven't gotten any definitive answers (despite 12 upvotes and a bounty posted). It could be there's no a... | If the domain is topologically trivial, then, as explained in the other answers, "is a curl" is the same as "incompressible," i.e., has zero divergence. So that's your answer.
In examples like the electric field of a point charge, the domain has a hole in it. This breaks the equivalence between incompressibility and is... | {
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Slowing a beam of light In the description of the phenomenon below, apart from slowing the absorption and emission of a wave by an atom, does the wave propagation between atoms also slow down?
https://www.seas.harvard.edu/haulab/publications/pdf/Ginsberg-Garner-and-Hau-Nature-445-623-(2007).pdf
I confess without beatin... | Photons are elementary particles, massless, they always travel at speed c in vacuum, when measured locally.
Though, you are correct, light can slow down in media, but what actually slows down in media is the wavefront.
You are asking whether between atoms light travels at speed c or not.
Individual photons still trave... | {
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Why does foam in a rotating liquid accumulate near the centre? I first noticed this while having a coffee. When the coffee was rotating in the cup, most of its foam accumulated near the centre.
I recreated the effect with some soap and water. The accumulated foam formed a beautiful dome. You can see the dome formation ... | The water experiences a greater centrifugal force than the bubbles
Both the bubbles and the water experience a centrifugal force. However, since the centrifugal force is given by:
$$ F_c = m R \omega ^2 $$
You can see that a more massive object (the water) will experience a greater centrifugal force. From the perspecti... | {
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Is the relation between change in potential energy and work by internal conservative force can be used even in presence of non conservative forces? We know that work done by internal conservative forces is the negative of change in potential energy of the system stored in conservative force field. But does this logic s... | The relation between potential energy and charge will remain. The total mechanical energy in a system is $E = KE + PE$. In a conservative system (a single particle orbiting a particle of opposite sign, not including EM radiation), that total energy remains constant. This is like a frictionless pendulum. If a system inc... | {
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How can the mechanism of electrons in an atom be explained? I am a high school student who takes both Physics and Chemistry.
Recently I learnt about the quantum mechanical point of view of looking at electrons or nuclei. I also learnt that the wave functions can be obtained by solving the Schrodinger's equation with va... | It's true that because of QM you can't think of the electrons in the atoms as having precise positions. It's not just position that is affected by QM but all "observable" phenomena. You are right that a theory that explains forces as a function of position is therefore likely to run into problems. But there are quantum... | {
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How does a time varying magnetic field confined in a cylindrical region produces induced electric field even outside the cylindrical region? We know from Faraday's Law of Electromagnetic Induction that due to Time Varying Magnetic Field (TVMF), a non conservative electric field will be induced.
Now if we consider a cyl... | Faraday's Law states that a time-varying $\textbf{magnetic flux}$ through a surface induces a electric field in said surface's border.
Now, take a circumference concentric with the cylinder in where there's a TVMF. The flux - "how much the magnetic field goes through " - the surface delimited by the circumference, vari... | {
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What is orbit that could place satellite to be always under the Sun? I just thinking that, if we could place satellite to orbit earth in opposite direction of earth rotation, inverse of geostationary orbit. If we carefully choose a speed to sync with earth rotation, it would have that satellite stay exactly the same po... | I think what you're talking about are Lagrangian points:
Image Credit: Anynobody / Wikimedia Commons
They are points such that the combined gravitational effects from the Earth and the Sun give rise to areas that would have the same angular velocity as the Earth. However, out of the five lagrange points shown below: 1... | {
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How is it possible that entropy of the universe has increased since big bang but temperature of the universe has decreased? How is it possible that entropy of the universe has increased since the big bang, but the temperature of the universe has decreased?
I know that the increasing temperature of the system tends to i... | Maybe this wikipedia definitions will help:
In statistical mechanics, entropy is an extensive property of a thermodynamic system. It is closely related to the number Ω of microscopic configurations (known as microstates) that are consistent with the macroscopic quantities that characterize the system (such as its volu... | {
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How does the Earth have enough gravity to hold on to its atmosphere? I'm looking for numbers/math that describe how earth (or any other planet) holds on to it's atmosphere.
Presumably, we would be able to determine the exact atmospheric pressure that we would expect to have on a planet of a given radius/mass/density, a... | This actually isn't too hard. The Maxwell-Boltzmann distribution provides the average velocity of gases. The most probable speed (which is only good for order of magnitude estimates) is:
$v_p=\sqrt{\frac{2kT}{m}}$
You can put in the numbers: $T$ is the temperature of the Earth's surface, about $300K$, and $m$ is the ma... | {
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Does the expansion of the universe stretch distances in non-radial/angular directions? At time $t = t_0$ a galaxy is situated at a proper distance $r_0$ and has a proper diameter $D_0$. Setting $a(t_0) = 1$ the proper distance to the galaxy will then of course evolve with the expansion of the universe as:
$$r = a\chi =... | FLRW metric can be written as,
$$ds^2 = -c^2dt^2 + a(t)^2[dr^2 + S_{\kappa}(r)^2d\Omega^2]$$
In the calculations of the angular diameter distance, we set $dt = dr = d\phi =0$ which leads to
$$ds = a(t_e)S_{\kappa}(r)d\theta$$
If the object has a diameter $D$ then we can write.
$$D = a(t_e)S_{\kappa}(r)d\theta$$
or
$... | {
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Constant $g$ acceleration from astronaut's frame of reference When a spaceship is experiencing a constant acceleration of $10m/s^2$, the astronauts will be moving at nearly the speed of light after about a year in the earth's reference frame. This means the spaceship's energy will start to diverge as a function of the ... | If you know how much fuel (mass) you need to travel from the earth to the next object , you can answer the question how much energy you need , remember that energy is equivalent to mass.
I found the answer in this dokument
http://math.ucr.edu/home/baez/physics/Relativity/SR/Rocket/rocket.html
$$\frac{m_F}{m_L}=\ex... | {
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Can the forces change with frame of reference? Consider a ball kept on man's head (mass $M$) on the Earth. Now supposing I throw the ball from height $h$ of tall building then why does he gets more hurt? Isn't the force still mg?
I would like to know what happens in ideal case (no air resistance)
and then in real case ... |
Now supposing I throw the ball from height ℎ of tall building then why
does he gets more hurt? Isn't the force still mg?
The impact force of the ball falling on the man's head is not the same as the weight of the ball on the persons head. This is because it takes a force to perform work in order to absorb the kinet... | {
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Why in mercury barometer pressure inside the glass tube at a point is same as the pressure outside the glass tube at the same height? I am quite familiar with the pascal’s law but i still think that being on the same points still they should have different pressures as above on one point is atmosphere and on the other ... |
Let understand this by the figure, if we notice that pressure at surface of mercury would be the atmospheric pressure. And same pressure at the bottom of the mercury tube and if we go a height h above.
Now the pressure in the space above the mercury is less than atmospheric pressure and equilibrium is attained when $... | {
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Banana vs Brazilian Nuts Radiation Looking online I can find that the BED (Banana Equivalent Dose) is around 0.1uSv, but Brazilian Nuts can have up to 444Bq/kg.
I know both of those foods are safe, I just wanted to understand how those units compare to each other, how much more radioactive is a Brazilian Nut compared t... | Answering directly to "I just wanted to understand how those units compare to each other":
You can't convert directly between Sievert (Sv) and Becquerel, since they represent different physical quantities.
Quoting the definition of Sievert from the Wikipedia:
1 Sv = 1 joule/kilogram – a biological effect.
The siever... | {
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Is it a typo in David Tong's derivation of spin-orbit interaction? A few lines below equation 7.8 D. Tong writes
The final fact is the Lorentz transformation of the electric field: as electron moving with velocity $\vec{v}$ in an electric field E will experience a magnetic field $\vec{B}=\frac{\gamma}{c^2}(\vec{v}\tim... | $\vec{p}=\gamma m\vec{v}$ is the technically correct equation, but for non-relativistic particles where $|\vec{v}|\ll c$, the Lorentz factor becomes
\begin{equation}
\gamma=\frac{1}{\sqrt{1-v^2/c^2}}\approx 1,
\end{equation}
and so can be neglected.
For your reference, I had a quick look and I believe Eq. (6.45) of his... | {
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Particle falling into a Kerr black hole Let's say that a particle starts a radial free fall towards a Kerr black hole with zero initial energy at $r\rightarrow\infty$. The initial angular momentum of the particle is zero ($p_\phi = 0)$. From the Kerr metric, $p_\phi$ and $E$ are the constants of motion for the particle... | No the angular momentum of the particle would remain zero (it is still a constant of motion). The angular velocity of the particle, on the other hand, would steadily increase as the particle approaches the Kerr black hole (i.e. the Newtonian relationship between angular momentum and angular velocity does not hold in GR... | {
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Why can we assume long structural members to be in plane strain?
In plane strain, the strain in one direction is assumed to be zero. It is taught that if we have a structural member that is very long in one direction compared to the others, the strain in the long direction can be assumed to be zero. A dam is a popular... | I think that we can often deal with long structural members as plain strain due to friction along the length, which acts as a practical restriction to displacement.
In the case of the dam, the friction with the soil under its own huge weight avoids longitudinal displacement.
Another example is rolling of steel sheets. ... | {
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Why does atmospheric pressure act on us? I have a bit of misconception about weight which I want to clarify.
The air pressure is explained as the weight of the air column above our head acting per unit area. But since air is not continuous how can the weight of all the air molecules (above our head) be acting on our h... | The reason air pressure acts on us as humans really has nothing to do with mathematics, its science. Our bodies are more water than mass, so the pressure exerted on us by air pressure acts on our blood and other body fluids, making increases and decreases in our own pressures. Its really only common sense - this is why... | {
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Entropy of mixing Consider the case of a wall dividing a box into sections 1 and 2, each of volume $V_0$.
Let be $X$ is an ideal gases. Section 1 contains $N$ particles of $X$ and section 2 contains $N$ particles of $X$.
The entropy of mixing (removing the divider) is $0$ in the above case. I understand that an argum... | So when you mix the gases, say that the probability of any gas particle existing in the i'th state is $p_i$, so now what do you say is the probability of particles being in various states?
$\Pi_ip_i$. Now entropy is defined as the average value of $-log(p_i)$, and as $p_i$ is multiplicative, $-log(p_i)$ is additive, i.... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/518641",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 2,
"answer_id": 1
} |
The net charge of Earth Shouldn't the earth have an over all small positive net charge? Cosmic rays in the form of light or high energy particles can ionize atoms, when that happens the electron and the positive ion recoils and the electron gets a whole lot more velocity than the positive ion.
Meaning the electron had... | There are other effects at play. In particular, solar wind provides protons and electrons which can be attracted by bodies with a charge. If the earth were to develop a negative charge, more protons would be attracted to it than electrons, and the charges would neutralize.
In theory there is some equilibrium balance ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/519329",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 1,
"answer_id": 0
} |
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