Q stringlengths 18 13.7k | A stringlengths 1 16.1k | meta dict |
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If the faster I go, the slower time becomes for me, then does that mean the slower I go the faster time becomes? Disclaimer - I’m not a trained physicist. I just have an interest in the subject so this question is probably going to come across really confusing but I’m trying my hardest to explain.
So firstly, this is ... | No. If you are at rest with respect to the earth, you experience time the same way people on earth do.
If you are at motion with respect to the earth, any kind of motion, you experience the time dilation the way you sketched.
The relative motion between you and the earth cannot be "slower" than zero, which is the case ... | {
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Ray Optics: Reflection and Refraction Suppose you have extremely sensitive photographic film and you can expose it in an optical system for a very long time. Will you be able to record a virtual image on film?
| No. Remember that images look like objects because light comes from images in the same way that it comes from objects.
Consider a point source of light. (More complicated objects can be treated a set of point sources.) If a lens, mirror etc. produces a situation where rays of light pass through a point and then dive... | {
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Why doesn't saturation current in the photoelectric effect depend on the frequency of light absorbed by the metal emitter? If current $I$ is given by $I = nAev$, where $n$ is the number of electrons per unit volume, $A$ is the area, $e$ is the charge of an electron and $v$ is the velocity of the electron, it must mean ... | Increasing intensity means increase in rays of light, so it will hit more numbers of electrons but doesn't give enough speed to the electrons.
Increasing frequency means increase in energy of photon. So electrons will go faster, and more regarding potential will be needed i.e. stopping potential increased.
Electric cur... | {
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Why does energy always wants to propagate? This might sound easy but its really a extremely fundamental question. The answer of this question has diverse implications. From thermodynamics to dark energy
The question is Why does energy always wants to propagate? In other words why does energy density always decrease per... | It is called the Second Law of Thermodynamics : The entropy of any isolated system always increases.
To understand that fully, you need to understand the definition of Entropy, which is not trivial.
Simplified, Entropy is a measure of how unorganized / random a system is.
Ordered systems (like one place hot, another on... | {
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Are position and momentum spaces of a particle in classical mechanics related by Fourier transform? Please don't be so harsh on me and correct me if I'm wrong, since physics is not my major and I am not native English speaker.
The article position and momentum space (https://en.wikipedia.org/wiki/Position_and_momentum_... | In classical mechanics, position and momentum are independent variables on phase space and are not related by Fourier transformation at all.
Their Fourier relation in quantum mechanics arises from the Stone-von Neumann theorem, saying that all unitary representations of the canonical commutation relations $[x,p] = \mat... | {
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The Science of Tearing Paper-bag Handles My mother came back from a market which bags the products in paper-bags with handles, and asked me to move the bags from the trunk of the car to the house. Being the lazy human I am, I hung a few bags on each arm so I could cut the number of trips back and forth. As I was walkin... | Cort Ammon is correct. It might be added that when a human carries a load on a weak handle he minimizes by subtle countermovements the inertial forces which are exerted on the handle due to the walking movements in addition to the weight of the load. This is obviously more difficult to do for more than one load.
Thus y... | {
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Electric field from a varying magnetic field and a solid conductive disk I am given this question:
On the second to last line, it asked for an electric field. However, I'm wondering where does the electric field come from?
Can somebody give me an idea? I know that a varying magnetic field produces an electric field,... | The electric field $\vec E$ appears in Faraday's law
$\displaystyle \oint_{\rm loop}\vec E \cdot d\vec l= - \dfrac {d\Phi_{\rm B,surface}}{dt}$
Note that
$\displaystyle \oint_{\rm loop}\vec E \cdot d\vec l$ is the induced emf.
So choose a loop which is a circle centred at the centre of the disc.
The bit about the ma... | {
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Is $\delta Q – \delta W$ a state function? I know that internal energy, $Q+W$ is a state function.
But
$$dU=\delta Q-\delta W,$$
is the change in internal energy, where $dU$ is change in internal energy, $\delta Q$ is the heat supplied to the system and $\delta W$ is the work done by the system. Is this a state functi... | The quantity $dU=\delta Q-\delta W$ is not a state function simply because it is not a function, it is a differential of a function. In that case a differential of the state function $U$.
The fact that there is a function $U$ such that the differential $\delta Q-\delta W$ is the differential of $U$ means that the diff... | {
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Given torque, what is the direction of motion? Torque is the cross product $\vec \tau = \vec r \times \vec F$, which means it is perpendicular to both $\vec r$ and $\vec F$.
Consider some essentially two-dimension problem, like a horizontal iron bar with one end fixed, affected by gravity. The direction of the torque i... | Suppose the force $\vec F$ and displacement $\vec r$ are in the xy plane.
Then you would expect the the angular acceleration would be anticlockwise looking down from the top just from the direction of the force.
The torque $\vec \tau = \vec r \times \vec F$ is in the $\hat z$ direction but so is the the direction of t... | {
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Why do air bubbles rise to surface of water? I was asked this question by my son and I want to give him the correct answer. So keep it simple please.
Here is what he asked. Why do air bubbles rise when they are released underwater?
| The answer you seek depends on the age of your son.
You could use Archimedes principle which states the upward force on a body in a fluid is equal to the weight of the fluid displaced by the body.
So the two parameters are the weight of the body and the weight of the fluid it displaces.
If the weight of the body (... | {
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Actual classical time evolution in a closed Cavity I'm stuck with the question how the actual time evolution of a given classical electric field in a closed cavity will look like.
The initial conditions are a given function $u(x)$ in a one dimensional region between the points $0$ and $L$. At those points there are mi... | It's a perfect electrical conductor (PEC) at the endpoints. Assuming $u(x)$ represents a component of the electric field perpendicular to the $x$-axis, the boundary conditions are $u(0)=u(L)=0$, which implies that the tangential component of the electric field is zero.
| {
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what is meant by solar spectrum? How can we get absorption lines in solar spectrum instead of emissions lines at such high temperature?
Is solar spectrum contains emission lines?
| The solar spectrum itself originates as a close-to-perfect blackbody emission for an object at about 5800K. That is what produces the nice curve you see. The absorption lines in the spectrum are not always something that comes from the Sun itself but, in most common situations, the absorption lines you will hear referr... | {
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Is the existence of a photon relative? If an observer passes an electron, in such a way that the observer is accelerating, the observer would see photons because accelerating charges induce electromagnetic waves.
But from point of view of the electron or an inertial observer there is no magnetic field nor an accelerat... | To start with, accelerated frames are not inertial frames.
Secondly electrons and photons are elementary particles and are described in a quantum mechanical framework, where everything is particles and interactions of particles.
The blanket term "observer" has to be defined in terms of interactions, in order to be abl... | {
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Why is the mol a fundamental physical quantity? I am starting to study physics in detail and as I read about physical quantities, I was puzzled why mol (amount of substance) is taken as a physical quantity.
A physical quantity is any quantity which we can measure and has a unit associated with it. But a mol represents ... | The mole definitely isn't a fundamental physical quantity. It's just a shorthand for Avogadro's number, to make really big numbers more tractable. It's purely there for convenience, there's nothing fundamentally physically significant about it.
| {
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Adiabatic free expansion of real (Van der Waal's model) gas below/at/above inversion temperature For an adiabatic free expansion, $W = 0$ and $Q=0$. Therefore, by the first law of thermodynamics, $\Delta U = Q -W = 0$.
For a Van der Waals model of a real gas, $\Delta U = n C_v \Delta T - a\,n^2 \left(\frac{1}{V_2}-\fra... | this is more a comment on your answer: in any free expansion the pressures in each side are not kept constant: the pressure decreases in one side and increases in the other side. The correct statement is: "It is only when the gas flows between two regions of different pressures (each kept constant) that the total enta... | {
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Why most of the minority carriers make it across the base as the base width is small? I am studying about BJT from an online lecture note. I made a question in the image below. The reference in the image is from the two lectures, lecture 18 and lecture 19.
Could anyone help me with the question in the image?
| When the hole concentration at the $x=0$ boundary is held constant at $n_0$ and holes are allowed to diffuse in the $0 < x < W$ region, they each travel a certain distance before being annihilated through recombination. The quantity $L_B$ in your notation represents the hole diffusion length, or the average distance tr... | {
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What is the change in net internal energy? Suppose a person is hanging on a tree and he falls down to the ground. I consider the person, and the tree as a system and the Earth as surrounding. Applying the energy principle,
$$\Delta K_{trans} + \Delta K_{rel} + \Delta E_{int} = W_{net, ext}$$
What is the work done by ex... | If you are considering the person (and the tree) as the system then as the person falls the external force acting on the person is the gravitational attraction of the Earth on the person $mg$.
If the person (centre of mass) falls a distance $h$ then the work done by the external force on the person is $mgh$ and so the ... | {
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Do selection rules apply only for radiative transitions or any other type of transition as well? Selection rules mentioned in all books on atomic physics state that for example orbital quantum number must change by 1 when electron does transition between energy states of an atom. Does this apply only for radiative tran... | As far as I can tell, "selection rules" is terminology applicable only to radiative transitions. The rules originate in the multiple expansion of the potential.
Dipole transitions change angular momentum by $0$ or $\hbar$ because the dipole moment is the $L=1$ multipole. Quadrupole transitions change angular momentum... | {
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Does Earth experience any significant, measurable time dilation at perihelion? Is there any measurable time dilation when Earth reaches perihelion? Can we measure such a phenomena relative to the motion of the outer planets?
| We can calculate the time dilation for an object moving in the Sun's gravitational field using the Schwarzschild metric. Strictly speaking this is an approximation since the Sun is rotating and not spherical, but it will give us a pretty good answer.
The Schwarzschild metric is (writing it in terms of the proper time):... | {
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Why does the proton have a parity $P=1$ and an anti-symmetric wave function? The overall parity of a proton is 1 because the parity of a quark is 1. How does this go together with the proton's wave function being anti-symmetric?
Is the reason for the proton's wave function's anti-symmetry the fact that in $SU(3)_C$ you... | The spatial parity of the proton (and the quark) is +1 by convention. Fermion and antifermion have opposite spatial parity. So the antiproton has spatial parity -1, by the same convention. But it could equally well be the other way about, provided you're consistent.
The proton wave function is antisymmetric under per... | {
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Is the speed of light the only speed that exists? Well, it seems to me that if I move faster in space I move slower in the dimension of time which is orthogonal to the dimension of space.
All speeds are then equal. Is this statement correct?
| The norm of the four velocity is always $c$, but of course not all four velocities are equal because they can point in different directions and vectors that point in different directions are not identical.
But to claim the word speed means the norm of the four-velocity seems unjustified. By speed we normally mean (the ... | {
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Is the time period of oscillations in the underground tunnel constant for all lengths? I know that we can very easily derive an expression for the time period of oscillations in an underground tunnel due to gravity. It does not depend on length or inclination of the tunnel, and is 5050 seconds.
But if that's true it sh... | Yes, it is the same for all lengths of tunnel. This is really no more surprising than that the period of a mass on an ideal spring is independent of its amplitude. A larger amplitude causes the mass to move more rapidly, covering a greater distance in the same time.
The formula derived by Naveen Balaji in Period of osc... | {
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Shooting a bullet into an MRI What happens, if one shoots a bullet into an MRI system? Is there any chance to fully stop the bullet?
Boundary condifitions:
Consider an MRI machine with a reasonalby strong magnetic field (~3T) and tunable gradient coils. Furthermore, suppose we have a standard gun and bullet to shoot i... | New Version (as I had my doubts on the orders of magnetude...and it turned out that I made a mistake)
To simplify things I assume:
*
*velocity $v=1000\; \mathrm m /\mathrm s$
*perfectly conducting bullet
*density of $\rho=10000\; \mathrm{kg}/\mathrm{m}^3$
*A $B_\mathrm{max}=5\;\mathrm T$ and constant gradient of ... | {
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Resolution of acceleration due to gravity along initial direction of projectile While solving problems regarding projectiles cant we resolve the acceleration due to gravity along (or against) the direction of initial velocity and use this in the equations of motion to derive the answer?
| You could do that, but you would need to write equations of motion using coordinates which are not horizontal and vertical coordinates. You would have a zero initial velocity in the coordinate perpendicular to the initial velocity, but you would have accelerations in both coordinates. The coordinate directions would be... | {
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Sound wave equation in 3D closed Box We have the sound wave equation
$\Delta p - \frac{1}{v^2} \frac{d^2}{dt^2} p = 0$
in a closed Box. So we got Dirichlet boundary conditions and I can combine the solution for the 1D case to a 3D solution. In my quantum physics course we multiplied the 1D solution but in this lecture ... | Either you are dismembering what was taught or your professor. I don't want to speculate who made the mistake, but the solution by your quantum physics professor is correct. The separation of variables method assumes that the solution is of the form:
$$ p(x,y,z,t) = X(x).Y(y).Z(z)e^{i\omega t}$$
So all your cosines nee... | {
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What are the differences between light from the Sun and light from a laser? The sun and the laser both give off photons, but there is clearly going to be a difference(s) in the light I receive from both sources. What are those differences (energy, intensity, orientation of photons, phases etc... literally any differenc... | No difference between "single" photons, however for a laser you can think of the photons as in step with each other (technical term would be "in phase"). Light from the laser is generated in a special ordered way of (more or less) one wavelength. The light from the sun is generated in a higgledy-piggledy way consisting... | {
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Noether's Theorem: form of infinitesimal transformation Noether's theorem states that if the functional $J$ is an extremal and invariant under infinitesimal transformation,
$$ t' = t+ \epsilon \tau + ...,\tag{1}$$
$$ q^{\mu'} = q^{\mu} + \epsilon \zeta^{\mu} +... .\tag{2}$$
Then the following conservation law holds:
$$... | As a partial answer let us mention that (i) in a Hamiltonian formulation and (ii) for purely vertical infinitesimal quasi-symmetry transformations
$$\delta z^I~=~\epsilon \zeta^Iz^I,\tag{A}$$
meaning that OP's $\tau=0$ is assumed zero,
$$ \delta t~=~\epsilon\tau~=~0, \tag{B}$$
then the vertical generator
$$\zeta^I~=~... | {
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Motion of bodies connected by springs Two blocks $A$ and $B$ of masses $m$ are connected by a spring of length $L$ and spring constant $k$. They rest on the frictionless floor. Another body of mass m moving with velocity $v$ collides elastically with $A$. The spring compresses and at maximum compression velocity of bot... | Welcome to StackExchange!
To answer your question, apply conservation of momentum. I will assume the collision gave the block A some velocity v. Now the initial momentum of the system would be p=mv.
Suppose at some time, lets say the block A now has a speed u. By momentum conservation, you would get speed of block B to... | {
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Books on undergraduate experimental physics? In undergraduate exams, problems sets etc, their are often questions that take the form:
Describe an experiment in which you can measure $x$, $y$ and $z$.
Does anyone known of any resources, covering a wide range of topics, where one can look up e.g. 'Hall coefficient' and... | A classic text recommended in many advanced undergraduate physics lab courses is Experiments in Modern Physics by Melissinos. It covers everything from alpha particle ionization to the Zeeman effect, including the Hall coefficient, and is most suitable for upper-level labs after first year. The 2003 Second Edition by... | {
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Solar neutrino momentum flux through Earth According to wikipedia, the sun emits enough neutrinos that the number passing through a square meter of area oriented perpendicular to the sun at Earth distance is around $6.5 \times 10^{14}$ per second.
What is the momentum flux of these neutrinos? If you counted up the mome... | There are two approaches to the calculation.
One is to know that the vast majority of solar neutrinos come from a p+p reaction that yields neutrinos with a maximum of 0.42 MeV. The spectrum yields an average neutrino energy of around 0.3 MeV.
As the neutrinos are highly relativistic, then $p = E/c$. The momentum flux i... | {
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Is the Charge on proton is $3.2\times10^{-19}$ greater than that of charge on electron? As the charge on electron is $$e^-=-1.6\times10^{-19}C$$ and charge on proton is $$p^+=+1.6\times10^{-19}C$$
Does this mean that the charge on electron is $3.2\times10^{-19}C$ less than that of charge on proton?
| The sign has nothing to do with the charge itself. It is just a convention. Just because we write an electron's charge as $-1.6\times10^{-19}$, it does not make the electron negative or its charge to be less than that of a proton.
We could have called charge on a proton to be $-1.6\times 10^{-19} C$ and the charge on a... | {
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Is there a Birkhoff-like theorem for stationary axisymmetric metrics? I know about the theorem by Robinson and Carter about the uniqueness of the Kerr metric in the case of stationary axisymmetric (SA) black holes. Are there any uniqueness theorems like Birkhoff's theorem for stationary axisymmetric metrics?
| There is nothing as strong as the Birkhoff theorem in the case of stationarity and axisymmetry. Note that the Birkhoff theorem in its strongest form can be stated as:
"If even a piece of the space-time is spherically symmetric and a vacuum, then it is a piece of the Schwarzschild space-time."
There are various theorems... | {
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Ratio of Forces Problem. An object is dropped from a building. After travelling $\text{10 m}$ freely, a force $F_1$ is applied on the object for $1$ second and the object comes to rest. If one would apply another force $F_2$ for $2$ seconds instead of $F_1,$ the body would come to rest. Find $F_1:F_2.$
Progress. We kno... | I think that this question is not homework question as @Eeshan has posted his procedure for solving the question. So this question deserves an explanation.
My answer:
The velocity of the particle after the fall of $10m$ is $10\sqrt{2}\frac{m}{s}$.
Let Force $F_1$ and $F_2$ produce an acceleration of $a_1$ and $a_2$ res... | {
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Van der Waals forces & Partial charges We're told that charge is quantized. That the charge any body carries has to be an integral multiple of the fundamental unit of charge: $e=1.602×10^{-19}C$ such that $q=ne$ where $n$ is an integer.
But my book says (while explaining van der Waals forces) that the partial charges o... | Imagine that you live in a world where the fundamental particles are cones with mass 1. But at some moment you want to know the weight of the halfs (the tip and the basis). Nobody forbids to calculate this masses. And this could be useful to calculate vibrations and rotations of such fundamental particles.
So it makes ... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Is there any direction of pressure i.e. according to force applied or something..? I was reading about pressure in general and came to know that it is a scalar and being scalar it has no direction(by definition of scalars).
But I think that there is some direction as when we push a wall we apply pressure on it in a par... | Pressure (in the sense of the hydrostatic pressure $P$, i.e., the normal stress on all sides) is a scalar. Pressure (in the sense of the stress $\sigma$ in the context of materials science) is not a scalar but is instead a 3×3 matrix.
The matrix $\sigma=\sigma_{ij}$ arises because of the variety in possible directions... | {
"language": "en",
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What is the complete proof that the speed of light in vacuum is constant in relativistic mechanics? I study maths in uni and we have a course about relativity.
In the main principles I've read that the speed of light is invariant since we can calculate it from the Maxwell equations.
My problem is that the Maxwell equ... | Maxwell equations are invariant under Lorentz transformations, which is the same as saying that they follow special relativity.
You can try to convince yourself by transforming to another inertial reference frame $S'$ and deriving the wave-equation of the fields, you should find that $c' = c$
| {
"language": "en",
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"source": "stackexchange",
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How does centripetal force changes the direction of velocity? Isn't it a violation to Newton's second law of motion? Newton's second law is a vector law.
When when we resolve it in component form along the x, y and z axes we can conclude that force changes only the component of velocity along it, for example if the onl... | One can always express the position of some object with respect to some origin as a vector in as $\mathbf r = r \hat r$ where $\mathbf r$ is the object's position vector, $r$ is the magnitude of that position vector, and $\hat r$ is the unit vector parallel to $\mathbf r$. Differentiating with respect to time yields $\... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/326214",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Is light deflected by external electric and magnetic field? I recently read about the Maxwell's laws of Electromagnetic Waves and I found that Light is made up of both Electric and magnetic fields.
So now if i pass the light through a capacitor such that the plates are parallel to the light will the light be deflected?... | All electromagnetic waves have the electric and magnetic fields vibrating perpendicular to each other. But this does not mean that they are affected by electric and magnetic fields.
The quantum theory shows that light is made up of photons which do not carry charge, during to which it is unaffected by electric or magne... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Absorbtion of photon Electrons in an atom absorbs an incoming Photon to gain energy and jump to a higher energy level (shell or different orbital) considering the fact that the photon doesn't have enough energy to make the electron jump to any higher energy level would the electron still absorb the photon?
| First of all , the electron and the atom are in one quantum mechanical state. The whole atom will be aborbing the photon if there exists a difference between energy levels that, within widths, equal to the energy of the photon. If there exists, then a photon hitting an atom will turn it into an excited state, with the ... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Why a circular camera lens captures rectangular pictures? I want to know how a circular camera lens captures a rectangular picture.
Moreover what will happen if the lens was rectangular.
I have tried a lot to think about it but i could not figure out anything.
| In short, cameras produce rectangular pictures because the sensor is rectangular; the illuminated area is circular and some light is wasted off the edges of the sensor. In film cameras the sensor is the film, which is stored in a roll as tape, and making the frames bigger so they catch all the light would waste film. I... | {
"language": "en",
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Geocentric Ecliptic to Perifocal Coordinate Transformation I'm self-studying elementary orbital mechanics and am experimenting with transforming satellite position and velocity vectors between different coordinate systems. I know there are coordinate transformation matrices between Geocentric Ecliptic and Geocentric E... | After thinking about this problem further I finally figured out that making the coordinate transformation from ecliptic to perifocal is nearly the same as from geocentric to perifocal. The only difference is that you use an inclination value 23.4 degrees less, which is the angle between the ecliptic plane and the equa... | {
"language": "en",
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How to deduce the charge of an electron from the charge of an oil drop in the Millikan experiment? In the Millikan experiment we measure the charge of one oil drop. But how can I measure charge of one electron when I’m not sure how many electrons are contained within one oil drop?
| Strong peaks on a graph are expected if charge is packaged in discrete
units, but not if charge is infinitely divisible.
One constructs a histogram of the charge measured, and accumulates a few thousand
data points, with very fine drops in a relatively high field. The intent
was to only observe oil drops with small ch... | {
"language": "en",
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How do you measure entanglement for type-II downconversion? I am going to do an experiment for a class, which will be using type-II downconversion to entangle pairs of photons pumped from a laser diode. We're planning on using a camera to take pics of the rings that'd be formed, but we need to also measure/quantify our... | So from what I know, proving entanglement in formal terms can be tricky since you need to do a succession of experiments to show that your system breaks Bell's inequalities. I never did it myself but it is documented in literature and even in Wikipedia.
In your case, if you only want to give a flavour of entanglement,... | {
"language": "en",
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Can force change the mass of an object? I have a difficulty in understanding this 'mass never changes'. Say, i punch/hit a ball until it deflates, or bursting a balloon with a needle - doesn't the mass of the ball/balloon change? the air already diffuses out from the ball.
| Let's look at your system: a needle, a balloon skin, and a gas inside the skin. There is some total mass in this system.
Force of the needle pressed against the skin causes a stress which exceeds the strength of the skin material, making a hole. The air escapes through the hole after the force is gone, but the mass of ... | {
"language": "en",
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Is really the electric field felt in every thing in space? I was wondering if the action/force of the electric field is really felt everywhere. I know it does reduce as you get further, but my thoughts concerned more about materials.
So, I know that the electric field is strictly related to Coulomb's Law, and Coulomb's... | Look up something called dielectric constant. It's a measure of how the electric field due to a charge is affected when the charge is placed in another medium. The reference, of course, is made with respect to vacuum.
Vacuum has a dielectric constant $K$=1. While other material media have $K>1$.
Basically the term $K... | {
"language": "en",
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Potential energy for a crystal lattice I would like some help understanding the following passage:
Consider a crystal lattice such that its unit cell has 27 ions arranged such that there are alternative positive and negative ions for same magnitude.
Then the electrical potential of the crystal lattice is just the pote... | You are correct in asserting that the equation gives the potential energy for a single ion and then multiplies it by the number of ions to obtain the total potential energy.
The reason the effects of the boundary can be ignored is based on two factors:
*
*Nearby ions have more influence on the potential of a given ... | {
"language": "en",
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Why are lower energy systems stable? Apart form the practical evidence that the systems that exist in nature try to attain lowest energy possible and hence, maximum stability, and atoms forms bonds to attain low potential energy but do we have any reason why is that ? Why low energy systems are stable?
What happens whe... | Atoms and molecules are coupled with the electromagnetic field. The electrons of the atom and molecule are accelerating and then it will emit electromagnetic radiation, making the system losing energy.
Classical mechanics will predict a total collapse of the atom. Turns out that Quantum Mechanics saves the day, introd... | {
"language": "en",
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Degree of freedom of a BEC I would like to know how many degrees of freedom an atomic gas has. What about the Bose-Einstein condensation from that gas?
| It all depends on the type of gas and on its temperature.
If the gas is made of single atoms like $^{87}Rb$ or $^{39}K$ (typical atoms that are Bose-Condensed, since you are asking), then it as $3$ degrees of freedom - motion along $x, y,$ and $z$.
If the constituents are diatomic molecules, like $H_2$, then the two at... | {
"language": "en",
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Why solid angle of a closed surface from exterior is zero? Actually my question comes from Gauss law which says charges outside a closed surface, doesn't effect on the whole electric flux of the surface.
The reason of that is that the solid angle of a closed surface while measuring it from outside of the surface, is ze... | As viewed from a point outside the surface, the closed surface has a far side and a near side. For example, for a cube there is a front face and a back face.
If there were a point charge situated where the viewer is, the flux from this charge goes into the enclosed volume across one surface and out of the enclosed vol... | {
"language": "en",
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Why does gravity act at the center of mass? Sorry if this is a trivial question.
Why does gravity act at the center of mass?
If we have a solid $E$, shouldn't gravity act on all the points $(x,y,z)$ in $E$? Why then when we do problems we only only consider the weight force from the center of mass?
| Suppose I have a collection of n vectors $x_i\quad \forall i\in(1,n), i\in \mathbb{Z}$ such that the corresponding masses at each $x_i$ is $m_i$. This is your body $E$ and if the total mass of your body is $M$, then $$M=\sum_{i=1}^{n}m_i$$
In that case, if $E$ is subjected to a uniform acceleration field $\vec{g}$, as ... | {
"language": "en",
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Explicit calculation of the two-point function by path integrals I need help carrying out the following calculation:
We have the generating functional of free theory:
$$Z[f] = \exp\left(\frac{i}{2} \int d^4xd^4y f(x)f(y)\Delta(x-y)\right) $$
where $f$ is an external field and $\Delta(x-y)$ the Green function of the Kle... | Omitting space-time indices (cf. DeWitt notation):
$$
Z[f]=\mathrm e^{\frac12f\cdot\Delta\cdot f}
$$
Therefore,
$$
Z'[f]=\Delta\cdot f\ \mathrm e^{\frac12f\cdot\Delta\cdot f}
$$
and
$$
Z''[f]=\Delta\ \mathrm e^{\frac12f\cdot\Delta\cdot f}+(\Delta\cdot f)^2\ \mathrm e^{\frac12f\cdot\Delta\cdot f}
$$
Therefore, setting $... | {
"language": "en",
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Why is dipole the simplest source in electrodynamics? I see this sort of statement in many materials, for example this:
The smallest radiating unit is a dipole, an electromagnetic point source.
and this:
The simplest infinitesimal radiating element, called a Hertzian dipole…
However, none of them includes a clear e... | The smallest radiating unit is an accelerating dipole moment. That can of course be produced by an accelerated single charge, which can be made equivalent to an oscillating dipole.
$$ \ddot{p} = q\ddot{r},$$
where $r$ is a displacement of the charge around some fiducial point.
You don't get a radiation field unless th... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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What does a volume integral of $\textbf{J}$ mean? Assume stationary currents in vacuum, $\text{curl}\textbf{B} = \mu_0\textbf{J}$. With $\text{curl}\textbf{A}=\textbf{B}$ and $\text{div}\textbf{A} =0$ the vector potential $\textbf{A}$ can be written explicitly as a spatial integral over all space of the current density... | It's best to think relativisticly. We are solving the Maxwell equation $d\star (d A)=\star J$ where
$$
A=-\phi dt+ A_x dx +A_ydy+A_zdz\\
J= -\rho dt + j_x dx+j_ydy+j_z dz
$$
are 1-forms in four dimensions and $\star$ is the Hodge dual. So $\star J$ is a three form.
The $j_x$ appearsin $\star J$ with $dy\wedge dz \we... | {
"language": "en",
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Crash simulation on Mythbusters I remember an episode of mythbusters where they were busting myths to do with a head on collision between two cars.
They said that instead of crashing two cars into each other at 50mph they would crash a car into a stationary object at 100mph because the energy involved in the crash woul... | Imagine a thought experiment in which the two cars and their contents are identical mirror images of each other.
In this perfectly symmetrical universe, after a 50 mph crash, the cars break up symmetrically: because the cars and contents are identical in every way, every fragment is emitted at exactly the same time fro... | {
"language": "en",
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How many photons enter our eyes per second when looking at the blue sky on a sunny day? How many photons enter our eyes per second when looking at the blue sky on a sunny day? Say the sun is directly over head and you are looking at the blue sky on the horizon. Say that the pupil is 2mm in diameter. I'm looking for an ... | The surface brightness of the Sun is -10.6 mag per square arcsecond.
The full moon on the other hand is about 14.5 (astronomical) magnitudes fainter than the Sun, has a similar apparent angular size and is just visible in a bright daytime sky.
The flux from the daylight sky incident upon the eye is therefore around $10... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/329971",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Example of Poincare recurrence theorem? Is it possible to explain Milankovitch cycles (or some other arbitrary planetary configuration that recurs to some approximation) in terms of the Poincare recurrence theorem?
More generally, is there a good physical example of the Poincare recurrence theorem?
| We just had a pedagogical paper on Poincare recurrence:
https://arxiv.org/abs/1705.01444
Yes, for the planetary configuration problem, some of the recurrences can be predicted accurately. It reduces to a classic problem in number theory, namely, the simultaneous Diophantine approximation problem for real numbers. Math... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/330139",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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In flat spacetime, what is the mixed (invariant?) form of the metric tensor? In flat space, the metric tensor is (in one of the two conventions)
$$\eta^\mu{} ^\nu = \begin{bmatrix}1&0&0&0\\0&-1&0&0\\0&0&-1&0\\0&0&0&-1\end{bmatrix} = \eta_\mu{}_\nu$$
What is $\eta^\mu{}_\nu$ or $\eta_\mu{}^\nu$? I read here it was the s... | For any metric (either on flat or curved spacetime), $g^\mu_{\ \ \nu} = g^{\ \ \nu}_\mu = \delta^\mu_\nu$. See here for the explanation.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/330313",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "5",
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Thin Film Interference, thinning each layer one by one I have three layers of different complex refraction index.
I am shining with a laser of wavelength lambda onto the layers.
Through etching, each layer is etched one by one, and hence one by one, the thickness is reduced of each layer until zero.
Experimentally, I... | This isn't directly an answer since the method of doing the calculation is rather long and tedious, if basically straightforward, but I can tell you where to find the answer because I did precisely this as part of my PhD. The method is described in Optical Properties of Thin Solid Films by O. S. Heavens, Butterworths S... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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When can I pull out the identity operator? I have a problem that requires figuring out the sum:
$\sum_{n>1} |\langle n10| \hat{z} |100 \rangle|^2 = \sum_{n>1} \langle 100|\hat{z}|n10 \rangle \langle n10|\hat{z}|100 \rangle$
where $|nlm\rangle$ are Hydrogen wave functions, and $\hat{z} = r\cos\theta$. For n=1, this term... | I've figured it out. In this case, this is the identity operator, in the sense that we could change this to a sum over all the hydrogen wavefunctions since this integral over all of these other terms is zero.
| {
"language": "en",
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How to tell whether a Feynman diagram is $t$-channel or $s$-channel by looking? By looking at a diagram, how does one tell whether it represents a $s$-channel process or a $t$-channel process i.e., without finding the amplitude? I'm familiar with Mandelstam variables but I've trouble understanding what a $s$-channel or... | I think the easiest way is to check the agreement beetween fermions/antifermions and the directions of their arrows.
Take this for example:
You can label all the fermions $e^-$ and it's t-channel. If you label the top left and bottom right $e^-$ and the other two $e^+$, it's s-channel.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/330717",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
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Spring-Mass-Pendulum "via Newton's Laws" Good Night everyone:
I have one problem here that I KNOW how to solve using Lagragian Dynamics. But, I really want to know how to solve using Vector decomposition, Newton's Laws, first-year physics and so on.....
I really apreciate tips and hints, both mathematical and physical.... | A good start is to make a free body diagram of all parts. Mark known and unknown forces. Remember that if you have a force $\mathbf{F}$ on one part at the contact point with another part, on the contacting part you have a force $-\mathbf{F}$. Then set up a differential equation for the motion given the total forces on ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/330803",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
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Magnets and entropy While teaching thermodynamics our chemistry teacher (physics syllabus covers only first law) told us that a process is reversible if and only if no entropy is created.
Coming back to everyday life while playing with magnets we have observed that some substances stay magnetized for a very very long t... | A system in equilibrium corresponds to a free energy minimum which is a compromise between a minimum of the internal energy with a maximisation of the entropy. When you introduce, say, an unmagnetised ferromagnet to a magnetic field, alignment of the atomic magnetic moments with the external field reduces the internal ... | {
"language": "en",
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"source": "stackexchange",
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Is value of speed equal to the magnitude of velocity? For example: - suppose a body covers a semi-circle in $5$ seconds, then distance$=\pi * r$, where $r$ is the radius of the semi-circle. Displacement is $2r$ only. Then the value of speed is $[\pi * r] / 5$ while that of velocity is $2r/5$. Here we can see that magni... | Instantaneous speed always equals the magnitude of instantaneous velocity (because the instantaneous displacement is small enough to be regarded as straight-line). In your example, you are comparing average speed and the magnitude of average velocity - and the two of them can be different as you have correctly calculat... | {
"language": "en",
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Is Earth part of the system when writing Gravitational Potential Energy? Here is a question which stumped me when teaching high school students.
The Work-Energy equation can be written as:
$$
W_{ext} + W_{non-conservative} = \Delta{U} + \Delta{K}
$$
Here, $\Delta{U}$ refers to the difference in potential energy of the... | The usual approach is to treat the block as the 'system' and Earth as the 'environment.' Then gravity is an external force acting on the system, or stated alternatively: An interaction between the system and Earth. In the energy balance, one may either put gravity in the tally of external work (done on the system), xor... | {
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Why do charges on the sphere not fly? Consider a uniformly charged conducting solid sphere. As we know, all of the charge must reside on the surface of the sphere, so let's only take this uniformly charged spherical plane into consideration.
I have color-labelled six representative charge elements ($dq$) on this spheri... | Standard answer for a discountinous field is to take the average of the inside and outside field. So in your case the field on the sphere would be $\sigma/(2\epsilon_0)$. See for example Purcells Electricity and Magnetism.
For your second question: In a conductor the electic charge is only allowed to flow inside the c... | {
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How do varying static point charges exert the same force on each other? If you have two point charges one being 1 Coulomb and the other being 1 Trillion Coulomb, it is said that the electric force from the 1 Coulomb point charge exerted on the 1 trillion Coulomb point charge is equivalent to the electric force from the... | Perhaps this analogy will help:
Imagine I have two fans - one with a huge diameter, the other with a tiny diameter. When I put them facing each other, with the huge fan running, I will be able to extract a small amount of power from the tiny fan (because only a tiny fraction of the wind generated by the big fan will in... | {
"language": "en",
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} |
What is Thermal expansion?
"Thermal expansion arises from the asymmetrical nature of potential
energy curve for atoms in a solid. If oscillators were truly harmonic
separation would not change regardless of the amplitude of vibration."
I don't understand how a temperature increase might not affect the volume of a... | If the interatomic potential were a perfect parabola, it is true that there would be no thermal expansion. Why? Well, as atoms vibrated more and more, the mean atom position would not change. Sure, it would wobble around more, but it would wobble as much to one side as to the other. The change in average atomic positio... | {
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One loop diagram in $\phi^4$ theory I know that in the $\phi^4$ theory the tree-level diagram for two in-going and two out-going particles is simply a 'cross' where all the external legs meet at one point.
I'm now interested in a slightly more complicated case where I have 4 rather than 2 outgoing particles and I want... | Yes, that is the correct one loop topology that appears assuming no snail and/or one particle reducible contributions (inclusion of these gives you a plethora of other diagrams, such as ones where you decorate the tree level contribution with snails etc). With a labelling of the external momenta in place, you can show ... | {
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Can we theoretically "derive" the mass of a particle? I read a pop sci book on the Higgs which said that particles get their mass due to interacting with the Higgs field. If that is true, could we use first principles to derive the mass of, say, an electron? After all, QED is built on the interactions of particles and ... | This is the table of the elementary particles of the standard model, SM.
The masses have been measured experimentally and the whole table is part of the postulates/axioms of the standard model. These masses within the SM are generated by the Higgs mechanism. The SM up to now is very successful in describing and predi... | {
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Why do papers describe the ytterbium ion as having only a single excited state? Multiple papers describe the ytterbium Yb IV ion as having only two energy levels. Why aren't there more levels in its spectrum?
| There are more levels.
For many experiments, one can choose combinations of laser frequencies such that only a few energy levels are relevant; when reporting those experiments, one can just report a simplified energy-level diagram that only includes the states that are relevant to the experiment.
However, that doesn't ... | {
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Qualitative description of how an inhomogeneous broadening mechanism can lead to multimode oscillation in a laser cavity I understand that when there is inhomogeneous broadening in a laser cavity, the resultant gain profile is a Gaussian (as opposed to a Lorentzian profile for homogeneous broadening). Due to the wider ... | First of all, in-homogeneous broadening doesn't have to be Gaussian, it happens to be like that only for Doppler broadening (due to Maxwell-Boltzmann distribution of velocities). Other in-homogeneous broadening don't result in a Gaussian gain profile.
In the same way, homogeneous broadening doesn't have to be a Lorent... | {
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What is the meaning of "kay effective" $k_{\rm eff}$ in SHM? I am really confused studying for my Physics lectures on oscillations, namely Simple Harmonic Motion. You see, my Professor introduced the topic: when he solved some examples, I noticed that when working with springs, he either:
*
*Uses the actual $k$ of t... | $k$ is the spring constant experienced by the body due to actual string. $k'$ effective is the constant in the expression $m\frac{d^2x}{dt^2} = - k'x$ after you've done some rearrangements to your differential equations. For example, supposes you have a mass on two springs of spring constants $k_1$ and $k_2$. Then, you... | {
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Do point charge really exist? Do point charge really exist experimentally?
Am I right with definition of point charge? According to me point charge is a charge having 0 (zero) mass and have 0 (zero) volume.
| In your definition, you have put the mass $=0$ condition. You cannot have a massless charged particle. Permitting them to exist will predict a decay for electrons and we have no evidence that that happens. Of course, the assumption here is that QED is correct and we have no evidence that it is not.
However, if you drop... | {
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What is the total energy stored in the capacitors? Shouldn't the repulsive potential energy stored be included? Is there the repulsive energy stored in the capacitors or that energy is already included in the conventional calculation of the stored capacitor energy?
| Assuming no dissipation, the energy stored in a charged capacitor equals the work done in charging the capacitor.
But the work required to increase the charge $Q$ of a capacitor by $\Delta Q$ increases with $Q$; the more charged a capacitor is, the more work is required to increase the charge by $\Delta Q$.
You might t... | {
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Why does water in a glass ripple but oil does not? When I place a glass of water on the table and hit the table from below I can clearly see ripples in the water with their center in the middle of the glass. However when I do the same with a glass filled with oil there are no ripples. The oil seems much more stable.
Wh... | The oil has a far higher viscosity than the water. Since this is a direct measure of the resistance to gradual deformation from a stress, the oil has far smaller ripples than the water for an equal forces - the ripples will also appear to propagate slower through the oil.
| {
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Field confinement inside superconductor cylinder I'm learning about the Meissner effect, but I can't really grasp an example of
Bleaney's book on electricity and magnetism.
Let's assume a hollow thick cylinder made of superconductor material, with it's axis
in the orientation of an applied field $B_1$. We cool it under... | The cylinder is a perfect conductor.
Lenz's law says that when there is a change of flux inside a coil, this will set up an e.m.f. to resist that change. But the moment an e.m.f. is generated, this will create a current in the coil that resists the change in flux.
When the resistance is zero, any change in the flux wil... | {
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Does a capacitor have a resistance? Does a capacitor have a resistance? And why? When I asked my physics teacher, he said certainly not, but I didn't figure out why. Can anyone please clarify? Thanks in advance.
| I feel, capacitor has infinite resistance, since charge generally does not flow through a capacitor, it stores the charge. It generally has a dielectric medium which does not conduct electricity. Thus its resistance will be same as the resistance of the medium. Very high voltage has to be applied across it so that cur... | {
"language": "en",
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Tension In A Massive Rope My book says :the horizontal component of the tension in a massive rope is constant.
It does not seem intuitive to me as I don't think that the above approximation (I guess) is possible.I don't know though
Can anyone help me out with this as I am just not getting it.
Any help and hints are ... | Any section of the rope can be considered as a Free Body. If the section is not accelerating then the horizontal and vertical components of force on it are balanced.
If there are no forces external to the rope acting horizontally on the section, then the forces from the rope at the left and right (ie tension) must be ... | {
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Electrical conductivity of massless fermions in case of finite temperature I was asked to find conductivity $ \sigma (\omega, T) $ using methods of qft, or more exactly using Matsubara Green's function, for the following system:
qed with massless dirac fermions in case $ T \neq 0 $.
As I understand, coductivity is a li... | Conductivity can be written as polarization operator divided by frequency (what is known as Kubo formula). As soon as you calculate the polarization operator (one-loop diagram where the Matsubara green functions do enter) at finite T you obtain the conductivity.
Please have a look at the following papers where this ver... | {
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The Langevin equation - nature of the forces The Langevin equation is given by:
$$m\ddot x=-\gamma \dot x+f(t)$$
where $f(t)$ is some stochastic force. I know that the first term on the RHS is to do with viscous drag and the second term is to do with random fluctuations in the number particle collisions. I have also h... | The first term on the RHS arises from the assumption that the particle is moving through a viscous fluid (in this case, with no net flow velocity). The collisions from the front deliver a higher impulse than collisions from the rear, on average, which leads to a coherent net force directed opposite the particle veloci... | {
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What's the observer in double slit experiment? I watched a video on youtube about double slit and it said that when we try to observe electrons it starts to act like a particle but what are these observers that they use? they're shooting one electron at a time so how can they detect them while they're moving in front o... | An observer is you or someone looking at the electron. It can also be a detector or camera taking pictures etc. it is wrong to think that the mind of a conscious observer will cause an observer effect. The thing is if you look at an electron as it's traveling through the slits you will affect it's a trajectory because... | {
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Intuitive reason for the $T^4$ term in Stefan Boltzmann law The Stefan Boltzmann Law gives a relation between the total energy radiated per unit area and the temperature of a blackbody. Specifically it states that, $$ j= \sigma {T}^4$$ Now using the thermodynamic derivation of the energy radiated we can derive the abov... | If you know Quantum Mechanics, you know that you can set length to have dimensions of the inverse of energy. This means that $j$ must have dimensions of energy to the four. If you consider that the only variable with energy units is the temperature, then the energy density must be proportional to $T^4$.
If you consid... | {
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What is an operator times one of its eigenstates? I am trying to get a hold of caluclating with matrix elements. I have a Hamiltionian $\hat{H}$ in a two-dimensional Hilbert space, having eigenstates $\psi_1$ and $\psi_2$. My professor wrote down these equations:
$$\hat{H} \psi_1 = H_{11} \psi_1 + H_{12}\psi_2 \\
\hat{... | I highly doubt that there being "alternative ways to write the matrix elements" mentioned by the professor has any conceptual significance. After choosing a basis of the two-dimensional Hilbert space, operators can be expressed as matrices,
$$H=\begin{pmatrix}H_{11} & H_{12}\\ H_{21} & H_{22}\end{pmatrix}$$ where $H_{1... | {
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How to show that Chern number gives the amount of edge states? When talking about topological insulator and talking about bulk-edge correspondence, it seems to be widely accepted conclusion that the band Chern number (winding number) is equal to, when the boundary becomes open, the amount of edge states. But why? For ... | Yes, there is a proof of that. The first one appeared by a beautiful paper of Hatsugai in 1993 https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.71.3697 for a particular special classes of models of the IQHE. More general proofs ensued, but it does turn out that the proofs rely on some non-trivial math, the mos... | {
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Does temperature of boiling solution stay constant? Let us suppose we have a liquid with non-volatile solute, and the solution is raised to its boiling point by applying heat.
Since the solvent is being evaporated, the concentration of solute will increase. Thus, the vapour pressure of solution will decrease and the bo... | "The temperature of a boiling liquid is constant until all liquid is evaporated" is true only if the nature of the liquid doesn't change. When you have a changing concentration of a solute (because of the evaporation of the solvent), you don't have the "same" liquid as time goes on ... therefore there is no contradicti... | {
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Why can we not measure the distance to the Sun directly using Radar? My question is specifically WHY CAN WE NOT USE Radar to measure the distance to the Sun? What is the reason for that?
Sorry if this is a lame question, I'm not an expert on these things and just occurred to me why not use radar to measure the distanc... | The strength of the radar signal falls rapidly with distance so for objects within the Solar System we are dealing with very faint reflected signals. That isn't a problem with objects like Venus because with suitable signal processing we can extract the radar reflection from the background noise. The problem with the S... | {
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What is the accepted meaning of atomic orbitals and elementary particles in Quantum Field Theory? If elementary particles are represented as oscillations of their respective fields, why are atomic orbitals said to represent the probability of finding an electron at a specific location in the electron cloud or orbitals ... | This is what I have found at
https://en.wikibooks.org/wiki/Quantum_Mechanics/Waves_and_Modes
An electronic orbital is a normal mode of oscillation of the electronic quantum field, very similar to a light mode in an optical cavity being a normal mode of oscillation of the electromagnetic field.
| {
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How does index of refraction have direction? I found it in my textbook that there are some quantities like the elastic spring constant and index of refraction that have magnitude as well as direction, but are not called 'vectors'. I wonder how they have directions - I can somewhat make some sense of the spring constant... | Almost certainly what's being talked about here is the refractive index of an anisotropic material. In this case, there are preferred directions in the material in question and the refractive index, i.e. the reciprocal of the phase velocity of the wave, depends in general both on the wave's direction and polarization.
... | {
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Is there a connection between Bertrands theorem and Chaos theory? Bertrand's theorem states
Among central force potentials with bound orbits, there are only two
types of central force potentials with the property that all bound
orbits are also closed orbits, the inverse-square force potential and the
harmonic os... | Demonstrating Bertrand's theorem has attracted lots of interest, and there is quite a bunch of proofs using various methods. My library of papers feature one article [1] which would qualify I think, but it is in French. Here is the published abstract in English
"When a point mass undergoes a central, attractive, gradie... | {
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Special relativity: train, dock and inclined beam I am sure there is a flaw in my reasoning; but how could I make it right?
• In a stationary wagon, an experiment is carried out: a photon is sent from point $A$ to point $B$ by reflection at $C$ (equidistant from $A$ and $B$); The values $H$ and $L$ are known.
Two synch... | The problem with your analysis is that it has more unknowns than it has equations, which means you should not expect it to be able to determine the values of any of the unknowns.
Write (as you have) $\Delta t_w$ and $\Delta t_q$ for the transit time of the light beam, measured in the two frames. Write $L_w$ and $L_q$ ... | {
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If Hawking radiation is true why isn't the entire universe glowing? It says hawking radiation appears due to a particle and anti-particle pair one of which gets sucked in and other one escapes , these particles are said to appear out of nowhere , appear everywhere in the universe and are opposite of each other.
As suc... | Hawking radiation comes from the region near a black hole, it is not produced 'throughout space' as you suggest. In this respect the situation is not very different from a star, where the emitted radiation comes from the outer layers. In the case of the black hole it is the region fairly near to but outside the event h... | {
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Why is $\gamma^5$ used to define the projection operator? The properties of the projection operators are defined as:
$$P_+ = \frac{1}{2}(1+\gamma^5)$$
$$P_- = \frac{1}{2}(1-\gamma^5)$$
where $\gamma^5 = -i\gamma^0\gamma^1\gamma^2\gamma^3$
and their key properties are that $P_+^2 = P_+, P_+P_- = 1, P_-^2 = P_-$.
But sin... |
Why do we then bother to define $\gamma^5$ at all if we could use $\gamma^0$ to define the projection operators?
The key observation is that chirality should be preserved under the Lorentz transformation. Hence the $X$ in the chiral projection
$$
P_{\pm} = \frac{1}{2}(1 \pm X)
$$
should commute with 6 Lorentz algebra... | {
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Paradox from mass transfer in a close stellar binary I'm considering a simple binary system made of two stars, of mass $m_1$ and $m_2 < m_1$, on circular orbits around their center of mass. Using Newton's theory of gravitation, it is easy to prove the following formulae for the total mechanical energy and angular mome... | One star cannot transfer mass (conservatively) to the other without the material losing specific angular momentum.
In practice what happens is that an accretion disk forms around the accreting star. Viscous processes occur which transfer angular momentum outwards and allow mass to flow inwards. The viscous processes re... | {
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Why is light bent but not accelerated? Light is bent near a mass (for example when passing close to the sun as demonstrated in the famous sun eclipse of 1919). I interpret this as an effect of gravity on the light.
However, it seems (to me, at least) that light is not accelerated when it travels directly toward the (ba... | In Einstein's 1911 paper "The influence of gravitation on the propagation of light", he pointed out that from his generalizrd theory of relativity, the speed of light as viewed from us is different at different locations in a gravitational field. From the Huygens principle, a change in the speed of light causes the wav... | {
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Schwarzschild geometry, what is physical meaning of coordinates? A past exam has a question:
For the Schwarzschild metric external to a non-spinning spherical mass, what is the physical significance to the coordinates $t,r,\theta,\phi$?
Not sure how to answer this question, I am thinking there is some obvious canonic... | $t$ and $\phi$ are adapted coordinates to the generators of unidimensional translation symmetry in time and rotation symmetry in $\phi$. Noether's theorem, in this particular setting the Killing equation, dictates that conserved currents are related to those symmetries. The related charges are the Komar mass and Komar ... | {
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Where is a classical computer better than a quantum one? Where is a classical computer better than a quantum computer? Is there any known domain where classical algorithms always beat quantum ones, say, both in terms of time and space complexity?
If yes, could you please give me examples?
If no, could you please pro... | You can simulate a classical computer on a quantum computer (with essentially no overhead), but not vice versa. Here's a link to a list of quantum gates that have been found to be useful:
https://en.wikipedia.org/wiki/Quantum_gate
If you look close to the bottom, you can find an implementation of the quantum Toffoli g... | {
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Average induced emf in a rotating coil after rotating by 180 degrees When a coil rotates in a magnetic field an emf is induced, and when the coil starts its motion from the position at which its plane is parallel to the field lines, and then it rotates by 180 degrees, the average induced emf in it is zero. I don't unde... | For this question we must understand that the EMF produced is directly proportional to the rate of change of Magnetic flux linkage.
As the field is parallel to the plane at first we can write that the magnetic flux density, B=k ( assuming be a constant).
Then the function of the flux through the coil will be Flux,F = ... | {
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Does a photon also come to rest after some time while travelling through a medium? If you fire a bullet in air, after some time it comes to rest because of air resistance forces. But what about photons? If they are also particles, then the same thing should happen with them. It does not matter how long it takes but th... | A photon is a particle but it has no mass, that is, mass is zero. Because it's mass is zero, it must always travel at the speed of light: $299,792,458$ m/s. Thus, it is never at rest -- Never.
However, this does not mean that a photon is constantly moving forever. Photons interact with other particles that just get ... | {
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In the proof of the parallel axis theorem, why is the averaged $x$-coordinate "zero by construction"? According to Wikipedia to prove $I=I_{cm}+md^2$:
$I_\mathrm{cm} = \int (x^2 + y^2) \, dm.$ $$I = \int
\left[(x + d)^2 + y^2\right] \, dm$$
Expanding the brackets yields
$$I = \int (x^2 + y^2) \, dm + d^2 \int dm + 2... | It's zero by definition of the centre of mass.
We define the centre of mass as the unique point $\vec{r}_{CM}$ where $\int dm (\vec{r}-\vec{r}_{CM}) = 0$.
Then we define the moment of inertia about an axis passing through the point $O$ with position vector $\vec{r}_O$ as:
$I_O = \int dm (\vec{r} - \vec{r}_O)^2$
In thi... | {
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} |
What is Gray, from a physics POV? Quora explains how white and black colors fit into the spectrum of visible light. It explains that white is all colors together while black is the lack of color.
So, where is Gray? Gray is the mix of all-colors and no-color!! What does that mean? Can somebody explain Gray, the mysterio... | All colors are only in the mind. Light has a mix of wavelengths, but it doesn't have color until someone sees it.
When light enters the eye, it hits rods and cones in the retina. Cones are color receptors. There are three kinds. Each kind is sensitive to a range of wavelengths. Color is the result of stimulation of th... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/339130",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "14",
"answer_count": 2,
"answer_id": 1
} |
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