Q stringlengths 18 13.7k | A stringlengths 1 16.1k | meta dict |
|---|---|---|
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... | If a perfect semiconductor/insulator is at zero temperature, than indeed all its electrons are in the valence band, and exciting them to the conduction band requires, as a minimum, the gap energy, $E_g$.
If a uniform electric field is applied, then, obviously, there will be degeneracy between the valence band and the c... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/503638",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
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'Drummy' sound when striking with a hammer In building there is a common test for masonsry structures that involves striking the structure with a hammer and listening to the resulting sound. If the sound is ringing the structure is fine but if the sound is 'drummy' (maybe like a dull thud) then there is an issue with t... | in the ringing sound, the structure is vibrating as if it were a solid, seamless metal bar like in a xylophone or a wind chime, which indicates that all the individual bricks in it are tightly and firmly cemented together into a single mass, which is a good thing.
if the sound instead is dull and "drummy", it means the... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/503946",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
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Photoelectric current vs anode potential Attached is the graph of photoelectric current vs Anode potential as given in my book for same intensity and different frequencies of incident light for the same metal(hence same work function).
In my opinion this graph isn't the graph for the conditions as mentioned rather, it ... | Yes, you are right.
What you drew can be confirmed from here:
Stopping Potential vs Frequency
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/504152",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
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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... | No, it's not purely empirical. If the curl of an electrostatic magnetic field was going to be nonzero, it would have to be determined by some new term on the right-hand side of that Maxwell's equation. There is nothing available to serve that purpose that would preserve linearity and have the right symmetry properties ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/504292",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Heat produced if earth stops rotating In my textbook there is a question that is as follows:-
If earth stops rotating about it's own axis,the increase in its temprature will be(Here R=radius of earth,ω=angular velocity of earth,J=mechanical equivalent of heat,C=average specific heat capacity of earth)
Here i have doubt... | I agree with the comments of @G.Smith and @Pounik. I'm thinking that one possible explanation as to why the temperature of the earth might increase is due to the inertia of the molten core. The crust would stop but the molten core would continue to rotate. This would result in friction between the molten core and the ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/504495",
"timestamp": "2023-03-29T00:00:00",
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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?
| Potentials and charge distributions are not mathematical, they are physical observation that lead to mathematical models, which have to describe the data.
The classical Maxwell equation solutions fit a multitude of observations with great accuracy and also are predictive for new systems. BUT note the term classical. It... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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What is a free parameter? Soft question here, but I was wondering just what exactly free parameters are? I have a murky understanding on the concept but I would much appreciate someone shedding some light on the matter. Is Newton's gravitational constant $G$ a free parameter of that theory? What exactly are the require... | Free parameters are not predefined but must be estimated by theory or experimentally. Or it can be a parameter used in fitting a dataset with an expression. The free parameters are varied to get a good fit to the data.
G in Newton's gravitational equation is a free parameter and has been measured but not with high accu... | {
"language": "en",
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Derivation of density of states (free electrons) I am reading Condensed matter physics from M.Marder.
This is the derivation for the density of states for free electrons.
$\begin{aligned} D(\mathcal{E}) &=\int[d \vec{k}] \delta\left(\mathcal{E}-\mathcal{E}_{\vec{k}}^{0}\right) \\ &=4 \pi \frac{2}{(2 \pi)^{3}} \int_{0}^... | In step one, the angular part of the integral is $4\pi$ because the $\vec{k}$ integral is an integral in 3 dimensions, so you're integrating over a sphere:
$$\int d\vec{k} = \underbrace{\int_{0}^{2\pi} \,d\phi \int_{0}^\pi \sin\theta \,d\theta }_{=\,4\pi} \int_0^\infty k^2 \,dk \,.$$
In step two, the lower bound of the... | {
"language": "en",
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How to calculate inertia tensor of composite shape with angle? I have I have some objects assembled like this :
The inertia tensor would be :
$$I=I_1+I_2+I_3-m_1 \,\tilde{r}_{01}\,\tilde{r}_{01}-m_3\,\,\tilde{r}_{03}\,\tilde{r}_{03}$$
Where :
$$\tilde{r}_{01}=\begin{bmatrix}
0 & -z & 0 \\
z & 0 & 0 \\
0 & 0 ... | The inertia tensor obeys the congruent transformation from the local coordinates to the world coordinates.
If you have a 3×3 rotation matrix $\mathbf{R}$ then you have
$$ \mathbf{I}_{\rm world} = \mathbf{R} \, \mathbf{I}_{\rm body} \mathbf{R}^\top $$
So the combined inertia would be
$$ \mathbf{I} = \mathbf{R} \, \left(... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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Is the Olympic running race fair? I noticed that the 200-meter sprints are conducted on curved tracks. (See this video: world championship semifinals 2009)
Isn't that weird? I mean, just look at the curvatures of each lane!
(Source)
Since they use staggered start lines, the total track length is the same. But the p... | Runners generally prefer the middle lanes, and that's where the highest-seeded runners usually get assigned. While it is true that the tighter curve of the inner lanes means that you effectively have more weight on your feet (by about 1% relative to the outermost lane), it is also considered an advantage to be able to... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/505988",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "10",
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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?
| Electric and magnetic fields are best understood using the terminology "electric field ${\bf E}$" and "magnetic field $\bf B$". In the case of a magnetic field this is better terminology than "lines of force" because the force produced by a magnetic field on a small object such as a current-carrying wire or a moving ch... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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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... | In fact the answer is a general result for all particles taken slowly from one point to another when it is on any inclined surface.
The Normal reaction is given as:-$$N=mg\cos\theta$$ This relation is valid as the body is hauled up slowly so the acceleration perpendicular to the surface tends to zero.
$\theta$ is the v... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/506329",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
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Modern form of Brown-Henneaux formula Almost every paper mentioning Brown and Henneaux's matching of asymptotic symmetries of AdS$_3$ with the Virasoro algebra of a $1{+}1$-dimensional CFT summarizes their results in the formula
$$c=\frac{3R}{2G},$$ whereby the central charge $c$ is expressed in terms of the AdS radius... | Computing the Poisson bracket gives
$$I=i\{L_{m}^{(+)},L_{n}^{(+)}\}=\frac{il}{\kappa}\int_{0}^{2\pi}d\phi e^{imx^{+}}\left(e^{inx^{+}}\partial_{+}L_{+}+2L_{+}\partial_{+}e^{inx^{+}}-\frac{1}{2}\partial_{+}^{3}e^{inx^{+}} \right),$$
where $\kappa=8\pi G$ and $L_{m}^{(\pm)} = \frac{l}{\kappa}\int_{0}^{2\pi}d\phi\ L_{\pm... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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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
| Contrary to what the other answers say, resistors do change their value with time, even the most accurate ones, even at perfectly constant temperature. This is due to various phenomena, e.g. release of internal stresses, contamination from impurities etc. For instance, National Metrology Institutes keep historical reco... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/507131",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
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How do we calculate the force applied by a ball on a wall which bounces back? If we have a ball which we throw toward a wall which touches the wall and bounces back then how will you calculate the force applied by the wall on the ball because the the contact time of the ball and the wall is infinitely small so force mu... | For something like a tennis ball, one or two assumptions are in order:
1) Assume some amount of "flatness" of the ball when it is most compressed against the wall.
2) Estimate the distance from the center of the ball to the wall at this point. Call this distance "d".
Note that before the collision, the distance from t... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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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... | Work isn’t $Fd$ when the force changes with position. It’s an integral, and the integral is finite even over an infinite distance because the force goes to zero sufficiently rapidly at large distances.
The integral is a standard homework problem so I am not going to write it or evaluate it.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/507661",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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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... | The wave function will necessarily include all degrees of freedom the particle has: position, orientation, deformations, etc.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/507757",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
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Physics of air flow in Kipchoge's sub-2:00 marathon Yesterday Eliud Kipchoge became the first human to run a marathon distance in under two hours. Part of what allowed him to do it seems to have been that he had pacers running along with him to break the wind. These pacers ran in a strange formation like a "Y:"
Kipcho... | Maybe this will help: a picture of the flow around 8 cylinders. This is a viscous 2D flow of an incompressible fluid. The color in the figures corresponds to the magnitude of the flow velocity. A numerical solution is obtained by integrating the Navier-Stokes equations using FEM - see code on community.wolfram.com/grou... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/507881",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "12",
"answer_count": 1,
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Are Imaginary Numbers Really “Imaginary?” I find the naming convention of “Imaginary” misleading, as it does give a sense that the quantity is merely an abstract construct used to mitigate the difficulties of performing some mathematical operations.
My question is, other than the wavefunction for example, where else do... | It is possible to do all computations that traditionally involve complex numbers, without reference to imaginary numbers at all. An equation written in complex notation can always be separated into two equations in real notation. Example:
$$Z_1^2 +Z_2^2 = C$$
is the same as $$x_1^2 -y_1^2 + 2i(x_1y_1) + x_2^2-y_2^2 +... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/507966",
"timestamp": "2023-03-29T00:00:00",
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What is the difference in the way a single rope and a double rope would behave under dynamic load? Suppose I have a single rope attached to a fixed point via a load cell, which gives a number (in kN) based on the load it's experiencing. I take a weight (x) and attach it to the rope at a fixed point and raise it up to a... | Is this a question about rock climbing? If so, then the answer is never to use twin ropes, because they're a total pain, and their theoretical advantages never show up in actual climbing. (And note that (1) twin ropes have different physical specs, and (2) the twin ropes will usually not share the load at all equally.)... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/508069",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
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Do Hermite polynomials imply a weight for quantum harmonic oscillator wavefunctions? I know that solutions of quantum harmonic oscillator can be expressed in the form of Hermite polynomials.
But I recently came to know that Hermite polynomials are actually orthogonal polynomials having $e^{-x^2}$ weight function.
So, h... | Absolutely. The Hermite polynomials
$$
H_n(x) = (-1)^n e^{x^2} \partial_x^n e^{-x^2} = \left(2x - \partial_x\right)^n \cdot 1
$$
are orthogonalized by
$$
\int_{-\infty}^\infty H_m(x) H_n(x)\, e^{-x^2} \,dx = \sqrt{\pi}\, 2^n n! ~ \delta_{nm} ~,
$$
whereas the (nonpolynomial) Hermite functions
$$
\psi_n(x) = \left (... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/508227",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
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How unique is the length scale picked out by intelligent life? Our human bodies pick out a length scale (let’s say 1m). How unique is this scale and why did it arise?
In other words, how much smaller could humans, or multicellular lifeforms in general, be while sticking with approximately the same architecture of life... | This answer is extremely approximative:
The scale of life should be somewhere between the smallest size physically meaningfull: the Planck lenght $\ell_{\textsf{P}} \approx 1,6 \times 10^{-35}~\mathrm{m}$, and the largest size set by causality in our universe: the Hubble lenght $\ell_{\textsf{H}} \approx 2 \times 10^{2... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/508377",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "7",
"answer_count": 3,
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Doubt in understanding the potential energy of dipole in external electric field? When a dipole is placed in external electric field it experiences a torque $$\vec \tau = \vec p \ \times \vec E $$
whose magnitude is
$$||\vec \tau|| = ||\vec p|| \cdot ||\vec E|| \cdot sin\theta$$
On calculating the potential energy:
$$... | Let me start from the beginning
Wnet = $\Delta$K.E
Wconservative+Wnon-conser.+Wexternal = $\Delta$K.E
Wnon-conser. = Zero [No non-conservative force is acting ]
$\Delta$K.E = zero [Assumption here is that the dipole is rotated very slowly therefore change amounts to zero]
Therefore the equation reduces to
-Wconservati... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/508660",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Expand superspace function into component form In 2D (1,1) superconformal field theory, the invariant "distance" between two points $Z_1=(z_1,\theta_1)$ and $Z_1=(z_1,\theta_1)$ in superspace is $$Z_{12}=z_1-z_2-\theta_1\theta_2.$$
My question is how to compute the quantities when the $\theta$ appears in denominator ... | TL;DR: It is defined by expanding in the finite Taylor series of the $\theta$s.
More details:
*
*Recall that a supernumber $z=z_B+z_S$ has a body $z_B\in\mathbb{C}$, which is a complex number; and a soul $z_S$, which belongs to the ideal generated by Grassmann-odd generators.
*For any analytic function $f$, the sup... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/508799",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
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Is dark matter inside galaxies different from dark matter in intergalactic space? I just read a text about astronomy and when talking about dark matter the author says:
[...], the dark matter responsible for the orbits of the stars in the Milky Way is probably different from the dark matter responsible for the orbit o... | The standard model of cosmology (for now) is called Lambda-Cold-Dark-Matter. It has only one kind of dark matter, and it agrees well with the observational data.
Other types of dark matter, such as “warm” or “hot” rather than “cold”, have been considered, and some people have considered models in which more than one ki... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/508909",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "12",
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Confusion about Ohm's law So does ohms law say if the resistance is increased the voltage will also increase but not the current? And in non ohmic conductors the current increases with the voltage even though the resistance is also increasing? (meaning it shouldn't but still is, defying the law thereby)
| Ohms law relates three variables.
If you change one of those, then the other two have to change in a coordinated way: if R goes up, the V has to go up, or I has to go down, or some combination.
How do you figure out what happens? The resistor has given you one relation, but that’s not enough. There needs to be some o... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/509154",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
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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... |
Would a very long diffraction grating produce a diffraction pattern?
Yes. You might need to set the screen further back to ensure that the far-field condition is still satisfied, but given that the screen is sufficiently far away (for the length of the grating), arbitrarily large gratings can be used.
(Alternatively,... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/509247",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
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Why does heating an atom make it emit certain wavelengths? We're going over quantum basics in chemistry right now and I'm very confused.
Electrons can only accept in discreet quanta to move up an energy level, right? And they reflect other forms of light that don't supply energy in their specific quanta, right? And fl... | There's not really any such thing as heating an individual atom. When you heat a gas like in a candle flame, the heat is the random motion of all the different atoms. The randomness is what makes us call it heat. If there's only one atom, there's no way to say if its motion is random or not.
And they reflect other for... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/509653",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Measuring mass density of electrons in the universe Pardon me if the question is too naive, but only baryon and dark matter masses are considered while making measurements of the mass density in the universe.
What I am interested to know is how small is the total mass of electrons, relative to the other two that it was... | If we assume the universe is electrically neutral (it might not be completely neutral, but it is neutral to a large degree) then there are roughly the same number of protons as there are electrons. Because the mass of protons (and neutrons) is about 1836 times that of electrons, it's safe to assume that the contributio... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/509792",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
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Small amplitude approximation in waves on string In transverse waves on a string, we neglect the longitudinal displacement of the particles, the reason given in most books is that the slope and the amplitude of the string is very small.
Can someone please prove it mathematically that it's reasonable to neglect the long... |
( The angle $\phi$ is exaggerated in figure)
A very small displacement, d, would create a very small angle, ϕ, with the strings original position. The transverse displacement, T, would be proportional to d∗cos(ϕ) and the longitudinal displacement,L, would be proportional to d∗sin(ϕ). So as ϕ tends to zero the transver... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/509924",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Why does it seem everything I push moves at a constant velocity? I am aware that a constant force causes a constant acceleration but friction can counteract this. However, if I push something across a table, for example, it seems no matter how hard I push, the object travels at a constant velocity, even if I apply more... |
The object seems to always travel at the same velocity as my hand,
does this mean I am not actually applying a constant force?
Yes it does mean you are not applying a constant force. The force is due to an interaction at the surfaces of your hand and the object, and that interaction depends on how closely in contac... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/510002",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "16",
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"answer_id": 10
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Confusion regarding the Fermi-Dirac distribution and related formulas I'm studying semiconductor physics and having a problem with some of the terms.
The definition we were given in class for the Fermi-Dirac distribution is:
$$f_{FD}(E)
= \frac{1}{1+e^\frac{E-E_f}{kT}}
$$
From this formula it appears that $E_f$ is a ... | It depends whether you are keeping the number of particles fixed or not. Usually we write
$$
f(\mu, T,E)= \frac 1{1+\exp\{(E-\mu)/kT\}},
$$
where $\mu$ is the chemical potential. Then the total number of particles is
$$
N=\int dE g(E) f(\mu,T,E).
$$
Here $g(E)$ is the energy density of states.
If we want $N$ to stay f... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/510152",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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If a particle and its antiparticle annihilate upon contact, how do they form bound states? I am reading about some old discoveries in particle physics and early collider experiments from Perkin's Introduction to High Energy Physics. However, I didn't get the answers to all my questions.
If two beams of electrons and po... | A bound state is possible for awhile because the particle and antiparticle are separated in space and not significantly “in contact”. You can think of them as orbiting each other; their kinetic energy and angular momentum keep them apart. But, just as in a hydrogen atom, they are really described by wavefunctions. Even... | {
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Does the wavelength of a particle depend on the relative motion of the particle and the observer? The de Broglie wave equation states:
$$\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... | Your understanding is correct: the de Broeglie wavelength of a particle as measured by an observer depends on the relative motion of the observer and particle. It doesn't make a lot of sense to state that an interaction depends on the relative wavelengths of two particles, because an observer on either particle will p... | {
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Equilibrium in a spoon hanging from a toothpick While searching about equilibrium I came to this YouTube video which was quite astonishing but the video maker didn't explained the physics behind it. My query is that why the spoons aren't falling? The obvious answer that someone might give would be that they are in equi... | The short answer is the location of the toothpick on the rim of the glass happens to be the location of the center of mass of the system which, in turn, happens to not be located at a point on the system itself. Since it’s the location of the center of mass, balance is achieved.
Hope this helps
| {
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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... | Since all frames of reference are equally valid, in a uniformly descending, non accelerating elevator, all physical occurrences would be indistinguishable from an elevator considered at rest. So in both cases the bolt would release the same energy on impact with the floor. If you were in the moving elevator, you would ... | {
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Heisenberg vs. Bandwidth Principle Is it true that the Heisenberg Uncertainty Principle is "obvious" because of the Bandwidth Theorem (Fourier Transforms)?
| 'Obvious' is a subjective term- my wife might not agree with my obvious excellent taste in ties.
However, the Heisenberg uncertainty principle is easy to understand if you are familiar with the properties of Fourier transforms. To localise a wave packet more tightly you need an increasing spread of frequency component... | {
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Derivatives of polar coordiantes? I'm a undergraduate and I was reading about the polar coordinate system specifically this paper. I don't understand the term: $$\frac{de_r}{d\theta} = e_\theta \text{, and } \frac{de_\theta}{d\theta} = -e_r$$
I don't see how you can have a the derivative of $de_r$ over $d\theta$ sinc... | $\hat{e}_r$ is a radial unit vector. It obviously points in different directions for different values of $\theta$. So it has a derivative expressing that rate of change.
| {
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What does the magnitude of centripetal acceleration actually represents? A fan moving with an angular velocity of 5π rad/second has a centripetal acceleration of 175.185 m/s^2.The Centripetal acceleration doesnt express the change in velocity as it is constant. Then what does 175.185 m/s^2 actually represents?
| In addition to the previous answers:
The precise value, $175.185 \text{ m/s} ^2$ is the linear acceleration of any point on the fan blade exactly $0.71$ metres from the axis of rotation, if any such point exists.
The formula for centripetal acceleration is:$$a=\omega ^2r=\frac{v^2}{r}$$where
$a$ = the linear acceler... | {
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Equations of motion in curved spacetime I'm trying to understand how to use covariant actions to derive equations of motion. A simple example would be the free scalar field
$$
S = \int\;d^4x\; \sqrt{-g} \left( -\frac{1}{2}\nabla_\mu\phi\nabla^\mu\phi-\frac{1}{2}m^2\phi^2 \right)
$$
Now from classical mechanics we know ... | From Ref. 1, one sees that the Euler-Lagrange equations generalize to $$\frac{\partial \mathcal{L}}{\partial\phi}=\nabla_\mu\left(\frac{\partial\mathcal{L}}{\partial(\nabla_\mu\phi)}\right)$$
In general, when one does these things, one must make sure of two things: that the index placement is the same, and that the ind... | {
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Double slit experiment with electron one at a time I understand how a wave create the interference pattern, but what is the mechanism for a single electron after it pass the slit and scatter and land at different location on the screen to produce the same interference pattern.
Does the electron pass through one slit or... | All matter has both wave and particle properties, for small particles it is possible to observe the wave properties. For massive particles it is impossible to observe the wave properties, the theoretical wavelength is too short. The reason particles have wave properties is because all matter interacts with each other... | {
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WKB treatment for unstable particle I was wondering if the WKB treatment of particles entering a potential (there is some reflection (R) and transmission (T) coefficient such that R+T =1) works only for stable particles. Essentially the WKB gives me a wave function of a state and the probability it will be reflected/tr... | This is not a complete answer, but is too long for a comment.
Interesting question. I guess spontaneous fission would be an example, since it takes place by tunneling through a barrier. (The coordinate is some measure of the shape of the nucleus, leading to a saddle point and then scission.) People certainly do use WKB... | {
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Why gapped systems are called incompressible? I study quantum Hall systems and I haven't studied Fermi liquid theory yet. But I understand the concept of having gap or being gapless. But why do we use the term incompressibility to correspond the presence of gap in the bulk state? Is there any relation to physical compr... | The electronic compressibility $\kappa$ is defined as
$$\kappa =\frac{\partial \rho}{\partial \mu} $$
where $\rho$ is the electron density, and $\mu$ the chemical potential. The region where the $\rho(\mu)$ is constant indeed indicates that there is an energy gap. This can simply be understood by the fact that in the ... | {
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How do I experimentally measure the surface area of a rock? I hope this is the right place to ask this question.
Suppose I found a small irregular shaped rock, and I wish to find the surface area of the rock experimentally. Unlike for volume, where I can simply use Archimedes principle, I cannot think of a way to find ... | If you have access to a planimeter, then you might try the method used in this research paper on the strength of cements used on teeth.
In order to compare the strength of the cement, the authors needed to separate the effect due to the cement from effect due to the varying surface areas of the real teeth used in the t... | {
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Velocity in SHM
By book defines SHM as
Simple harmonic motion is defined as the projection on any diameter of a graph point moving in a circle with uniform speed.
but in the next line it says -
Moving back and forth along the line AB, the mass point is continually changing speed vx' Starting from rest at the end p... | SHM is governed by the following equation:- $$\ddot x+\omega^2 x=0$$
Here $\omega$ is a positive constant which is also known as angular frequency of simple harmonic motion and $x$ is the displacement from the mean position.
The diagram given in the post gives an analogue of simple harmonic motion which simplifies the ... | {
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Is nuclear force a kind of strong interaction? I'm trying to understand the role of Yukawa potential, and it seems to describe the nuclear force. But at the top of the article it says:
This article is about the force that holds nucleons together in a nucleus. For the force that holds quarks together in a nucleon, see ... | Behind the scenes, it is the strong force. But on the nuclear scale, it looks quite different, and is mediated by pions (composed of two quarks) rather than gluons. Sometimes the resulting force is called the residual strong force.
| {
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Why don't people just put a water sprinkler on their roof for cooling? Some air conditioners work with evaporative processes. So I'm not sure why people wouldn't just use a sprinkler that turns on for a minute every hour or half hour or whatever in order to wet the roof. The water will not only absorb the heat from the... | This is a waste of water and will catastrophically exacerbate the effects of heat and drought when applied at large scale. Paint your roof white, insulate your house (roof, walls, floor, double glazing) and use solar power for your airco is the way to go.
| {
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Is there any relationship between S-matrix elements and the path integral? Reading Peskin&Schroeder I've made the following curious observation: Comparing S-matrix elements to the definition of the path-integral they look remarkably similar:
$$_{out}\langle \mathbf{p}_1 \mathbf{p}_1| \mathbf{k}_A \mathbf{k}_B\rangle_{... | Yes, you can write down S-matrix elements directly in terms of path integrals. This was figured out by L. Fadeev and is explained in his 1975 Les Houches lecture notes. A review of his work is also in Bailin and Love's gauge field theory textbook.
References:
Ludwig Faddeev, Introduction to Functional Methods, p. 1-39 ... | {
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Mass Dimension 6 QED-Lagrangian Consider the QED Lagrangian
$$\mathcal{L}_{\text{QED}}=-\frac{1}{4} F^{\mu \nu} F_{\mu \nu} + \bar{\psi}(i D_{\mu} \gamma^\mu -m) \psi.$$
I need to extend the Lagrangian up to mass dimension 6, of course respecting all the symmetries/invariances of the theory.
My professor told me, that ... | We are talking about chiral invariance, right?
First of all, the mass term
$$
m\bar{\psi} \psi
$$
breaks the chiral symmetry. So if your professor demands chiral invariance, then we are dealing with massless QED.
For massless QED, you can add a chiral symmetric mass dimension 6 term like (NJL 4-fermion interaction)
$$
... | {
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How and why Liquid helium climbs the walls of the container it is kept in? Liquid helium (He-II) shows a strange phenomenon, where it flows on its own, forming films across the surfaces of the container it is kept in. How and why this happens and how is it possible?
| Liquid Helium as He-IV and He-III behave in this manner. The property of a material to have zero viscosity is known as superfluidity. This is only possible at cryogenic temperatures at the nano-kelvin level.
You may know viscosity as a measure of the 'thickness' of the fluid or a measure of how easily it can flow. When... | {
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Local phase invariance of our lagrangian So in lectures we have just started looking at classical field theory. We were introduced to symmetries and we were told in general our lagrangian wont be invariance wrt to local phase changes but if we require it to be we can introduce the covariant derivative. This introduces ... | If you use Noether's theorem, there is a locally conserved current associated with local $U(1)$ symmetry. We can then identify this current as electric current. Without the symmetry, we wouldn't have a locally conserved current to use for electric current, so it's pretty important. As an additional note, we can find La... | {
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Help understanding unit: Micromoles per square meter per second The context is light, illumnination, photons.
The units seem to suggest something different from the definitions I have found:
$$\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... | 1 mol is defined as Avogadro's number $6.022\cdot10^{23}$ and you could count anything using moles. We could count some events happening in a fixed time, for example water molecules flowing through a pipe. If we divide the total count of those molecules by elapsed time we get rate of flow which in this case would measu... | {
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A problem on thermal stress Here's the question:
There are 2 rods placed between rigid supports. Where $Y_{i}, \alpha_{i}$ and $A_{i}$ are the Young's Modulus, Coefficient of linear expansion and Cross sectional area of the rods. When the system is heated to temperature $\theta_{2} $ from $\theta_1$, find the relation... | The reason you take the complete area on $A_{1}$ is because its an approximation: no matter how locally the stress on its surface is being applied, the whole object feels the stress as if it were applied evenly across its cross-section. Otherwise there would be local deformation.
This isn't true in reality though.
| {
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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... | It is the normal force ( https://en.wikipedia.org/wiki/Normal_force ) of the Earth against the supports that hold the platform up. Normal force is what keeps our feet from sinking into the Earth, due to our weight, it keeps a book on a table from falling through the table. It will keep the supports from falling into th... | {
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Creating Em waves Is it necessary for creation of em waves be from same source.
If a positive charge particle and negative charge particle is accelerating with same acceleration will the em waves created be identical in all aspects?
|
If a positive charge particle and negative charge particle is accelerating with same acceleration will the em waves created be identical in all aspects?
Just for the record, your statement is true only for a charge and its anti-particle. To show that this is the case, one has to imagine that the acceleration of an el... | {
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Speed of light in different mediums with different frequencies As I know the speed of the light doesn't change while it travels through a vacuum. But while it travels through a prism, it shows different deviation angles to different frequencies.
So according to the $$ n = \frac {sin (A+D)/2}{sin (A/2)} $$ formula $n... | Light’s velocity in a medium changes compared with its velocity in vacuum because the electrons in the atoms of the medium experience forces due to the light passing through, and, as they are accelerated, radiate light of their own which superposes with the incoming light. (Showing that this additional radiated light c... | {
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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! ... | It does not make sense to discuss a force with units of $\rm N/s$ since those are not the units of force. The physical quantity that has these units is called yank and refers to the derivative of force with respect to time.
An airplane's engine thrust is simply given as a force, but this must be a force applied by th... | {
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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... | In the general case -- i.e in any number of dimensions, the analogue of $\nabla\times(\nabla \phi)=0$ and $\nabla\cdot(\nabla\times {\bf A})=0$ is $d^2=0$ where $d$ is the exterior derivative anding on $p$-forms. This means that if $\omega=d\eta$ then $d\omega=0$. A p-form $\omega$ such that $d\omega=0$ is said to be c... | {
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Is there some truth to the often told story that the running of couplings is the result of screening through virtual particles? It's a well established fact that coupling parameters changes with the energy scale at which we probe a given process:
A popular way to explain this phenomenon goes as follows. Particles are... | To give some context for what I have in mind, here's the best answer I came up with myself. Corrections, comments and better answers would be much appreciated.
The proper mathematical context to discuss this question are the renormalization group equations. For example, in $\phi^4$-theory we have:
$$ \lambda_R(s_1) ... | {
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Dependence Of A Cross-Section I am trying to understand the dependence of a differential cross-section on $$\sigma(\theta) = \left(\frac{s}{ \sin \theta}\right)\left|\frac{ds}{d\theta}\right|,$$ where $s$ is the impact parameter and $\theta$ is an angle that is between the scattered and incident directions.
Any explan... | I can't give a complete answer but I'm sure someone will. For a low energy projectile, lower than the first excited state of the target, where the projectile is neutrons, this is just the elastic or inelastic scattering cross-section. The neutron scatters like a billiard ball off the stationary nucleus. Applying conser... | {
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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... | Non-conservative forces change the total mechanical energy of the system, since
$$W_\text{nc}=\Delta E=\Delta K+\Delta U$$
assuming all conservative forces are internal to the system.
However, nothing from this tells us how the kinetic and potential energies change. More information is needed. For example, with a mass ... | {
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Because things smell, is everything evaporating? Everything, in theory, can have a smell, but that is not the whole point of this question.
My main query is, since things do smell, does that mean that everything is slowly evaporating (or, sublimating, I suppose)?
For example, if we perceive metal to have a scent, this ... | Technically, everything IS evaporating, it's just a question if our olfactory abilities are advanced enough to detect it.
But the metal smell coming off metal is actually the result of a reductive chemical reaction between skin lipid peroxides and the metal itself. These usually produce an array of molecules that do ev... | {
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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... | Outside the solenoid, I assume this is the system that you have mind, is a vector potential. It falls off as 1/r and is directed tangentially. When the current through the solenoid is varied, dA/dt acts as an electric field.
| {
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QED electron self-energy in 1PI effective action The electron self-energy at one-loop is given by the one-particle irreducible graph
I know how to calculate it using the Feynman rules but I was wondering how this diagram appears in the QED effective action (which it in principal should as a 1PI graph).
With
\begin{equ... | *
*The 1-loop quantum correction to the 1PI effective action is given by a functional superdeterminant$^1$
$$ \begin{align}\Gamma_{\text{1-loop}}[\phi_{\rm cl}]
~=~&\frac{i\hbar}{2} \ln{\rm sDet}\left(S^{-1}_2 \frac{\delta^2 S[\phi_{\rm cl}]}{\delta \phi_{\rm cl} \delta \phi_{\rm cl}}\right)\cr
~=~&\frac{i\hbar}{2} {\... | {
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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... | The universe is expanding, so its volume is constantly increasing, stretching out radiation wavelength and cooling down and decreasing the density of matter, which increases entropy, also entropy always increases in an isolated system. Entropy increasing/decreasing with temperature is only valid when kept in the same v... | {
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Why is electric field Fourier transformed to produce image in radio astronomy? In radio interferometry, to get an image, the correlation of electric field observed in different antennas are Fourier transformed. This gives the "brightness function in sky coordinates".
Why do we need to Fourier transform? Does not the el... | Think about using a photo camera. If you simply take the photo sensor without any lens in front of it you are not getting an image on your sensor. You need to put the objective in front of the sensor to form an image. The electro-magnetic wave in the lens plane and the sensor plane are directly connected to each other ... | {
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Meaning of "harmonic" I'm trying to understand the meaning of the term "harmonic". IE, appearing in following sentence of Fluctuation-dissipation relations for stochastic gradient descent
The second relation (FDR2) further helps us determine the properties
of the loss function landscape, including the strength of its ... | If you make the equivalence between the loss surface (or loss function) and a physical potential then the "harmonic limit" here is the one of a Brownian evolution into a harmonic (or quadratic) potential. That means the stochastic gradient views as a stochastic process is the same than the evolution of a particle drive... | {
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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 ... | From the rocket's frame of reference, the rocket is at rest and the Earth is travelling faster and faster, approaching c. In both frames of reference, the relative velocity approaches c so the energy needed diverges.
I'm not sure whether this answers your question.
| {
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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 ... | The force is still $mg$, but note - it is the force that is applied on the ball, not on the man's head!
As the ball falls from above, it picks up speed due to its constant acceleration $g$, which respectively increases its momentum, $p = mv$. Bigger momentum means a bigger force, so that's why the poor person's head su... | {
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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 ... | The pressure inside the tube at height is not equal to the pressure outside. It is a vacuum, or partial vacuum created by the weight of the column of mercury in the tube. Higher atmospheric pressure at the open pool of mercury at the base of the tube will push the column of mercury higher in the tube. Lower atmospheric... | {
"language": "en",
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Solving a differential equation using factorisation In Griffiths Introduction to Quantum Mechanics, when discussing ladder operators in Chapter 2, he write Schrodinger's equation as,
$$
\frac{1}{2m}\left[\left(\frac{\hbar}{\mathrm i}\,\frac{\mathrm d}{\mathrm dx}\right)^2+\left(m\omega x\right)^2\right]\psi=E\psi\tag{2... | The basic idea behind the factorization is to replace a 2nd-order differential equation by a pair of first order ones. It was made popular in physics by the work of Hull and Infeld:
Infeld, Leopold, and T. E. Hull. "The factorization method." Reviews of modern Physics 23.1 (1951): 21
although in fact earlier example... | {
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Effective power of a lens-mirror combination In case of thin lenses in contact the effective power of the combination is given as: $P=P_1+P_2+P_3$.....
For a lens - mirror in contact, like a lens with silvered surface (where lens and mirror are seperated by virtually $0$ distance) can we say that the effective power is... | For a silvered lens, the power formula would be $P_{eqv.}=P_{lens}+P_{mirror}+P_{lens}$.
(the lens power is doubled as rays travel through it twice).
eg. for a biconvex lens ($\eta,R$) with one side mirrored:
1. $f_{lens}=\frac{R}{2(\eta-1)}$
2. $f_{mirror}=R/2$
3. $P_{eqv.}=\frac{2(2\eta-1)}{R}$
4. in other words $P... | {
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Tension in a massless string being pulled at its ends with unequal forces There is a question in my textbook. If a massless inextensible string is pulled on with a force of $10 N$, at both ends, what is the tension in the string?
It’s a very common question. The answer is $10 N$, cf. e.g. this & this Phys.SE posts. It... | The arrangement you describe is impossible. The tension of the string will be 70N. Whatever was trying to restrain the end of the string with a force of 60N will be subject to a force of 70N by the string. As a result it will accelerate subject to a net force of 10N. The reaction on the string will be 70N.
| {
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How does a Wehnelt electrode both extract and focus electrons? Now that I can try to pronounce it I'd like to understand how a Wehnelt lens, grid, cap, etc. extracts electrons from a cathode and simultaneously focuses them.
Naively I'd think that it would have a positive potential with respect to the filament in order ... |
How does a Wehnelt electrode both extract and focus electrons?
It doesn't. Since it is biased negative with respect to the cathode it would suppress electron emission rather than extract them if it were the only electrode.
Instead, the anode further down stream is positive with respect to the cathode and the opening... | {
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What are laws in physics? Many times a precise definition of something in physics is not available but yet there exist some rough definitions that guide us through. I need the same rough (if not precise) definition of physical laws. The reason being that we would consider $\mathbf a= \frac {d \mathbf v}{dt}$ as a mere ... | As pointed out by Safesphere, the physical laws that rule the world are expressed at a higher and more general level of (mathematical) abstraction which underlie Newton's laws. We can then derive Newton's laws from them as needed to solve everyday problems in real-world dynamics.
These more general relationships are g... | {
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Viewing LEDs at great distance Say I put a satellite in orbit with several LEDs on the outside: red, yellow, blue, white and green. Could I see them from the ground with consumer-grade binoculars or telescopes?
If I can see them, could I differentiate between the colors? (e.g. would the color affect how well I could s... | It really depends on the resolution of your binoculars...
| {
"language": "en",
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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... | You are surprised that $S(T, 2V, 2N) = 2S(T, V, N)$ but this formula can be obtained with statistical physics considering a mix of two identical gas
When you remove the barriers and the two gas are identicals you do not increase the number of unknowns configurations of the system, therefore, entropy does not increase. ... | {
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Where does the power delivered to car's wheels go? Okay, so power is work/time. Most cases, when power is provided to something, energy is gained as kinetic energy or lost to friction.
But in a car, the engine puts power ( torque x rpm/5252) to wheels, but very little ends up in the wheels, assuming friction keeps them... | The engine applies torque to the wheels. The wheels turns and apply friction force to the road. By Newton's third law the road applies force to the wheels which make the car moving. Engine power goes to kinetic energy of the car, dissipated heat to friction, air resistance force, battery charging and air conditioning
| {
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Why is frequency a fundamental property of waves? We are taught that although wavelength can change from one medium to other, frequency of a wave doesn't whenever Velocity varies in different media.
But why at a deep level, is frequency so fundamental? Why can't both frequency and wavelength change? Or why isn't wavel... | If a chunk of matter absorbs 100 wave crests and emits 101 wave crests, then we would say that the chunk of matter created some wave crests by itself, at least one. Right?
If 100 crests go in and then 100 crests come out at slower rate, then it is possible that the waves that came out are the same as the waves that wen... | {
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I can't understand one of deduction in Simple Harnomic Motion, can anyone help? source:http://farside.ph.utexas.edu/teaching/336k/lectures/node18.html#e4.8
in order $x=0$ to be a stable equilibrium point we require both
$$f(0)=0$$
and
$$\frac {df(0)}{dx}<0$$
Now, our particle obeys Newton's second law of motion,
$$m \f... | Physically, $\omega_0$ is the angular frequency of the simple harmonic motion. It is related to the period by $T = 2\pi / \omega_0$. The definition of $\omega_0$ is (in the notation of your link)
\begin{align}
\omega_0 = \sqrt{-\frac{1}{m}\frac{df}{dx}\bigg|_0}.
\end{align}
The reason we define $\omega_0$ this way is b... | {
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Brownian Motion I’m currently interested in learning some topics about the Brownian motion and the random walk (in general, from a pure statistical and probabilistic way).
For that, I would like to ask you if you can recommend some books so I can learn the basic stuff and prepare myself for the real deal.
As I learn th... | While you can construct mathematical models as simple as integrating white noise which evolve trajectories that have the appearance of Brownian motion, physical Brownian motion occurs due to a more complex, stochastic dynamic equilibrium between macroscopic particles and atoms/molecules. So if you are interested in rea... | {
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Why do the $L_z$ and $L^2$ operators share eigenfunctions, but the $L_x$ and $L_y$ operators don't? In my lecture notes the following was written:
I would understand in the case of an applied field if there was some symmetry breaking feature which would allow for a preferred axis or something which could explain why ... | The reason is quite simple:
The operators $\hat{L}^2$ and $\hat{L}_z$ have common eigen-functions
because they commute with each other, i.e. $[\hat{L}^2,\hat{L_z}]=0$.
The operators $\hat{L}_x$ and $\hat{L}_y$ don't have common eigen-functions
because they don't commute with each other, i.e. $[\hat{L}_x,\hat{L}_y]\ne 0... | {
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Why does the potential energy of the system decrease when two charge balls are connected using a connecting wire I am confused because I've seen in textbooks and online solutions to questions that when connected,the potential energy of a system of two charged spheres decreases.But according to law of conservation of en... | Simple answer is that there is no possibility for the system to gain energy, in any form whatsoever. So it can do two things either loose no energy, or release some energy of heat, assuming ideal behaviour. To prove that it would loose energy if there is any charge transfer consider the following
Initial charge on sphe... | {
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Echoes and Pitch Change I encountered something strange regarding echoes and pitch.
One Fourth of July , I saw rockets reach a height its hard for me to gauge. I'd call it two to three dozen meters.
I had noticed that shortly after a rocket went off, Pop!, I'd hear a Pang! echoed from the wall of a nearby building. Th... | I think this is most likely due to the doppler effect. the explosion of the rocket occurs while it is moving away from you which pitch-shifts the tone of the "pop" down. Meanwhile, the sound reflection off the sides of the nearby building (which is tall) will come sideways from the exploding rocket, and hence will be d... | {
"language": "en",
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Is it possible to conserve the total kinetic energy of a system, but not its momentum? It is possible to conserve momentum without conserving kinetic energy, as in inelastic
collisions. Is it possible to conserve the total kinetic energy of a system, but not its momentum? How?
To clarify, I am not necessarily talking a... | If non-isolated system are of interest, then what you’re looking for is an external force that does no work.
*
*The central force in a circular orbit: the satellites energy in unchanged, but its momentum is continuously changing.
*An electron moving across a constant magnetic field: ditto
| {
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Work done by battery on a capacitor Work done by battery on a capacitor is QV/2, where V is the final potential across the capacitor plates an Q is the charge. I know that the Q charge which gets stored on the capacitor comes from the connecting wires. However, since
Positive charge on one plate is reducing (Assuming c... | If the net charge on a plate is $0$, it takes no effort to move initial charge to that plate, so work done is $0$.
After you moved some charge to the plate, this excess charge on the plate opposes further new charge to be moved, so you must do positive work to overcome this opposition.
In a circuit, battery manages ... | {
"language": "en",
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Reference request for a mathematical motivation for the Born rule I was reading the popular science book The Hidden Reality by Brian Greene. My question is about a part in the notes at the end of the book. It is chapter 8, note 9. Brian Greene describes a mathematical motivation for the probabilistic interpretation (i.... | I have found an interesting discussion about this question in the book (in french) "Mécanique quantique, Bases et applications" by Constantin Piron.
He proves a Gleason-like theorem (A.2 Théorème fondamental, p.172) stating something like: if you would like to associate to each state (= vector) and proposition (= close... | {
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What would the water pressure be at this point in a static incompressible fluid? I have a bowl full of water. I invert a glass and place it upside down in the water, leaving a small pocket of air.
My question: what would the water pressure at positions P1 and P2 be? I know P1 = P2 because there's no hydrostatic effect ... | Let L be the total length of the glass (assuming constant cross sectional area), z be the depth that the lower lip of the glass is inserted below the water surface, and h be the height that water rises inside the glass above the lower lip. Then the pressure of the air trapped in the glass is given by:$$p_a=p_{atm}+\rh... | {
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Why is the normal contact force horizontal on an inclined ladder?
There is only one force acting on the ladder which is its weight and it acts vertically downwards. Then why does the normal contact force from the vertical wall act horizontally on the ladder? There must be a horizontal force acting on the wall to exert... | Normal forces act perpendicular to the surface in contact. The force acting in the ladder is actually somewhere in between the horizontal and vertical forces shown. Those are just the components of the normal force.
| {
"language": "en",
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"source": "stackexchange",
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Correct way of viewing a (1,1)-tensor returning a vector I am currently watching this excellent video series building up to general relativity. We have finally started looking at tensors and a question came up from the audience which (to my understanding) was asking why tensors are defined as multi-linear maps from set... | A $(n,m)$ tensor eats $n$ vectors and $m$ co-vectors and spits out a real number. A $(1,1)$ tensor eats one vector and one co-vector and spits out a real number. Let's call our $(1,1)$ tensor $f(.,.)\colon V \times V^{*} \mapsto \mathbb{R} $. The first argument is a vector and the second argument a co-vector. So for ge... | {
"language": "en",
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Why don't we define potential due to a magnetic field? We define electric potential and gravitational potential and use them quite often to solve problems and explain stuff. But I have never encountered magnetic potential, neither during my study (I am a high-schooler), nor during any discussion on physics.
So, does ma... | There is the vector potential $\bf A$ for which ${\bf \nabla} \times {\bf A} = {\bf B}$. So $B_z = dA_x/dy - dA_y/dx$ and similar for other components.
The classical field theory of electromagnetism is based on the four potential $A^\mu = (\phi,{\bf A})$ . $\phi$ is the Coulomb potential .
| {
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Adding Angular Momenta Operators in QM Consider $j,m$ to be the angular momentum magnitude and $z$-projection eigenvalues corresponding to a total angular momentum operator $\hat{J}$, composed of angular momentum $\hat{J}_1$ and $\hat{J}_2$ with eigenvalues $j_1,m_1$ and $j_2,m_2$. We want to know what values $j$ and $... | I am gonna give a much shorter answer than @Cyro.
*
*Yes it is also true for the other components of angular momentum.
*It is simply due to vector addition. The total angular momentum of the system (were it classical) would be $\mathbf{J} = \sum_i\mathbf{J}_i$. For quantum, it's the same thing, but you just quanti... | {
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Doubt regarding derivation of escape velocity In my text book the derivation goes like this:
The minimum speed required to project a body from the surface of the Earth so that it never returns to the surface of the Earth is called escape speed. If a velocity greater than the escape velocity is imparted, the body will ... |
Work done to displace the body from the surface of the Earth ($r=R_e$) to infinity ($r=\infty$) is given by:
$$\int dW=\int^{\infty}_{R_e}\frac{GM_e m}{r^2}dr$$
That's rather sloppy, and it's incorrect. Unfortunately, once a mistake gets into one physics text from India to mistake gets propagated to many physics text... | {
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Precise definition of the vertex factor Just a short question about the vertex factor in QFT. When I have an interaction Lagrangian
$$\mathcal{L}_{\mathrm{int}}=-\frac{\lambda}{3!}\phi^3$$
with a real scalar field $\phi$, is the vertex factor given by $-i\lambda$ or $-i\frac{\lambda}{3!}$?
Because as far as I learnt, ... | It is conventional to write interactions normalized by the number of permutations of identical fields. So, there will be a $\frac{1}{n!}$ factor for each interaction with $n$ identical fields. This factor is then canceled by the $n!$ ways of permuting the $n$ identical lines coming out of the same internal vertex.
Th... | {
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What is gravitational radiation? What is gravitational radiation (in association with gravitational waves)? Is it a form of energy/mass? Or is it just another word for gravitational waves?
| Strictly speaking gravitational waves are a subset of gravitational radiation. Gravitational radiation could in principle be radiated as solitons, and while these can be constructed from gravitational waves by Fourier synthesis we wouldn't normally describe them as a gravitational wave.
However this is a somewhat trifl... | {
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Is the energy of an electromagnetic radiation the sum of the energy of each photon? In A.P. French's Special relativity the author said,
We suppose that an amount
$E$ of radiant energy (a burst of photons) is emitted from one end
of a box of mass $M$ and length $L$ that is isolated from its surroundings
and is i... | Is the purchasing power of my checking account equal to the sum of the purchasing power of each dollar in my checking account? Well, in a sense yes. But in another sense, not really, because there is no such thing as an individual dollar in my checking account. If I have a five dollar balance, there is no meaningful... | {
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Why is $|\alpha\rangle$ not eigenstate of $a^{\dagger}$ for $\alpha^*$ I know that even if we have:
$$a |\alpha \rangle = \alpha |\alpha\rangle$$
We don't have:
$$a^{\dagger} |\alpha \rangle = \alpha^* |\alpha\rangle$$
Actually as explained in the second answer here Eigenvalue for the creation operator for a coherent s... | Your mistake - while $\alpha$ will be on the diagonal (and $\alpha^*$ on the diagonal of the hermitian conjugate) it is not guaranteed that all the other terms in the row (and the column in the Hermitian conjugate representation of $a^{\dagger}$) will be zero. Therefore it will not be an eigenstate. It will have the pr... | {
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Usually, how much does a phonon travel without scattering? Phonons propagate without problems in a lattice, until they scatter on something, like a defect, an electron, or another phonon. But in a typical solid at room temperature, how much (or how long) is the mean free path of a phonon? I know that depending on the t... | Phonons are lattice vibrations. The distance between two consecutive phonons is of the order of $1/N$ where $N$ is the number of atoms in the lattice. At room temperature a phonon travels approx 10 to 100 lattice constants before scattering.
In this article
they say that a phonon travels $< 1 \mu m$ before scattering,... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/522988",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
"answer_count": 2,
"answer_id": 0
} |
Why is the sunset not bluer My question is a duplicate of this; Clarification on Rayleigh scattering causing various sky colors.
The accepted answer from the link above says that at sunset the scattering occurs farther away and does not reach the observer, which is unsatisfactory and vague to me. (not even sure if it's... | When you look at the sun overhead (not advisable) you see the white light from the sun with a little bit of the blue scattered horizontally. The blue sky is blue light scattered from sunbeams going elsewhere. When the sun is near your horizon, its light passes through a much greater distance of dense atmosphere, and ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/523093",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
"answer_count": 4,
"answer_id": 3
} |
On the derivation of the north-south aberration angle In A.P. French's Special relativity, page $39$, the author said the north-south aberration angle $\alpha$ below, in figure (b), is equal to $v\sin(\theta_{0})/{c}$, where $\theta_{0}$ is the angle when the earth is stationary (no aberration).
How did $v\sin(\theta_... | Use 4-vectors (with $c\equiv 1$):
$$ k_{\mu} = (\omega, k_x, k_y, k_z) = k(1, -\cos{\theta_0}, -\sin{\theta_0}, 0) $$
is the wave-vector in the stationary frame. The angle of arrival is given by
$$\theta = \tan^{-1}{\frac{k_y}{k_x}}=\tan^{-1}{\frac{-\sin\theta_0}{-\cos\theta_0}}=\theta_0$$
Boost by $v$:
$$ k'_{\mu} = (... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/523210",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 2,
"answer_id": 0
} |
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