Q stringlengths 18 13.7k | A stringlengths 1 16.1k | meta dict |
|---|---|---|
Many cells in parallel If two or more cells of unequal voltages are connected in parallel (with the same terminal on the same side), is there a formula that gives the net potential difference?
Also, by Kirchoff's loop law, if we go round in the loop (the internal one, not the external one), we gain $V_1$ going in the d... | You cannot connect ideal cells of unequal emf in parallel. The potential difference between the common ends would then have two or more different values at the same time, which is impossible. See Combination of ideal voltage sources.
All real cells have a non-zero internal resistance. This allows their terminal PD to d... | {
"language": "en",
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Why spinning a pen makes it easier to remove it from the stand? I have a ballpoint pen stand on my desk. The pens are held inside their caps with the point down, like this one (but not as fancy):
If I try to simply pull up one pen, the friction between cap and pen is strong enough to lift the stand, instead of simply ... | For the same reason if you try to push a block or your coffee mug placed on the table it take some force before it move but when it starts moving you can lower the amount of force you applied but the block/mug keeps moving.
| {
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Why is a sine wave considered the fundamental building block of any signal? Why not some other function? It is mathematically possible to express a given signal as a sum of functions other than sines and cosines. With that in mind, why does signal processing always revolve around breaking down the signal into component... | You refer to Fourier Series. The brilliance of Fourier was to use sin to express a function.You know that you can create any vector from the sum of some unit vectors.Exactly the same think happens here. The number you multiply the unit vectors is the coefficients in F.S.
To answer to your question of why we use sin and... | {
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Reynolds Average Navier Stokes equations and turbulence scale To obtain the time average of an unsteady term like $\frac{\partial u_{i}}{\partial t}$ by definition we perform the following:
\begin{align}
\overline{\frac{\partial u_{i}}{\partial t}} &= \frac{1}{T}\int_{t}^{t+T} \frac{\partial }{\partial t}(U_i + {u}'_i... | This is a very good question, which illustrates that Reynolds averaging is a very special form of averaging. Indeed the Reynolds averaging procedure assumes three properties of the averaging operator:
*
*Linearity: Let $a,b$ be constants and $f,g$ observables $\overline{af+bg} = a \overline{f}+ b \overline{g}$.
*Co... | {
"language": "en",
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Dirac delta function definition in scattering theory I'm studying scattering theory from Sakurai's book.
In the first pages he gets to the following expression:
$$\langle n|U_I(t, t_0)|i\rangle=\delta_{ni}-\frac{i}{\hbar}\langle n|V|i\rangle\int_{t_0}^t e^{i\omega_{ni}t'} dt',\tag{1.9}$$
where $U$ is the propagator in... | I think the point is that if you took the limits to infinity without doing anything else, you'd be implicitly redefining the matrix element in order to make the equations consistent. So he just calls the redefined matrix element $T_{ni}$ instead of $V_{ni}$. Later he solves for $T_{ni}$ in terms of $V_{nj}$ (see the se... | {
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Are Hubble Telescope Images in true color? Like many others, I have marveled at the images made available from the Hubble Space Telescope over the years. But, I have always had a curiosity about the color shown in these images. An example is shown below. Are the colors we see, such as the yellows, blues, and so on t... | I find myself now answering my own question but only because the comment feature is not suited to this "comment". I have selected the answer by @HDE 226868 as my answer and primarily due to the linked Space.com reference. Very good answer to my question.
In particular, I also thought this quote from the same page as ... | {
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Why is there an energy gap in superconductors? I'm a little out of my depth here...
I'm trying to understand quasiparticle tunnelling in superconductor-insulator-superconductor junctions. Many books use the "semiconductor model" to explain this:
(source: wikimedia.org)
These diagrams show the available quasiparticle ... | The lower part is not filled with quasi-particles. At zero Kelvin, in zero magnetic field and with zero disorder all free electrons condense and form the superconducting condensate. The semiconductor model now describes the breaking of Cooper pairs not as resulting in two electron-, but in one electron- and hole-like e... | {
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How to predict bound states in a 1D triangular well? Assume we have a (single) particle in a potential well of the following shape:
For $x \leq 0$, $V = \infty$ (Region I)
For $x \geq L$, $V = 0$ (Region III)
For the interval $x > 0$ to $x < L$, $V = -V_0\frac{L-x}{L}$ (Region II).
The potential geometry is reminiscent... | Disclaimer: In this answer, we will just derive a rough semiclassical estimate for the threshold between the existence of zero and one bound state. Of course, one should keep in mind that the semiclassical WKB method is not reliable$^1$ for predicting the ground state. We leave it to others to perform a full numerical ... | {
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Would a solid door handle get hotter than a hollow one if there is a fire behind the door? I am a designer (mechanical engineer) who works for a fire company. My boss asked me to develop and build a new door handle and lock mechanism. Which I did successfully. It has a 16mm Solid vertical handle on the right of the doo... | A hollow handle is preferred. It will transfer less heat as it has a reduced cross section. It cools off by radiation and convection at at least at the same rate as a solid one, so the equilibrium temperature will be lower.
| {
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Difference between $|d{\bf r}|$ and $d|{\bf r}|$ What is the difference between $|d{\bf r}|$ and $d|{\bf r}|$ and why are both of them not always equal to each other?
My question might seem stupid to some and will probably get downvoted but I have thought on the question but still can't comprehend any difference betwee... | As shown in the diagram $|dr|$ represents the magnitude of the vector difference(that involves the laws of vector addition/subtraction) between $\vec{r_2}\quad \& \quad \vec{r_1}$ while $d|r|$ represents the difference between magnitudes of two vectors which is simply the difference in their lengths.
| {
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What does it mean for a physical quantity if its mixed second partial derivatives are not equal? This goes for every problem (either in electromagnetism or fluid dynamics) that has to do with vector fields. Say we have a fluid flowing in a closed circular pipe (or an electromagnetic field, the concept does not matter).... | Singularities in functions often lead to non commuting second derivatives. As for a Physical interpretation I think the following exercise may help:
*
*The partial derivative can be from First Principles can be written as
df(x,y)/dx = (f(x+h,y)-f(x,y))/h i.e the function is incremented by h and then the derivative ... | {
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What is the relationship between quantum physics and chaos theory? I am not a physicist, I am looking for a non-technical explanation.
Articles such as this one seem to hint at the fact that "macro reality" regulated by classical mechanics is somehow a pattern emerging out of quantum-level chaos. Is that correct? Can a... | There is a SHM wave equation based on Schroedinger's equation and Maxwell's equation for an elliptical wave function which produces chaos (Langtons ant).
It has Fermi statistics emerging from some of the variables and also has a beautiful thermodynamic Hamiltonian ($\theta$). It has the maths and the Octave code. This ... | {
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Creating complex interference figures with simple sources 3D printers that use Stereolithography usually have to build a 3D object layer by layer, each layer being constructed by having a laser travel across the surface until it has hardened all the layer's interesting parts.
Thus I was wondering if it would be possibl... | In principle I think your idea is sound, but there are serious complications that you probably haven't recognized. The complications have to do with "coherence". So your n sources actually have functions
$s_k = S_k \cos(kd + \omega t + \phi_k)$
where $\phi_k$ are phase constants associated with each source. Even fo... | {
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Is a bomb's shockwave strong enough to kill? I'm watching a movie, The Hurt Locker, and the first scene shows an IED explosion which kills a soldier. Of course movies don't depict explosions with maximum realism, but I noticed the debris and smoke / flame didn't reach him, and it made me curious about whether invisible... | The blast overpressure of the explosion is a very strong shock wave which can kill humans. There are a number of ways an explosion without shrapnel can do harm to people:
*
*Rupturing of the hollow organs due to rapid compression and expansion by the shock wave.
*The body can get thrown through the air if a strong ... | {
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How does the Higgss field change with the expanding universe? Does the expanding universe really have an effect on the Higgs field? Say, is it like the matter getting diluted with the expanding universe? Or does the expansion does not have any effect on the Higgs field, just like the Dark Energy maintaining its energy ... | At the moment there does not exist a quantized unified theory of gravitation and the standard model. The only candidate to date is string theories which are at a research level, and in which I am not able to form an answer.
There exist effective quantizations of gravity and effective models including the standard mode... | {
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How many pairs of nuclei collide in heavy ion collisions? As each bunch of heavy ions consist of a large number of nuclei it does not seem unlikely that multiple binary ion collisions will occur as it does in p-p collisions. However, should this be the case, I do not see how a possible azimuthal anisotropy could be rel... | ALICE is a heavy ion experiment at CERN.
Here is a lead lead collision
One of the LHC's first lead-ion collisions, as recorded by the ALICE detector.
Thanks to the advances of computing the vertex is determined by the tracks , measured and pointing back to it, even though there are thousands of tracks from each vert... | {
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What range of light wavelengths can a typical mirror reflect? A typical mirror is capable of reflecting the full spectrum of visible light. Can it also reflect other wavelengths both longer and shorter? What is the range?
| The reflectance of a typical mirror depends on the metallic coating used, but usually it is usually aluminum or silver in more expensive mirrors. Special optical coatings can be used to reflect or scatter EM waves at specific wavelengths.
Here is a photo of a mirror reflecting IR (700nm - 1mm wavelength):
Mirrors are ... | {
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Can a classical 50/50 probability be distinguished from a quantum superposition with a single measurement? $\renewcommand{\ket}[1]{|#1\rangle}$
A "false" (equally superimposed qubit) is created by mechanically firing with 50/50 probability a resonance photon at a Hydrogen atom qubit in the ground state. This qubit is ... | The minimum probability of error for correctly identifying one of two states $\rho$ and $\sigma$ prepared with equal probability (where minimization is over POVMs and the pair of states is fixed) is related to the trace distance $\|\rho-\sigma\|_1$ between them via the Helstrom bound $p_\text{min}=\frac{1}{2}-\frac{1}{... | {
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Can you huddle next to a fridge in sub-zero temperatures and keep warm? There's a saying I've heard in so many places.. "It was so cold that we used to huddle next to our refrigerator to keep warm..." I had heard this phrase uttered some 30 or so years ago, and it's stuck with me ever since...
Which gets me thinking...... | According to the second law of thermodynamics, sustained cooling below the ambient temperature requires work. The fridge's electric motor does this work to cool the air inside the fridge, in the same time it has to warm air outside the fridge - this is how one can "huddle next to a fridge" to keep warm (you can easily ... | {
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Why do physicists always give "event rates"? Many times I see plots for expected/measured "event rates", but what's the motivation for this? Why not generate/use plots for expected/measured event numbers/counts instead?
| Actual number of events measured will depend on how long an experiment is run, the efficiency of a detector, the size or thickness of a target, the intensity of an incoming beam among other things. Each of these is unique to a given experiment.
Science is done with the expectation of reproducibility, so these factors w... | {
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What is the time period of an oscillator with varying spring constant? It is well known that the time period of a harmonic oscillator when mass $m$ and spring constant $k$ are constant is $T=2\pi\sqrt{m/k}$.
However, I would be interested to know what the time period is if $k$ is not constant. I have searched hours af... | Here is a solution for a spring force that varies directly with displacement. It thus varies with time implicitly, but has no explicit dependence on time or any other variable.
Givens and Assumptions
*
*oscillator with mass $m$
*amplitude of oscillation $A$
*oscillator displacement, $x$, varies with time, but $x(t... | {
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How to form the spin triplet - singlet states from two electrons with spin not an eigenstate of $ S_z $ (spins not along z-axis)) For a two electron system, we know that the total $ J^2 $ states (Triplet - Singlet) are related with the $\uparrow \downarrow $ , $\downarrow \uparrow$ , $\uparrow \uparrow$ , $\downarrow \... | You are looking for the Wigner d-functions. They relate angular momentum eigenstates through rotation. As you can see in the link the definition is
$$d^{(j)}_{m,m'}(\theta) = \langle jm|e^{-i\theta J_y}|j m' \rangle$$
where $e^{-i\theta J_y}$ is a unitary rotation operator.
We'll have two sets of states: $|jm;0\rangle... | {
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Spherical and chromatic aberration correction I have some spherical lenses which are 5mm, 1mm and 0,5 mm in diameter, having 100x, 350x and 1000x magnification respectively. While looking at blood samples, I'm having big problems with spherical and chromatic aberration. The edges are completely out of focus and I get t... | The main effect here is lack of field flatness, or, cited in more geometric terms, the deviation between your imaging system's focal surface and the surface which you're imaging.
An imaging system generally images a plane onto the surface of an ellipsoid (approximately). i.e. light from a point surface on a plane will... | {
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Bohr Model of the Hydrogen Atom - Energy Levels of the Hydrogen Atom Q.1) What is the idea of stationary orbital of electron? As it is said energy tangled with mass and vice versa how is this energy always be in the form of cloud such as s, p, d, f? From where does this energy come from?Why don't the energy cloud vanis... | First of all let us make clear the the Bohr model posits orbits, with some imposed by hand quantization constraints, as the stationary assumption.
Orbitals for the hydrogen atom are the solutions of the Schrodinger equation with the hydrogen potential energy and helped develop quantum mechanical theory.
In QM the solut... | {
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Eigenspaces of angular momentum operator and its square (Casimir operator) The casimir operator $\textbf{L}^2$ commutates with the elements $L_i$ of the angular momentum operator $\textbf{L}$:
$$
[\textbf{L}^2, L_i] = 0.
$$
However, the $L_i$ do not commute among themselves:
$$
[L_i, L_j] = i\hbar\epsilon_{ijk}L_k.
$$
... | The $L_i$ has many eigenspaces corresponding to many eigenvalues. Each of those eigenspaces is also an eigenspace of the Casimir operator.
So they share common eigenspaces in the sense that there are eigenspaces that are eigen to both. But they don't share them in the sense that they are the same.
Look at the hydrogen ... | {
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Light Absorption of a glass I've the $n$ (refractive index of the glass sheet ) and $t$ (the thickness of the glass sheet)
with this information, how can I find the amount light absorption of the glass sheet?
| Possibly some semantic confusion here. Glass, with a simple refractive index, does not "absorb" light, it is transparent. Therefore the amount of light that emerges on the other side, for a given angle of incidence, is independent of the thickness of the glass.
Instead, some of the incident light is reflected from the ... | {
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What is the order of the gates making up the QFT on two qubits? The Quantum Fourier Transform consists of 2 gates. Controlled Phase Gates, and Hadamard gates. I'm assuming the Controlled Phase Gate is a combination of a Control Gate, and a Phase Gate.
But what is the order of operations on the Controlled Phase Gate? C... | You seem to have confused the CNOT gate with the controlled phase gate. There's no CNOT gate involved in the implementation of a C-phase-gate (let's denote it CPG for short), as all we do with it, is multiplying by a phase factor. For example on two qubits it is defined as:
$$
U_{CPG}(\phi) |xy\rangle = \exp(i(x\land ... | {
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Intepretation of area under velocity-time graph for a bouncing ball A typical velocity-time graph for a bouncing ball is shown below. I understand that the ball starts from rest at $t=0$, then it accelerates downwards and hits the floor at time $t_1$. Between time $t_1$ and $t_2$, the ball experiences an upward reactio... | No, all your reasoning is totally right. The conclusion isn't that the graphs are wrong, it's that the time of impact is less than 0.1 second. In this video, for example, the time of impact is just about 0.01 seconds.
| {
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Gravity and centre of mass Does gravity act entirely as if on the centre of mass? Often I have heard this, but it seems more realistic (even if less practical) if it acts on individual bits of matter, therefore weaker further away, shifting the "centre of gravitational attraction" closer to the attracting object than t... | You are right: gravity acts on individual bits of mass, and is stronger towards the source of the gravitational field. The center of mass and center of gravity correspond if you assume constant gravitational field (and rigid bodies I would say).
| {
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Free phonon propagator in imaginary time The free phonon propagator in Matsubara space is given by
$$D^0(i\omega_n)=\frac{1}{M}\frac{1}{(i\omega_n)^2-\Omega^2}.$$
I want to derive its representation in imaginary time. I know the result should be
$$D^0(\tau) = -\frac{1}{2M\Omega}\frac{\cosh[\Omega(\beta/2-|\tau|)]}{\sin... | I figured it out myself. The complex function used in the summation is
$$g(z) = e^{-z\tau}\left[\frac{1}{z-\Omega}-\frac{1}{z+\Omega}\right]$$
One can then write
$$\sum_{i\omega_n}g(i\omega_n) = \sum_{i\omega_n}\text{Res}[g(z)n_B(z)]_{z=i\omega_n} = \oint\mathrm dz\ g(z)n_B(z)$$
Then, one flips the contour and evaluate... | {
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Why don't photons split up into multiple lower energy versions of themselves? A photon could spontaneously split up into two or more versions of itself and all the conservation laws I'm aware of would not be violated by this process. (I think.) I've given this some thought, and a system consisting of multiple lower ene... | It is certainly thermodynamically possible for a high energy photon to vanish
and a multiplicity of lower energy photons to be created. This is observable as a cascade of events (photoelectric absorption of a photon, followed by multiple
fluorescence photons) in thermalization of a high energy photon interacting
wit... | {
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Why can black hole evaporate if objects need infinity time to reach event horizon (as seen by a distant observer)? I am new to black hole, but have a question about it:
*
*Object needs infinity time to reach event horizons (as seen by a distant observer).
*Particle-antiparticles separates, one of them drops into bl... | *
*Firstly particles can reach event horizon in finite time in the frame of an observer at infinitely far away (This is the frame of reference for describing black hole radiation).
*But the above phenomenon of particle reaching to the event horizon in finite time has nothing to do with black hole radiation. Hawkin... | {
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Can an egg be forced into a bottle by lowering the pressure inside the bottle using cold air? I just asked a question about why ice-cold water inside a thermos results in what feels like suction on the cap. The answer stated that the cold water cools the air inside the thermos, thus slowing it down, thereby decreasing ... |
the air [pressure] is lowered by heating the air inside the bottle.
I think you need to watch the video again. The air pressure is raised by heating the air, not lowered. This increase in pressure forces air out of the bottle, which is visible by the egg vibrating on the rim. The egg acts like a one-way valve. Wh... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/203669",
"timestamp": "2023-03-29T00:00:00",
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Reason for strange magnetic ball movement I was playing with a set of those neodymium magnet spheres and noticed a couple of strange behaviors (which I believe are related so I'm only positing a single question) and I was hoping to get an explanation for.
When I roll a single magnet in a straight line on a wooden table... | I've randomly found a possible explanation of what is occurring for one of the effects I noticed.
For the case of rapidly spinning magnet pair, it appears this is 'powered' by gravity via precession of the magnets. I can't find anything else to confirm / refute this though. Anyone care to weigh in?
http://amasci.com/a... | {
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Galvanic Cells and Electric Potential In a battery or a galvanic cell, the electric potential of the battery is due to a difference of charges between the two cells like in a capacitor? So it is the electric field due to this separation that is driving the electrons? if yes, why we call it electromotive force of a batt... | Galvanic cells are driven by a chemical reaction known as a Redox reaction.
Schematically speaking the cell contains a oxidiser $O$ and a reducing agent $R$, separated by a conductive membrane.
When the oxidiser reacts it loses electrons:
$O \to O' + n e^-$ (where $O'$ is the reduced form of $O$)
When the reducing agen... | {
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All possible photons wavelengths As far as I know all photons come from electrons loosing their energy. I remember from physics and chemistry classes, that electron can loose or get only certain determined amount of energy. Also I remember that every nucleous has finite amount of energy levels. Since photon is a wave... | Photons can come from a variety of sources, some of which are indeed transitions of electron levels (or nucleus levels or molecular levels), which are indeed discrete (it is also not because of wobbling).
The most common way of having photons of arbitrary wavelengths is via Bremsstrahlung radiation. This is the radiat... | {
"language": "en",
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Find constant acceleration with only initial speed and distance Given the problem:
"A car moving initially at 50 mi/h begins decelerating at a constant rate 60 ft short of a stoplight. If the car comes to a stop right at the light, what is the magnitude of its acceleration?"
While this problem seems simple, I can't see... | There are four kinematic equations that apply to this type of problem. One of those equations can be used to solve for acceleration when you don't how long it took for the car to stop. The equation is:
$v_f^2 = v_i^2 + 2a \Delta\ x $
The initial velocity is given, the final velocity is zero, and the distance traveled... | {
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Can I electrify a pin by applying current in its base? I imagine electric circuits as loops. So I wonder, if it is possible to electrify a pin without connecting its two edges, instead only applying current at its base. But I want the current to run across its tip. Is that possible? And if yes, how will the current flo... | If you charge a pin, most of the charge will accumulate in the tip, but you can't have current unless the charge is going somewhere. That's like asking for a waterfall without letting the water move.
You could take two pins, separated by an insulator, with joined tips, then apply voltage across the two bases. Then you'... | {
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Hermitian 2x2 matrix in terms of pauli matrices In my studies, I found the following question: Show that any 2x2 hermitian matrix can be written as
$$
M = \frac{1}{2}(a\mathbb{1}+\vec{p}\cdot \vec{\sigma})
$$
with $a=Tr(M)$, $p_i = Tr(M\sigma_i)$ and $\sigma = \sigma_x \hat{i}+\sigma_y \hat{j}+\sigma_z \hat{k}$.
I did... | First, check that the 2x2 hermitian matrices form a (finite dimensional) real vector space.
Convince yourself, that the set $\{1,\sigma_i\}$ is linearly independent.
You may now either directly expand a generic hermitian matrix in terms of $\{1,\sigma_i\}$, or note that the dimension of the aforementioned space is four... | {
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Physical interpretation of Convolution Let us say that we are interested in finding the voltage (potential difference) $y$ across the resistor.
The circuit consists of a battery, a resistor and an inductor. The problem can be solved by following the Laplace transform "recipe".
$$
-U + L\left(s\left(\frac{Y}{R}\right)... | To add to the mathematical explanations given in the other answers, physically speaking, an inductor is a device that resists changes in current, but which gradually allows current to change as time goes by if needed. That is, if a sudden change is applied, the current going through the inductor will gradually change ... | {
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Intuition for spin 1/2 and 1 propagators The propagator for a spin 0 particle is (in momentum space, dropping $i\epsilon$ and other factors)
$$\frac{1}{p^2-m^2}$$
which has the intuition "the particle likes to be on-shell". But the propagators for spin 1/2 and 1 are more complicated; they are
$$\frac{\gamma^\mu p_\mu +... | To get a better intuition consider a field with a general spin, this can be written as
\begin{align*}
\psi_\ell &\propto \sum_\sigma \int d^3 p \left( u_\ell (\vec{p},\sigma) e^{i p\cdot x}a(\vec{p},\sigma) + v_\ell (\vec{p},\sigma) e^{-i p\cdot x}a^\dagger (\vec{p},\sigma) \right)
\end{align*}
where $\ell$ is the spin... | {
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Does venus have plasma in its atmosphere? Is it hot enough on Venus for thermal collisions to ionize molecules? If not, what temperature would it have to be?
| See e.g. https://en.wikipedia.org/wiki/Saha_ionization_equation. Typical ionization energy for gases in planetary atmospheres are 14eV. The temperature on the surface of Venus is around 750K, which corresponds to an energy of 0.064eV. The exponential in the Saha-Langmuir equation will therefor basically completely supp... | {
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Motion of center of mass I was reading about COM and forces and came upon this in my book.
If a projectle explodes in air in different paths,the path of the centre of mass remains unchanged.This is because during explosion no external force (except gravity ) acts on the COM.
My question is, even though the author rea... | Because gravity was acting on the projectile before it exploded, it was already taken into account. It wasn't turned on at the time of the explosion.
The phrase "the path remains unchanged" is referring to the gravity-induced parabola that the object was on prior to the explosion, not to a straight line that it would ... | {
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Why is the K shell electron preferred in the photo electric effect? I have read in many books and on Internet as well that photoelectric effect is only possible when an electron is emitted from the K shell of the metal. Why not other bonded electrons?
| As others have pointed out, the premise is false. However, there is still an element of truth to it, which is pretty easy to explain. It is true that when a photon has enough energy to ionize either a tightly bound electron or a weakly bound electron, it has a much higher probability of doing the former. This higher pr... | {
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How to calculate the electric field due to a thin arc? I have been given to calculate the electric field at the centre of a thin arc with linear charge density as a function of $\cos\theta$ as $\lambda(\theta)=\lambda_0 \cos\theta$.
How I approached: The angle subtended by the ends of the arc at the centre is $\theta$.... | It's a good idea to approach this as you did, and you're certainly correct to choose a thin segment at an angle $\alpha$. This small segment subtends an angle $d\theta$. Remember that $\alpha$ is some arbitrary value of the variable $\theta$.
The charge carried by this segment is then $dq=\lambda d\theta=(\lambda_0\co... | {
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Does a gun exert enough gravity on the bullet it fired to stop it? My question is set in the following situation:
*
*You have a completely empty universe without boundaries.
*In this universe is a single gun which holds one bullet.
*The gun fires the bullet and the recoil sends both flying in opposite directions... | For a somewhat extreme answer: How massive should the gun be to have an escape velocity larger than the bullet speed? I am assuming we're using a 357 Magnum fired from a Desert Eagle, which is actually on the low to mid end of the muzzle velocity scale:
source: http://wredlich.com/ny/2013/01/projectiles-muzzle-energy-... | {
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Negative Electric Capacitance I know electric capacitance is always positive (otherwise it doesn't make any physical sense).
But the capacitance is related to the potential difference, which can be positive or negative, depends on who I choose to be first. Also, it is dependent on the charge, which can also have a nega... | Wikipedia defines capacitance of parallel plates as
$$C=\frac{Q}{V},$$
where $\pm Q$ is the charge on the plates (one sign for each plate) and $V$ is the voltage between them.
In other words, yes, if you calculate a capacitance to be negative from, say, $Q<0$, then you can just take the magnitude and call the capacitan... | {
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Is a flexible space tower using coaxial superconducting rings possible? Suppose we stack coaxially, vertically a large number of rings, made of some high temperature superconducting material, and start a current through each of the rings in alternate directions (e.g. the 1st ring CW, 2nd ring CCW, 3rd ring CW, etc). Ea... | The problem is that the system of one ring balanced on another is an unstable equilibrium. The rings will slide sideways and fall off. You've spotted this and you state in your question:
Using some simple mechanical restraining to keep the rings from sliding away horizontally from co-axiality
But your mechanical rest... | {
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Perturbations on a fluid thread and hydrodynamic instability I know that due to fluid instability there are some perturbations ( picture below )
after all of these, my question is the reason of existence of these perturbations.
Why exactly they appear? Shear stress or capillary pressure ?
if the parameters I mentioned... | The surface wave formed in a Rayleigh-Taylor instability is caused mainly by surface tension. Like i mentioned before, a liquid tends to minimize its surface area and $n$ droplets of volume $V/n$ have more surface area than a liquid column of volume $V$.
Initially, the film is uniform and surface tension will minimize ... | {
"language": "en",
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Would a pipe from the surface to the Earth's exosphere suck all atmosphere to the space? If I built a tube from Earth's surface to the exosphere, would all the air be sucked out to space?
If this pipe reached to a big planet, like Jupiter, would its gravity through the pipe suck our atmosphere?
If one end of the pipe w... | *
*No, it would not be sucked off, for the same reason that the earth has an atmosphere to begin with: gravity.
*No, for the same reason that Jupiter doesn't have a noticeable pull on you: the strength gravity decreases with the inverse square of distance.
*No, Gravity is too strong.
Your misconception seems to be c... | {
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How force is transferred from one body to another If there are 3 coins , namely 1 , 2 and 3 as in figure.
When coin $1$ strike coin $2$ ,the coin $2$ passes the force to coin $3$ and the coin $3$ moves away.
Case :1
How does this happen?
What exactly happens there and passes the force on coin $1$ to coin $3$?
How d... | Here is a very simplified picture:
Let's say you have a slow motion camera, and you can see in detail what happens in the fractions of second it takes for this process to occur. What you would see is that when 1 and 2 start touching they start deforming a bit.
This deformation is kinetic energy of 1 transforming into ... | {
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Near energy In the null of a Hertzian dipole Since $\mathbf E = -∇Φ - ∂\mathbf A/∂t$ one expects an oscillating $\mathbf E$ field even in the null of a Hertzian Dipole unless the two right hand side terms cancel -- which they do in the far field of the null.
However, in the near field of the null, the terms do not comp... | The example by CuriousOne is spot on - we know charged particle will accelerate in static external electric field, so generally, Poynting vector based on the external field does not need to be non-zero when charged particle gain kinetic energy.
The apparent problem with local energy conservation is caused by using the ... | {
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Why can scalars have a sign? I wondered to myself why some scalars have a sign, if they do not have a direction. After all, the plus and minus indicate the direction of the scalar on a one-dimensional axis.
So, for example, why can temperature have a sign? Why can't mass?
| The modern notions that separate "scalars" and "vectors" goes as follows:
*
*Scalars are elements of fields. Examples of fields include the rational numbers, the real numbers, and the complex numbers. Scalars can be added and multiplied and divided.
*Vectors are spaces over fields. These are basically just lists of... | {
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Why didn't accelerator mass spectrometry greatly improve the accuracy of carbon dating? My understanding of the limitation of radiometric dating is that background radiation swamps the radiation from C14 once the remaining atoms get few enough in number. Accelerator mass spectrometry seems to actually count every atom ... | After accepting an answer, I found an answer with a more experimental focus at talkorigins.org.
Why would the instrument reading be noisy if it counts every atom?
The second contribution, laboratory contamination, is largely due to sample chemistry (pretreatment, hydrolysis or combustion to CO2, and reduction to graph... | {
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Mathematically, where does polarization current come from? Mathematically speaking, where does polarization current in a material (due to time variant polarization) come from.
Griffith's introduces the concepts of bound charges and bound currents first as a mathematical trick, and then argues their physicality. But whe... | Assuming the polarization is not strong enough to ionize your material, the overall bound charge is neutral. Let's exploit this fact by integrating over the volume and surface of the bound charges,
$$\int_V\rho_b\:d^3r + \int_{\partial V}\sigma_b\:d^2r = 0,$$
which, by the divergence theorem, is satisfied if
$$\rho_b ... | {
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How to find kinetic energy given relativistic linear momentum? The relativistic energy of a particle is given by the expression
\begin{equation}
E^2 = m^2c^4 + p^2c^2
\end{equation}
The rest energy is $E_{0}=mc^2$ and the momentum is $p=mc$. In the rest frame, the kinetic energy is $T=E-mc^2$.
Ok, now in another frame... | The expressions are not true in general. The first one should be $E^2 = m^2c^4 + p^2c^2$, and the momentum is in general $p = \gamma m v$. The rest energy is $E_0 = m c^2$ and it doesn't depend on the frame (by definition), and the kinetic energy is always $T=E-mc^2 = (\gamma - 1) mc^2$.
You are (understandably) confus... | {
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Why don't constant motion charges produce waves? I'm a little confused about the origin of electromagnetic waves.
Although I can understand their origin mathematically, I get a little confused about the physical intuition of...
Information transfer is restricted to the speed of light; a local change in a field can onl... | For any charged particle in uniform motion there is an inertial frame in which that particle is at rest, and vice versa. So if the particle shed energy as EM waves due to uniform motion you would have the odd situation that a motionless particle would also have to shed energy as EM waves. Likewise if a motionless parti... | {
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at $T \approx 0 \, \text{K}$, will all energy levels within the electronic band structure be occupied up to a certain level? I saw this from the script of my teacher that I don't understand what does it mean
If we cool down a crystal to an absolute temperature of T ≈ 0K, all atoms of the crystal will exist at their gr... | The Pauli Exclusion Principle means that not every electron can be at the very lowest energy level.
| {
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Finding $\phi(k)$ If you have $\Psi(x,0) = c(\psi_1 + \psi_2)$ where $\psi_n$ is an Energy eigenfunction for a quantum number $n$. I'm supposed to find $\phi(k,t)$ at $t$ = 0. This is for an infinite square well from 0 to a.
I'm not exactly sure how to do this. I assume since $V(x)=0$ from $0<x<a$ then $\phi(k,t)$ w... | Firstly, the Shroedinger's equation is:
$$H\Psi(x,t)=i\hbar\frac{\partial}{\partial t}\Psi(x,t)$$
so, every wave funtion does evolve in time.
In the case of infinite square well (and also for cases where the potential V is independent of t), we can use separation of variable for the above Shroedinger's equation. Then:
... | {
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What is the meaning of spin of an particle is $1/2$ and $2$ or something? On which factor does these spin no. depend? I have read a book. The writer had written that if the spin of an particle is $\frac{1}{2}$, then we have to rotate it at $720$ degree. Imagine that there are two balls joined. Then we have to rotate th... | The spin of a particle is a number that describes its angular momentum. The earth orbits the sun, making years- that is angular orbital momentum. The earth spins on its own axis, making days- that is angular rotational momentum
The spin of a particle is analogous to the latter of those two. Not exactly alike due to the... | {
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Temperature of a falling meteor I am reading "What if?" article https://what-if.xkcd.com/20/ and I'm interested in it's scientific background. Mr. Munroe writes:
As it [the meteor] falls, it compresses the air in front of it. When the air is compressed, it heats it up. (This is the same thing that heats up spacecraft ... | Ram Pressure produces a large amount of atmospheric drag force, by the compression of the air located ahead of the meteor. It's equation is:
P = $\rho$v $^2$
P is the pressure, $\rho $ is the fluid density and v is the velocity of the meteor.
The remainder of your answer might be found here, Drag and Heat, so rather th... | {
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Clarification about Wave-particle duality Okay,so I am learning about the double slit experiment done with electrons. I saw this picture, which shows the interference pattern being built up slowly with increasing number of electrons:
I just wanted to confirm whether I have the correct understanding. The fact that the... |
The fact that the first image has a random distribution, shows that each electron interferes with itself and strikes a point on on the screen which would be dictated by the probability function.
Yes.
The interference pattern is the result of the same interference of many electrons and is a statistical property of m... | {
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Existence of bound states in 3D Yukawa potential For a 3D Yukawa potential
$$ V(r) = - \lambda { e^{-Mr} \over r}. $$
Bargmann's upper bound can be read as necessary condition for the existence of at least one bound state; we want $N_l>1$ and from $$\int r V(r) > (2 l +1) N_l$$ we had (for the $l=0$ wave)
$$\frac \lamb... | Bennett, Herbert S. "Upper Limits for the Number of Bound States Associated with the Yukawa Potential" Journal of Research of the National Bureau of Standards,
Vol. 86, No.5, September-October 1981 (PDF):
The number of bound-state solutions of the Schrodinger equation for
the screened Coulomb potential (Yukawa poten... | {
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Would a tachyon be able to escape a black hole? Or at least escape from a portion of the hole inside the photon horizon?
| Your question only really makes sense for a localized tachyon, i.e. one whose wavefunction in position space is constrained to a finite region of space (i.e. has compact support) because that is the only kind that will "fit" inside a horizon of a black hole. And the answer to your question for this kind of tachyon is t... | {
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What causes this pattern of sunlight reflected off a table leg?
My friend noticed an interference-like pattern around the table leg. However, we do know that interference patterns of sunlight produces rainbow colours. What seems to be happening here?
| I'm not convinced that variations in thickness are the cause. Variations in gloss (areas of specular reflection and areas of diffuse reflection) seem more likely: the "distribution requirements" are the same (in both cases the "defect" has to repeat at about equal distances), but the "thickness" hypothesis also require... | {
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Action max, min, or saddle? It is well known that $\delta S = 0$ lays the foundation for variational mechanics. But I am confused as to whether or not this S is a minimum, a maximum, or a saddle point. Some books address this issue by using the language of "Stationary Action" instead of the more well-known "Least Actio... | In analogy to the ordinary calculus you need to look at the second or quadratic variation, Gelfand and Fomins Calculus of Variations do a good job of explaining it with the minimum of fuss.
| {
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Why is induced current through an inductor more when switch is put off than when the switch is put on? This problem I saw somewhere got me thinking. I thought very hard about this but couldn't get to any conclusion. (here opened and closed are verbs, i mean when the current is flowing in the circuit and we cut the key ... | Imagine a circuit consisting of a battery, a wire, a switch, and an inductor, all in series. For "resistor" you could simply sum the internal resistance of battery and wire - it doesn't really matter (I just don't like "unrealistic" circuits for simple explanations).
When you close the switch, current will attempt to f... | {
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Amplitude of light across material boundaries Does the amplitude of the light ray decrease when it moves from a rarer to a denser medium?
I think that since amplitude depends upon the energy of the light ray, it should decrease. This is because of the kinetic energy of the light wave decreases (velocity decreases as li... | Fresnel's equations sum up the behaviour of light across medium boundaries in terms of linear dielectric response. This problem was solved in the 19th century.
| {
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What experiments have been done that confirm $E=mc^2$? What experiments have been done that confirm $E=mc^2$?
Are there experimental results that contradict $E=mc^2$?
Or are experimental results consistently showing this famous formula to be true?
| Emilio's answer was also the first that came to my mind, but I was not quick enough to post. However, even more precise experiments come from particle accelerators, and similar devices.
https://en.wikipedia.org/wiki/Tests_of_relativistic_energy_and_momentum
The power of the magnets in the LHC is determined by the relat... | {
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Why do voltmeters and ammeters have high and low resistance respectively? I understand why voltmeters are connected in parallel and ammeters are connected in series, but why is it that to measure voltage, you must have high resistance, and to measure current, you must have low resistance? Perhaps this is not within the... | Theoretically, these requirements arise from the way you connect the measurement devices to the rest of the circuit.
A voltmeter is connected in parallel, as you said. Say that you are trying to measure the voltage drop across a resistor $R$ through which passes a current $i$. If the internal resistance of the voltmete... | {
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How to calculate force / torque on non-flat lever, i.e. dolly See attached image. The mass is being rotated on a lever where the pivot point (P) is a certain distance ($L_2$) from the right angle at the bottom. How do I calculate the force necessary to apply horizontally at point U to lift the mass in the worst case (i... | You need to balance the moments about point P. The horizontal force F time $L_3$ will equal the mass $M$ times the horizontal distance $L_4$ between P and M.
$$F \times L_3 = M \times L_4$$
This calculates the force required in the current position you've shown.
Worst-case, an infinite force will be required after rot... | {
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Gaussian path integrals and convergence The Hamiltonian path integral in quantum mechanics, for a particle with coordinate $q$ and momentum $p$ and Hamiltonian $H=p^2/2m+V(q)$, is
$\int \mathcal{D}q(t)\mathcal{D}p(t)e^{i\int_0^T(p\dot{q}-\frac{p^2}{2m}-V(q))}$
Now, to go to the Lagrangian formulation, it seems like the... | The Gaussian integral with a purely imaginary exponent actually converges because of the increasingly fast oscillations. This Math.SE question has a bunch of (fully rigorous) proofs that $\int \sin(x^2)\, dx$ converges, which is of course the imaginary part of $\int \exp(ix^2)\, dx$. The real part can be similarly be p... | {
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Can tidal forces significantly alter the orbits of satellites? I would assume that there are other larger, more significant, forces acting on artificial satellites, but can tidal forces drastically alter the orbit of a satellite over time?
I was thinking this could especially be an issue for a satellite in geostationa... | Tidal force acting on a natural satellite, like the moon around the earth, is the result of the deformability of the earth as the moon affects it and slowly the moon recedes from the earth. In general these tidal forces can be accelerating or decelerating :
their orbital period is shorter than their planet's rotation.... | {
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Why must the speed of the aether wind be so small compared to the speed of light? I was doing some reading on the Michelson-Morley Experiment. One of the principle equations for the equations is this one.
$$\frac { 2w }{ c } \times \frac { 1 }{ 1-\frac { { v }^{ 2 } }{ { c }^{ 2 } } }$$
Where v is the speed aether wi... | If the velocity of the aether wind is a sizeable fraction of c, the apparent velocity of c will depend strongly and obviously on the direction in which the measurement is taken. Since this is not true, the aether wind velocity must be quite small, which requires a sensitive instrument to detect the effects. It was exac... | {
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What are the functions of these coefficients $c_1,c_2,c_3,c_4$ in $ \psi_{sp^3}= c_1\psi_{2s}+ c_2\psi_{2p_{x}} + c_3\psi_{2p_y}+ c_4\psi_{2p_{z}}$? Hybridised orbitals are linear combinations of atomic orbitals of same or nearly-same energies. Atomic orbitals interfere constructively or destructively to give rise to a... | Yes, hybridization is just that the hybrid state $\psi$ is a superposition of the different orbital states $\phi_1,\dots,\phi_n$.
Since the orbital states $\phi_i$ are assumed to be normalized ($\lvert\lvert \phi_i \rvert\rvert^2 = 1$) and orthogonal to each other, for the hybrid state to be normalized the squares of t... | {
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What is used to measure the spin of a particle? I was wondering what is the specific system or method that is used to measure spin of a particle? e.g. In a lab what would they use to tell what a particles spin is?
P.S. I am new to stack exchange so please tell me if I formatted this wrong or need to change anything abo... | Once the stable particles , electron and proton have had their spin determined by the stern gerlach method as discussed in the other answer, one can start building up the spins of the elementary particles and the resonances.
The spins of the particles have been determined by the angular distributions of decay products... | {
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Primitive unit cell of fcc When I consider the primitive unit cell of a fcc lattice (red in the image below) the lattice points are only partially part of the primitive unit cell. All in all the primitive unit cell contains only one single lattice point.
My question is how much each point at the corners of the red prim... | I'm guessing that the question is asking how you work out how many lattice points are in the cell. If so the standard procedure is to displace the cell a small distance along each of the lattice vectors than count the number of points the cell contains.
I'll illustrate this in 2D since my abilities to draw convincing 3... | {
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Where does the force appear when considering object interactions in another reference frame? Imagine I am sitting on an asteroid with my buddy and drinking a beer. When the bottles are empty we throw them simultaneously in opposite directions perpendicular to the asteroid's movement. What will happen?
From the logical ... | The mass of the asteroid changed, but the mass of the asteroid + bottles did not. Your outside observer would need to include the bottles in calculating total momentum; otherwise the system is not closed.
This is the same principle behind operating rockets in vacuum. We can change the momentum of a rocket by firing out... | {
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Does a changing magnetic field impart a force on a stationary charged particle? Does a collapsing and re-establishing magnetic field impart a force on a stationary charged particle? Does the charge particle get repelled and or attracted? Does it move or spin?
| Yes, it will create a force. The force is directed solenoidally around the change in a magnetic field.
To see this, look at Maxwell's equation $\nabla \times \mathbf{E} = -\partial_t \mathbf{B}$. This is analogous to the equation from magnetostatics: $\nabla \times \mathbf{B} = \mu_0 \mathbf{J}$. Thus a changing magnet... | {
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How does color (or reflection in general) work? I'm confused, does the absorption and emission determine the color of something? Or does that only happen when something is emitting energy?
When light hits an object, the photons get absorbed, then emitted with a different wavelength right?
| From a quantum mechanical perspective, all light scattering is a form of absorption and re-emission of light energy. Photons don't bounce off a surface.
When the energy (proportional to frequency, or color) of the light is far from resonance with an energy transition for the material, then the the re-emission happens ... | {
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Novel atomic clocks: can quantum and many-body effects help? I am trying to learn if there are any proposals concerning the application of quantum and many-body effects to atomic clocks.
From what I understand, optical lattices have been used for timekeeping only due to a superior signal to noise ratio (SNR). The inter... | You might want to look up the chip scale atomic clock made by symmetricom. It "resonates" with the hyperfine transition using CPT (coherent population trapping) weird QM Atom-light field interaction. SNR is many times worse than the standard Rb atomic clock.
| {
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Zero gravity means zero friction? The frictional force acting on a body placed on a horizontal plane is
$F=\mu{R}$
where $R$ is the normal reaction and is equal to weight of a body in this case. And $\mu$ is the coefficient of friction. But, if gravity is zero, then is the frictional force zero (ignoring all other fri... | There's no friction in space?
Strange how every screw just fell out of the ISS!
What's actually going on is you are looking at the friction between an object and the surface it's resting on, neglecting any other force that might be pushing the surfaces together.
| {
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Interpretation of cosmological redshift I was trying to understand why we cannot explain the observed redshift of distant galaxies using special relativity and I came upon this article by Davis and Lineweaver.
Unfortunately when I arrive at section 4.2, where the authors explain why we cannot use special relativity to ... | The Hubble parameter is defined to be $\dot{a}(t)/a(t)$, where $a$ is the scale factor of the universe. If you wished to have a model where redshifts were not due to expansion, but actually just due to things moving away from us (and this is what Davis & Lineweaver are doing in the section of paper you refer to), then ... | {
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Why is torque the cross product of the radius and force vectors? I understand the torque vector to be the cross product of the radius (moment arm) and force vectors, but that means the torque would be perpendicular to the radius and force vectors, which makes no sense to me, e.g. a force applied tangent to the surface ... | You are right in saying that the torque points along the line of axle. This doesn't make sense intuitively, but if you look at the formalism of angular momentum vector, this would be obvious.
So angular momentum is defined as $L = r \times p$. And torque is defined as $\tau = r \times F$ . It is clear that $$\frac{d\ve... | {
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What is a Christoffel symbol?
*
*What is a Christoffel symbol?
*I often see that Christoffel symbols describe gravitational field and at other times that they describe gravitational accelerations. Then, on some blogs and forums, people say this is wrong because Christoffel symbol is NOT a tensor and thus has no phy... | how i see it:
The Christoffel symbols represent the correction/changes to any parallel transported vector (like particle velocity) on a curve manifold (so that this vector "stays" on a geodesic of the manifold).
From Einstein equations, the energy/matter forges the structure of the (spacetime) manifold, and this struct... | {
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Sphere of uniform charge density with a cavity problem Suppose we have a sphere of radius $R$ with a uniform charge density $\rho$ that has a cavity of radius $R/2$, the surface of which touches the outer surface of the sphere. The question was to calculate the field inside the cavity.
Naively, I used Gauss' law to det... | The problem I see in your solution is with adding the $R/2$ term for the field inside the cavity (the negatively charged sphere that makes the "cavity"). The field inside of a uniformly charge sphere with charge density, $\rho$, can be found using Gauss' law to be:
$\vec{E}(r) = \frac{\rho r}{3\epsilon_0} \hat{r}$
You... | {
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Pendulum's motion is simple harmonic motion For a pendulum's motion to be simple harmonic motion (S.H.M.) is it necessary for a pendulum to have small amplitude or S.H.M. can be produced at large amplitudes as well?
If it is really necessary for an S.H.M. to have small amplitudes then why is it? because even at large ... |
In case of pendulum motion, when the angle of displacement is large(as shown in fig.), the direction of restoring force$(mg. sin \theta)$ is not exactly in the direction of equilibrium position. But the condition of S.H.M. is the restoring force must directed to the equilibrium position in all instant. So in case of l... | {
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Limitations of particle in cell method for high desnity plasma Are there any limitations of particle in cell (PIC) method for high density plasma? To be more specific, is modelling of a narrow channel of high density plasma possible or are there any limitations connected with PIC approximation?
| This is a very complex and broad question.
There are first some technical difficulties:
*
*The memory consumption, as noted by others.
*The time it takes to compute.
They can be very high, because a very large number of particles may be required to limit the statistical noise. This noise can create many problems,... | {
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Bernoulli principle and particle Bernoulli principle describes the flow of a fluid for steady, incompressible flow along a streamline. But it is said for a particle of a fluid along a streamline. My question is a particle of fluid refers to a molecule or a group of molecules?
| The Bernoulli principle is nothing but $F=ma$ for small volumes of fluid.
In other words, the only thing that can accelerate some fluid is a difference in pressure, and vice-versa.
A molecule of a fluid (since it has temperature) is moving quite fast, but it doesn't get very far because it collides with other molecules... | {
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Relativistic time dilation on Mars compared to Earth? What is the time dilation in Mars, compared to earth? Can we accurately calculate it? What information is needed to do these calculations?
| We can calculate the time dilation approximately using the weak field approximation. If the difference in the Newtonian gravitational potential between two points $A$ and $B$ is $\Delta\Phi$ then the weak field approximation tells us that the relative rate at which clocks at the two points tick is given by:
$$ \frac{\D... | {
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Does the ray transfer matrix for a gap change, based on the index of refraction of the medium? The ray transfer matrix for a gap is typically:
$$\begin{bmatrix}
1 & d \\
0 & 1\\
\end{bmatrix}$$
If I know that my glass is a thickness $L$ does the ray of light that goes into it travel a distance $n' \, L$ where $n'$ is t... | No, you would use the actual thickness of the glass $L$. This is because your ray matrix should change the angle of the incoming ray at the boundary using Snell's law, and to calculate the propagation accurately beyond that, you will want to use the distance covered by the ray in the lab frame.
| {
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Does the magnetic force depend on the reference frame? Force due to a moving charge = qvB
Immagine a charge moving with some velocity on earth and I calculate the force due to its magnetic field with Earth as reference frame for me.
An astronaut in space also calculates the force but space as reference frame.
For ease ... | The magnetic field and velocity vectors are not Lorentz invariants, so yes, the resulting force is frame-dependent.
| {
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Why are ultrasounds used for producing images of body organs? Low frequency waves can penetrate better than high frequency waves, then why are high frequency waves used in ultrasounds for sharper images?
Similar is the case in detection of flaws in metal blocks.Why are high frequency waves used here instead of low freq... | Ultrasound frequencies for diagnostic imaging range from about 1-10 MHz. Lower frequencies tend to be used for imaging of deeper tissues because they penetrate further as you rightly say. However, penetration is only one consideration. The "sharpness" of the imaging depends on the wavelength. Basically, you will not be... | {
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Electric field at $r=0$ How does classical physics justify the existence of an electric field at $r=0$?
Is this an edge case, an ambiguity, a "does not exist"?
Is this a trivial case or indicative of an actual fault in classical electrodynamics?
Obviuosly the math breaks down because the denominator is $r^2$...What I w... | To make it simple, it does not exist, there are no real point-like classical charged particles. That's why we learn, for example, the electric field of a homogeneous charged sphere right after the one for a point charge.
To put it in another way. A point charge $e$ could be thought of as made up by many $de$ tiny charg... | {
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Is specific heat really a constant? When we calculate heat lost or gained by a body according to equation $q=mc\Delta T$ where
*
*$m$ = mass of body
*$c$ = specific heat
*$\Delta T$ = temperature difference
In this equation, why do we take $c$ to be constant because we know $c$ depends on temperature? Why is the ... | No, specific heat varies with temperatures. Only at temperatures way beyond the Debye temperature is the specific heat of the body a constant. This equation treats the specific heat as a constant because the temperature range of operation is assumed to be small enough for a constant assumption of specific heat. The fin... | {
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Can two 2500 K light bulbs replace one 5000 K bulb for growing plants indoors? In an effort to assist an old Greek woman I find myself in need of greater minds.
A 5000 Kelvin light bulb is required for her indoor fig plant. Can I get away with substituting two bulbs each in separate fixtures emitting 2500 Kelvin each? ... | The output of a light bulb is characterized by (at least) two parameters: the Wattage, and the color temperature.
The wattage tells you how much total energy the bulb uses (and emits). The color temperature tells you how that energy is distributed. In principle, an incandescent object emits according to Planck's Law:
... | {
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Particle in a box: value for wave function $u(x)$ when potential $V(x)$ is infinity The time-independent Schrödinger equation (TISE) is:
$$ -\frac{\hbar^2}{2m}\frac{d^2 u(x)}{dx^2}+V(x)u(x)=Eu(x) \hspace{15pt}$$
where $E$ is a constant.
Imagine now a infinity potential well as we can see on the following picture:
Th... | Remember that the potential $V(x)$ is related to a force $F(x)$ via:
$$F(x)=-\frac{dV(x)}{dx}.$$
At $x \leq 0$ and $x \geq a$, $V=+\infty$, so in these areas:
$$x \geq a,$$ $$F(x) = -\infty \, .$$
and:
$$x \leq 0,$$ $$F(x) = +\infty.$$
So an infinite force acts on the particle at both borders of these areas, preventing... | {
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Can friction change the resonance frequency of a system? I am simulating the transient response of a mass-spring-damping system with friction. The excitation is given in the form of a base acceleration.
What I am not sure about is: can the friction change the resonance frequency of the system or will it affect only th... | The resonant frequency is equal to the natural frequency when no damping and no external force at all is applied to the system. When damping is applied so that now the decay time (decay of amplitude) is in effect, the resonant frequency decreases a little below depending on magnitude of damping.
| {
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Our Perception of Heat Our body temperature is roughly 37 degrees celsius (that is, when we measure our body temperature externally, by using a thermometer that measures the temperature of our skin usually between our arm and side torso), whereas most of us would say that 25 degrees would be a pretty hot day. Why do we... | You are correct in a sense of thermodynamics. The heat from a human body does indeed leave the body and into the surroundings. The body combats this by burning calories and producing more heat, keeping the internal body at a constant temperature.
I'm not a biologist however:
Perception of a hot day, is just because our... | {
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"url": "https://physics.stackexchange.com/questions/214432",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Effects of inner painting in the temperature of room which room will stay warmer for long time in winter night. The room with inner painting black or white?
| It will make no measurable difference.
Heat in a room is lost by conduction and convection - not (in significant amounts) by radiation.
Radiative heat transport occurs between two objects at different temperatures, so the surface of the wall would have to be colder than the rest of the (objects in the) room for radiati... | {
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"url": "https://physics.stackexchange.com/questions/214503",
"timestamp": "2023-03-29T00:00:00",
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