Q stringlengths 18 13.7k | A stringlengths 1 16.1k | meta dict |
|---|---|---|
Need proper interpretation of imploding/exploding self-gravitating sphere While searching for some nice and simple problems in Newton's theory of gravity, I've made this trivial calculation for which a proper physical interpretation is lacking. Some pieces are missing and I'm puzzled by the result, so here it is.
Cons... | My physics is less terrible this morning. I have a solution to my own question :
Yes, energy as defined by (3) cannot be conserved. If the sphere changed its radius, it's because something changed internally (obviously !). Some internal force is resisting gravity, until it changed for some reason. So there are at l... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/339251",
"timestamp": "2023-03-29T00:00:00",
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First law of thermodynamics, steady flow energy equation (SFEE) and $Vdp$ work Can first law of thermodynamics defined for a closed system be applied to the steady flow energy equation? Why?
I came across the derivation of $Vdp$ work and Every book applied the first law defined for closed system to steady flow energy e... | OH , i get it now. You are right.We can't apply the first law if you don't consider the entire system and if the energy can leak in or out by other means ,say a more energetic fluid comes in. But in steady state flow ,no particular trait of a fluid changes with time.This means that the property of a fluid at a particul... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/339457",
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Deviation when light passed through optical centre I recently get to know that when light pass through optical centre then it shows a very very slight deviation but why? Why doesnt it pass through optical centre extremely straight?
And can i conclude this that when an light is travelling in direction of optical centre ... | This is simply because real lenses have nonzero thickness, and we must one of several methods for dealing with them, such as those presented on the Hyperphysics Website. But this answer is really a slight generalization of Emilio Pisanty's comment:
Why do you find this that surprising? The same thing happens in a slab... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/339869",
"timestamp": "2023-03-29T00:00:00",
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What's the conversion between apparent magnitude and lux? I know the apparent magnitude of the sun, but I'd like the units in lux. Please also direct me to a reliable source if possible.
| We can convert from magnitude to lux using the equation
$$
E_v=10^{(-14.18-M_v)/2.5}
$$
where $M_v$ is the apparent magnitude in the visible band, and $E_v$ is the illuminance in lux. You can read more about it on this page: http://stjarnhimlen.se/comp/radfaq.html#7.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/340230",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
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Why are elements with even atomic number more abundant? In reading this article about the origins of elements, I found the following diagram:
What strikes me about this image is the very consistent zig-zagging of the line that appears to indicate that elements/isotopes with an even number are more abundant.
Am I corre... | I will add to the answer from @BowlofRed https://physics.stackexchange.com/a/158270/36194 that the nuclear pairing interaction lowers the energy in nuclei where the number of like nucleons is even: thus for instance there are more isotopes with even rather than odd number of neutrons. This also favors the formation of ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/340447",
"timestamp": "2023-03-29T00:00:00",
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Traveling close to the speed of light, would a person (or anything else) have a longer existence or would the existence be passing in slow motion? If something, let's say, an electron or a person, travels at some speed close to the speed of light, time would slow down, right?
But would it be passing in slow motion or ... | With respect to you, i.e, in your reference frame, you would be the same. You would not see length contraction or experience time dilation. However,say, from the frame of the earth, the people would see you at slow-mo.
| {
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Why is my solar panel more efficient as the temperature increases, rather than less efficient? I have recently performed an experiment in which I placed a solar panel inside a closed box, together with a heater and a lamp (60W). I increased the temperature using a heater from 20ºC to 50ºC. The lamp remained switched on... | Your voltages are increasing with temperature. This is in contraction to what one expects!
Was optical input power kept constant? Solar cells do get more efficient as sunlight is concentrate on to them. The voltage increase as you are seeing here. That’s one possible explanation. If the input power was kept constant, ... | {
"language": "en",
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The definition of the Lorenz gauge condition The inner product of two vectors in space-time is:
$$(x_1, y_1, z_1, t_1) \cdot (x_2, y_2, z_2, t_2) = x_1 x_2 + y_1 y_2 + z_1 z_2 - t_1 t_2$$
So
$$(\frac{\partial }{\partial x}, \frac{\partial }{\partial y}, \frac{\partial }{\partial z}, \frac 1c \frac{\partial }{\partial ... | The inner product of two spacetime vectors is given by
$$V^{\mu}W_{\mu}=V^{0}W_{0}+\textbf{V}\cdot\textbf{W}.$$
Note that there is no inherent minus sign in this definition. The minus signs only come in when your vector $W$ is naturally described with an upstairs (contravariant) index. In ths case, we would write
$$V^{... | {
"language": "en",
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What is a $D^{0 \ast}$ meson? What are the quark contents of $D^{0 \ast}$ meson?
How to distinguish between $D^{0 \ast}$ meson and $D^{0}$ meson as I guess both have same quark content.
| There are many excited states of flavoured mesons ($K$s, $D$s and $B$s), which are identified by their mass, spin and parity. The mass is usually written in parentheses in MeV (omitted for ground states), the subscript contains the spin (and the lighter quark if it isn't a $u$ or $d$), and the superscript contains the ... | {
"language": "en",
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Differences between optical laser and amplifier I am preparing for an applied optoelectronics exam and I am having some trouble with telling the differences between optical fiber laser and optical amplifier. For now I only came up with following differences:
*
*No Bragg reflectors and optical resonators in amplifi... | An optical laser without a feedback mechanism is essentially an optical amplifier. The feedback mechanism can be made using 2 reflectors, mirrors, or gratings that creates an optical resonator cavity.
Another difference between optical amplifier and laser is that amplifier integrates isolators to avoid feedback, backre... | {
"language": "en",
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Is there a more accurate form of the mirror equation $\frac{1}{f}=\frac{1}{u} + \frac{1}{v}$? In the mirror equation $$\frac{1}{f}=\frac{1}{u}+\frac{1}{v}$$
Q1: Are $u$ and $v$ the distances from the object to the mirror surface or the distance from the object along the principal axis to the pole?
These distances diff... | There is a more general (exact) formula for a spherical mirror. This formula was discovered by H. A. Elagha and was published in the journal of the optical society of america in 2012. The paper has the title: "Exact ray tracing formulas based on a nontrigonometric alternative to Snell's law" . This formula has the form... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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Fall of the number density $n$ with the scale factor $a(t)$ for a relativistic particle species in equilibrium? Consider the thermal dark matter (DM) scenario. Before the dark matter got frozen out, it was both in chemical and thermal equilibrium with the other particles in the early universe. At this point of time, wh... | The basic principle that is useful for addressing the issue you are talking about is conservation of entropy. In thermal equilibrium, the comoving entropy is conserved, and this can be used to find out how the temperature changes with the expansion of the universe.
Since the entropy density of relativistic species usu... | {
"language": "en",
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Why does a surface always exert force normal to it? In whichever angle an object is thrown at a surface, the surface always exert force normal to it. But why? According to Newton's third law, if an object hits a surface at an angle, the reaction force provided by the surface must be equal and opposite to the applied fo... | From a purely Newtonian-dynamics perspective the origin of the normal force (or any force) is not explained. Instead, we infer the existence and direction of the normal force by observations of acceleration: if you see two solid objects not sinking into one another despite the influence of gravity, they must be exertin... | {
"language": "en",
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Why would an infinity corrected objective lens produce an image without a tube lens? I'm having a hard time wrapping my head around this situation I've come across. I'm essentially recreating a homemade microscope that my understanding would suggest shouldn't work. This setup uses a 10X Olympus PLAN N objective attac... | Just like any other lens, Objective lens is a lens, without the Tube lens also it will form an image by following the Lens equations, Lens Equations.
It is just that if working distance of the objective lens would be changed, the camera can image at different distances.
The above link gives an equation for single lens ... | {
"language": "en",
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what is difference between region around a charge and region out of it? Basically I want to know what makes a region around a charge particle so affective that another charge will have energy when brought in this region or it will experience a force when enters into this region
| A Charge experiences a force when brought close to another charge because the charges have a field of force which is the electric field around them. For why these fields exist, no one really knows exactly why as some explanations include quantum field theory as that's how our universe works. For point charges the force... | {
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How is it that in a car crash, four 8mm bolts can anchor the seat to the car? In a car crash at for example twenty metres per second. I used suvat equations and newtons second law to work out the force as as body accelerates(negatively). I estimated that the distance travelled in the crash by the body would be roughly ... | You could apply a pseudo force and treat this a static problem.
The pseudo force is the mass of the seat and passenger times the deceleration. It acts forward on the centre of mass, applying a clockwise torque (assuming the car moves to the right). The seat pivots about the forward 2 bolts, the rear 2 bolts provide a ... | {
"language": "en",
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Ising anyon topological order and its edge $c=1/2$ CFT We know that conformal field theories are closely related to two-dimensional topological orders via edge-boundary correspondence. An Ising topological order can be obtained by gauging the fermion parity from a $p+ip$ superconductor. The anyon fusion rule $\sigma\ti... | p+ip superconductor is an invertible topological order whose intrinsic bulk excitations are fermions. There is no non-abelian anyons. The vortex with Majorana zero mode is not an intrinsic bulk excitation.
The $SU(2)_2$ QH state $\chi_1(z_i)\chi_2^2(z_i)$ and the Paffian QH state have Ising topological order. They hav... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/343326",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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How is the equation of Mach number derived? Wikipedia states that for a pitot-static tachometer, the mach number for subsonic flow equates to
$$M = \sqrt{5\left[\left(\frac{p_t}{p_s}\right)^\frac{2}{7}-1\right]}.$$
How did they get to that result? Is there a derivation, or is it just from a polynomial fit of a tabulate... | The factors are not obvious, I agree.
For instance, for a polytrope index, $\gamma$, of 7/5 the exponent of 2/7 corresponds to a term of the form $\left( \tfrac{\gamma - 1}{\gamma} \right)$, which is our first hint. The second hint is that the pitot tube system can be applied to a Bernoulli system. The third thing to... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/343439",
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At what temperature do the laws of physics break down? I heard that as approaching the temperature of a kugelblitz the laws of physics break down, I saw this in the video The Kugelblitz: A Black Hole Made From Light, by SciSchow Space.
| Hank Green is describing the concept of the Planck temperature,
$$
T_\mathrm{P} = \sqrt{\frac{\hbar c^5}{Gk_B^2}}\approx1.4\times 10^{32}\:\mathrm K,
$$
which is defined as $\frac{1}{k_B}$ times the Planck energy $E_\mathrm{P}=\sqrt{\hbar c^5/G}\approx 1.9\times 10^{9}\:\mathrm J$.
As with all the Planck units, we don'... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/344701",
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Why is Higgs particle detected much later than top quark when it's lighter? The Higgs boson is lighter than the top quark. But the top quark was discovered in the mid-1990s where the Higgs boson escaped detection for two more decades. So if the energy has already been achieved to produce Higgs boson, why did it escape ... | The Higgs being a scalar uncharged particle has the same quantum numbers as the vacuum, making it much harder to detect.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/344813",
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Will overlapping two different beams of coherent light with different wavelength cause interference? If I use two different wavelength lasers to transmit light into a single mode optic fiber will they interfere with each other? If so, how much will be that interference.
| Interference is a concept that only has true meaning when comparing two signals of the same wavelength/frequency.
For waves with different wavelength, it is true that the snapshots of the electric field (or magnetic field for that matter) will change because of the two signals, but there is nothing coherent about such... | {
"language": "en",
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Determining mass radius and charge radius of electrons First the mass radius problem:
Why can't the mass radius of electrons be determinded by shooting neutral particles on it. Similar to Rutherford's gold model only a bit more sophisticated.
Secondly the charge radius problem:
I often hear the term charge radius and... | One reason why a Rutherford-like experiment would't work in the case of the electron is because electron is an elementary particle i.e. it is not made of something else, so shooting particles at it won't have any effect in this sense (of course you can create another particle by colliding for example an electron and a ... | {
"language": "en",
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Conjugate variables in thermodynamics vs. Hamiltonian mechanics According to Wikipedia, the canonical coordinates $p, q$ of analytical mechanics form a conjugate variables' pair - not just a canonically conjugate one.
However, the "conjugate variables" I directly think of are the quantities of thermodynamics - e.g. Tem... | *
*Conjugate variables $(q^i, p_i)$ are given in thermodynamics via contact geometry as the first law of thermodynamics $$\mathrm{d}U~=~ \sum_{i=1}^np_i\mathrm{d}q^i,\tag{1}$$ where $U$ is internal energy. See also Ref. 1 and this & this Phys.SE posts.
*Conjugate variables $(q^i, p_i)$ are given in Hamiltonian mecha... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/345571",
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About light in the universe As a light source in the universe (e.g. sun) emits light in different directions, some of the light emitted reaches places like Earth, and some doesn't. So does the light that reaches the Earth disappear or it is reflected in other directions? And for the light that doesn't reach any place, ... | When any source emits light it may hit any objects like Earth and it will be reflected back in universe and yes the light which doesn't hit any thing will travel forever but that doesn't mean that the universe is going to be brighter because as the universe expands the light with in it gets red shifted and eventually g... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/346018",
"timestamp": "2023-03-29T00:00:00",
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Why surface normal is used while defining flux through an open surface? What is the significance behind defining normal to any surface? Why we do it?
| Suppose that you want to find out the rate of a river using a circular hoop which has attached to it a device which will measure the mass of water flowing through the circular hoop per second - the flux of water.
With the plane of the circular hoop placed at right angles to the river flow you get a reading of $M\, \r... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/346144",
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Maximum extension of a vertical spring when given a blow In the question mentioned above , i considered the length of the spring in the equilibrium position to be the natural length and the P.E. to be zero as we are free to consider any length as the natural length. After , giving a blow , we impart K.E. to the block e... | You should ignore the gravitational contribution since you are assuming that the initial position is the equilibrium position.
Adding the effect of gravity will shift the equilibrium position to a new height.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/346269",
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Why do hydrostatic fluid exert force on any wall normally with magnitude $ρgh$ always? I understand the derivation in middle of container, but for a container like an inverted cone the particle very near to the wall exerts pressure on wall of magnitude $\rho gh$ normally. I ask “why?” and tried to discover it, but I ha... | Imagine a piston of small area, A inside an empty cylinder, close to its bottom end, which is open. The cylinder is immersed in liquid, at any angle, so that the piston is at depth h and orientated at any angle. When the piston is pushed down the cylinder by a small distance $\Delta x$, let's say a force $F_\bot$ norma... | {
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Work done by static friction on a car The tires of a car execute pure rolling. Therefore, the work done by friction on the tires (and hence the car) is zero. If no external work is done, how does a car's kinetic energy increase?
| The increase in the car's kinetic energy comes from the internal energy of the car, stored, for example, in its gasoline or batteries.
The engine exerts torque over the wheels, which are prevented by the friction from simply rotating in place. The reaction from the ground on the car (wheels) makes it move faster.
| {
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"url": "https://physics.stackexchange.com/questions/346660",
"timestamp": "2023-03-29T00:00:00",
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$2\to 3$ cross-section phase space simplification Suppose the $2\to 3$ cross-section:
$$
\sigma = (2\pi)^4\int \frac{d^{3}\mathbf p_{3}}{(2\pi)2E_{3}}\frac{d^{3}\mathbf p_{4}}{(2\pi)^{3}2E_{4}}\frac{d^{3}\mathbf p_{5}}{(2\pi)^{3}2E_{5}}|M(\mathbf p_{1}, \mathbf p_2, \mathbf p_3,\mathbf p_4,\mathbf p_5)|^2\frac{\delta^{... | I can recommend you to read the paper of Tord and Riemann Phase space integrals for 2,3 and 4 particle production. The Idea is to factor the phase space into 2 2-particle phase spaces times $ds'$ where $s'=(p_1+p_2)^2$.
https://www-zeuthen.desy.de/~riemann/Teaching/ws20132014/script-tord-riemann-sm-2013_12pt-appA.pdf
| {
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How can I use Newton's laws of motion to determine the force acting on the rope? Imagine there is a painter, weighing $180~\rm lb$, that is working from a bosun's chair hung down the side of a tall building.
Suppose that he pulls down on a fall rope with such a force that he presses against the chair with a force of ... | Due to Newton's 3rd law, when he exerts 100lbs downwards on the chair, the chair exerts the same upwards on him. That upwards force comes from the string.
So, considering the man+chair as the system, there is an upwards force (string) of 100lbs and a downwards force (gravity) of 210 lbs. It looks like he is accelerati... | {
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Photon interactions with photovoltaic cells I was wondering how different energy photons interact with the electrons in a semiconductor in a PV cell.
If the photon has less energy than the band gap, then the photon passes through and does not interact with the semiconductor, right? Does it just keep traveling until it ... | If the photon has less energy than the bandgap, it will not be absorbed and the material is theoretically transparent to this wavelength as you can see here:
http://www.pveducation.org/pvcdrom/materials/optical-properties-of-silicon
If the energy is higher than the bandgap energy (a little) it can still be absorbed as ... | {
"language": "en",
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Why is there an upper energy limit on the photoelectric effect? I feel like I'm missing something really fundamental regarding the cross section of the photoelectric effect. I'm looking at this chart, and it seems that the lower the energy of the incident photon, the more likely a photoelectric interaction is to happen... | The cross section reduces for higher frequencies, because our material will get more and more transparent for the incoming light.
Think about it in this way: the electrons follow the oscillating E-field of the photons. Now imagine the field oscillates faster and faster. At some point the electrons will be unable to fol... | {
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Exerting Pressure I dip my finger into a container of water that is resting on a scale. Is it true that the force exerted on the scale by the container will increase because the finger creates a downward force?
| The surrounding water doesn't know that it is your finger that is filling the displaced space. It thinks that there is still water present there, or, more precisely, it develops a hydrostatic pressure distribution that is the same as if water was present in the submerged space occupied by your finger. This includes the... | {
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Why does Newton's Third Law actually work? My father explained to me how rockets work and he told me that Newton's Third Law of motion worked here. I asked him why it works and he didn't answer. I have wasted over a week thinking about this problem and now I am giving up.
Can anyone explain why Newton's Third Law works... | If you imagine pushing a spring between two fingers, the spring presses in each finger the same amount. Similarly with your arm, if you push against something you are simply straightening your arm, your arm pushes you away the same as the object.
The same is true of a rocket, When the fuel explodes it pushes out in all... | {
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Do commuting Hermitian operators correspond to compatible observables? As far as I know, two compatible observables have a complete set of common eigenvectors, and using this fact, one can prove that their corresponding operators are commutative. Well now is the converse true? Do any two commutative hermitian operators... | This is known as the compatibility theorem. The statement as well as a proof can be found on Wikipedia:
Complete Set of Commuting Observables
However, as Griffiths says in his book about Quantum Mechanics (3rd chapter, the one about formalism; subsection Eigenfunctions of a hermitian operator), the fact that eigenfunct... | {
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What is the problem of having an inertia tensor not satisfying the triangle inequality? It is well known that rigid body inertia tensors are 3 by 3 positive semidefinite matrices, which is the same as saying that their eigenvalues are all non-negative.
A little less known is the fact that those eigenvalues also satisfy... | A rigid body's principal moments of inertia are obtained from these equations :
$$I_1=\int_V\,(x_2^2+x_3^2)\,\rho\,dV$$
$$I_2=\int_V\,(x_3^2+x_1^2)\,\rho\,dV$$
$$I_3=\int_V\,(x_1^2+x_2^2)\,\rho\,dV$$
where $x=x_1~,y=x_2~,z=x_3$ and the inertia tensor is:
$$I= \left[ \begin {array}{ccc} I_{{1}}&0&0\\ 0&I_{{2}}&0
\\ 0&0&... | {
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Lorentz transformation of the four velocity Can we derive the velocity addition rule by directly transforming the four velocity?
|
Instead of the well-known 1-space-dimensional Lorentz Transformation the more general 3-space-dimensional one for the configuration of above Figure (see its 3D version in the end) and with finite variables is(1)
\begin{align}
\mathbf{x}^{\boldsymbol{\prime}} & = \mathbf{x}+(\gamma_{v}-1)(\mathbf{n}\... | {
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Prove there is an equipotential sphere between two point charges Given two point charges of opposite sign I need to prove that inside the electric field they create there is an equipotential sphere.
I'm very positive that this is more geometry than anything else and I really question why I've been given this exercise.... | I guess this can be done if we use polar coordinates. In polar coordinates, the equation of a sphere looks like $R=C_0,$ where $C_0$ is a constant. Then the thing can be dealt in this way:
EDIT: $\mathbf {Z= r_0-r_1}$
| {
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Why does acceleration due resulting force depends on mass while acceleration due gravity doesn't? Objects intrinsically resist to be accelerated due to their masses. A clear example would be kicking a soccer ball vs kicking a bowling ball. The latter ball will resist much more to be accelerated than the first one due t... | Well, the thing is that the gravitational force the earth or any other body exerts on another is given by gM,
where g is the acceleration due to gravity for that body, a constant for any given body and M is the mass of the other body.
In case of the earth g* equals g and hence the Force of gravity= Mg and hence, the ... | {
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Mistake in eq. (10.7.19) Weinberg Vol I? In Weinberg Vol I, he writes in equation 10.7.19,
$$
\left\langle 0 | \phi (0) | {\mathbf{k}} \right\rangle = ( 2\pi ) ^{ - 3/2} \left( 2 \sqrt{ {\mathbf{k}} ^2 + m ^2 } \right) ^{ - 1/2} N,
\tag{10.7.19}$$
where $\phi $ is a unrenormalized scalar field, $ \left| {\mathbf{k}} \... | I think the problem is you are taking the inner product to be Lorentz Invariant. In Weinberg's convention the inner products are not Lorentz Invariante, see Eqn. 2.5.19. For a covariant normalization the $\sqrt{2E}$ factor would be absent and your argument would go through.
| {
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Does increasing the resistance in a branch of a parallel circuit decrease the overall current?
In the above question, why does R3 increase? If R2 increases, wouldn't the parallel combination's resistance increase? If so, wouldn't the circuit have less current? Then why would the voltage across R3 increase?
| The voltage on all resistors in a parallel circuit is the same, so that means that the voltages on resistors $R_2,R_3,R_4$ in this example will always be the same. Since voltage is: $$U=I*R$$
this means that if we increase resistance value of element $R_2$, the voltage $U_2$ on that element will also increase, and sinc... | {
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How to approach estimating correction size in the BK equation? I am starting to do work in theoretical physics, and as a test, the professor I am working with asked me to estimate the size of a correction to an approximate solution to the BK equation. I am no really sure how to approach this, as I first tried to plug i... | The answer is by dimensional analysis
| {
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What is the name of the principle that replaces a history functional by internal/state variables? I just need to know the correct expression:
When narrowing down constitutive equations for the mechanics solids in continuum mechanics, one has in the very general case a Cauchy stress $\mathbf{T}$ as a result of the defo... | The replacement of the whole history by some (finite dimensional) internal variables is called state space formulation.
| {
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Moment of a force about a given axis (Torque) - Scalar or vectorial? I am studying Statics and saw that:
The moment of a force about a given axis (or Torque) is defined by the equation:
$M_X = (\vec r \times \vec F) \cdot \vec x \ \ \ $ (or $\ \tau_x = (\vec r \times \vec F) \cdot \vec x \ $)
But in my Physics class I ... | There are some application, where we might want to quantify both the torque, which is a vector, and the component of the torque about a particular axis, which is a scalar.
I illustrate an example of this in the figure below, which is from 1 and provided here under fair use for the purpose of scholarship. The door is h... | {
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Special Relativity: Does non inertial frame of reference work in SR? I started on my own learning about GR and SR two months ago, and I still do not have clear if it is possible or not. The following example was explained to me by someone who affirmed: "SR applies only on inertial reference frames":
Let's imagine we ha... | There is something called The Clock Hypothesis that lets you deal with accelerated frames by assuming that you can break an accelerated frame into infinitesimal inertial frames, each of them measuring the proper time. Some authors like Goldstein in his Classical Mechanics book refer to it like an "stratagem" to deal wi... | {
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Does this Nelson formula for Feynman integral have mistakes? In this paper (Maroun's PhD dissertation, 2013) at page 46 the following formula is given (apparently without a reference):
$$\int_0^{\infty } e^{i a x^s+i b x^p} \, dx=\sum _{n=0}^{\infty } \frac{\left(i b a^{\frac{1}{s}}\right)^n \exp \left(\frac{(i \pi ) (... | Taylor series Expansion of $e^{ibx^p}$ yields
$\sum_{n=0}^\infty \frac{(ib)^n}{n!}x^{np}$.
Then you have to evaluate every term of the series by a Substitution. You can use the Substitution $u = -iax^s$ which yields $x = (i\frac{u}{a})^{1/s}$ and
$dx = e^{\frac{i \pi}{2s}}a^{-1/s}u^{1/s-1}/s$.
The integral $I_n = \in... | {
"language": "en",
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Why are light bulbs black body radiation emitters? If the definition of a black body is:
"A blackbody is an object that absorbs all of the radiation that it receives (that is, it does not reflect any light, nor does it allow any light to pass through it and out the other side). The energy that the blackbody absorbs hea... | "The energy that the blackbody absorbs heats it up, and then it will emit its own radiation." --- This part may be a bit misleading. It should read as
The energy that the blackbody abosrbs heats it up, and will be emitted as part of its own radiation.
In fact as long as all radiation is absorbed, i.e. not reflected/... | {
"language": "en",
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weight of a canister of air Consider four scenarios:
(on a typical weighing scale)
*
*Measure the weight of a canister of air filled at atm pressure
*Measure the weight of a compressed canister of air
*Measure the weight of a canister with no air inside.
*Measure the weight of an empty canister on earth with no a... | Remember that air pressure acts in basically all directions on an object. Therefore a typical weighing scale would have the same reading weighing the same object in an atmosphere and outside of an atmosphere. There is less air in scenarios 3 and 4 so those canisters should be lighter than that in scenario 1 which is in... | {
"language": "en",
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Perpetual Motion Machines If you go on YouTube, you will find a large number of machines that work for almost forever. But why do all of them stop working after some time?
Which Law (Other than Conservation of Energy) prevents a machine from running till eternity?
|
Which Law (Other than Conservation of Energy) prevents a machine from running till eternity
Why is the law of energy conservation not fulfulling for you to answer that? There is always energy conservation, and that is the sole reason that you can't draw more energy out of a machine than is put in.
That the output is ... | {
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What is the Fabric of Spacetime? I always get the analogy of the pretend sun on a piece of cloth pulling everything down such as the image attached below:
But What I never really understood is what IS that piece of cloth. Like is it some sort of invisible force field or something? Sorry if I sound a little crazy, I onl... | The "fabric" you are asking about is the speed of time. Everything moves in time, but if the speed of time is different, then the motion is no longer straight and trajectories become curved. Why do things fall down in Earth? Because time there moves slower. Tragectories are always curved to where time moves slower. So ... | {
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Newtonian limit of a perfect fluid In special relativity, with metric tensor $\eta_{\mu\nu}=\text{diag}(-c^2,1,1,1)$, take a perfect fluid stress-energy tensor : $T^{\mu\nu} = \left( \rho + \frac{p}{c^2} \right) \, U^\mu\otimes U^\nu + p \, \eta^{\mu\nu}$, where $U^\mu$ is the 4-speed, $\rho$ the volumic mass and $p$ t... | Your approximations need to be consistent. In the non-relativistic limit, it's true that we should have $v/c<<1$, but that's not all. In particular, we should require that the mass energy of the fluid be much larger than the kinetic energy of the fluid.
Alternatively, one might demand that the sound speed in the flui... | {
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Does the earth has any electric field as the earth's magnetic field is changing over time?
Earth's magnetic field changes over time because it is generated by a geodynamo
-Wikipedia
A time-varying magnetic field can produce electric field. So does the earth has electric field due to changing magnetic field?
|
A time-varying magnetic field can produce electric field.
I think this statement is unclear. Rather: A time-varying magnetic field does produce an electric field. This is one of Maxwell's equation (maybe with some prefactors)
$$\nabla \times E = - \frac{dB}{dt}$$
If the right-hand-side does not vanish, the left-hand ... | {
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Oscillations of what cause quantum waves? Electromagnetic waves are produced by oscillating electric charges. In quantum mechanics this fact is represented by photons mediating electromagnetic interactions of particles with an electric charge.
However, in quantum mechanics, any particle can be viewed as a wave. Can thi... | Photons don't mediate electromagnetic interactions, Virtual photons do. They don't really exist like physical photons, they're just in mathematical formalisms. The photons emitted by accelerating charges are described by this.
AFAIK The 'waves' of matter in QM aren't waves in the same sense, depending on your interpre... | {
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Free particle propagation amplitude (Peskin & Schroeder 2.1) In section 2.1 on p. 14 of Peskin and Schroeder QFT, they calculate the amplitude of a free non-relativistic particle to propagate from $\mathbf{x_0}$ to $\mathbf{x}$ as
$$U(t) = \left<\mathbf{x}|e^{-i\left(\mathbf{p}^2/2m\right)t}|\mathbf{x_0}\right>$$
$$ = ... | The transition from the 2nd line to the 3rd simply uses the fact that
$$\langle \mathbf{p}|\mathbf{x} \rangle = e^{-i \mathbf{p}\cdot\mathbf{x}}.$$
The exponent of the Hamiltonian merely picks up the eigenvalue $\mathbf{p}$ from the state $|\mathbf{p}\rangle$, so you can take it out of the inner product, and what you h... | {
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Average value of $\cos^2(\theta)$ in Malus' law When the Malus' law is applied to a beam of unpolarized light, I can understand that the incident light has all the possible polarizations, so that I should apply the law for all the angles.
If I had three angles $\theta_1$, $\theta_2$ and $\theta_3$, I guess the equation... | The formula which you gave in the example is wrong, and I'll shortly show you why.
Unpolarized light can be taking as a mixture of light polarized in different directions, as shown in the figure. Thus, we must find the intensity due to each individual polarized light using malus law and add them up
Assume that there a... | {
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Effect of humidity on temperature When temperature changes, relative humidity changes. Imagine I have a closed room at a certain temperature; then, I blow water vapor at a similar temperature. Can a change in relative humidity induce a (small) change in temperature? If it does, would the temperature raise or decrease?
... | The point is that air at different temperatures can hold different amounts of water (the hotter, the more water). Therefore, the relative humidity decreases when heating up air and increases when cooling it. The absolute humidity, however, stays constant in an isolated setting, because water molecules are not leaving o... | {
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Why do heavier isotopes of the same element have smaller atomic radii than lighter isotopes of the same element? I have been trying to figure out why higher-mass isotopes have higher melting and boiling points than lower-mass isotopes of the same element.
A Quora answer on this topic explored the idea that electron or... | To make it clear: I don't know the answer. However, here is how I would try to answer the why question:
*
*The nuclear radius increases with the number of nuclei. Assuming that the nucleus is a sphere, we would expect that the radius of the nucleus scales like $R_n = R_0 \cdot A^{1/3}$, where $A$ is the mass of the ... | {
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What is a potential? I am self-studying electrodynamics and am wanting to know what is meant by a potential. I understand the concept of potential energy but what is meant by a potential? Is it the same thing as a field, like gravitation or electromagnetic?
| Electric potential and electric potential energy are two different concepts but they are closely related to each other. Consider an electric charge $q_1$ at some point $P$ near charge $q_2$ (assume that the charges have opposite signs).
Now, if we release charge $q_1$ at $P$, it begins to move toward charge $q_2$ and t... | {
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Why is the Michelson-Morley experiment considered a null-result? The Michelson-Morley experiment did not seem to be a null-result. Here is what Michelson and Morey say in their 1887 paper:
the displacement to be expected was 0.4 fringe. The actual displacement was certainly less than the twentieth part of this, and pr... | You can never say that anything is zero, you can only put an upper bound on it, because the effect can always just be made to be smaller and smaller until it is indistinguishable from zero to your apparatus. Saying "The expected result was $x$, but it was no more than $x/20$" is basically saying "I couldn't measure th... | {
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How is the 4-momentum, especially the transverse momentum, in a detector calorimeter measured? assuming a jet is produced in the detector at a hadron collider. Some of the jet particles are uncharged and will only interact with the hadronic calorimeter and therefore there is no information about their momentum from the... | Just found in Tao Han's "Collider Phenomenology", that many objects such as photons and light-quark and gluon jets are assumed to be massless, and therefore the transverse energy is equal to the transverse momentum.
| {
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Does work done depend on the frame of reference? Suppose I am sitting on a bench and looking at a moving car. Force is applied on the car by its engine, and it makes it displace, hence some work is done on the car. But what if I am sitting in the car and looking at the bench? The bench covers some displacement, but who... | If the frame of reference is on the accelerating car, we have a non inertial frame of reference, so a pseudoforce (~fictious force) is born on the bench, which makes it accelerates as to the non inertial frame of reference.
| {
"language": "en",
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Orbital period and nodal precession & apsidal precession In classical orbital mechanics as per Newton/Kepler, the time taken to complete one orbit around a body of mass $M_e$ is:
$$
T = 2 \pi \cdot \sqrt { \frac {a^3} {G \cdot M_e} }
$$
But also, for orbits around an oblate spheroid, we also have precession of the orbi... | Since the period $T$ doesn't appear in either of those formulas of precession angle, I don't understand why you need a definition of $T$ (the formulas are self-consistent without $T$). In fact, we can not define period very well in some cases, since the orbit may not close on itself due to precession, which makes the m... | {
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Can we derive Einstein-Hilbert action through action principle and Levi-Civita connection? Suppose that we take principle of least action as given. Also assume that any manifold allowed by the action would carry Levi-Civita connection (torsion-free characteristic). Also assume that the local symmetry imposed on the tan... | The way to get the Einstein-Hilbert action in 4 dimensions is to take those requirements along with the following ones :
*
*The stress-energy tensor has a null divergence
*The equation of motion has at most second derivatives in the metric
With those two extra conditions, the Einstein-Hilbert action, plus a cosm... | {
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Photoelectric effect, low frequency light Let's say we have a emitter, emitting light that has frequency f, less than the threshold frequency of a metal.
If you leave light shining onto that metal, for long enough, does the energy of the individual photons accumulate, on the electrons, so eventually they will ionize, o... | Energy from photon comes in packets and these do not accumulate. The point to be noted that a single photon transfers energy to the electron.
| {
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Why is the direction of magnetic field from South to North Pole inside a magnet? Since magnetic field lines are the path taken by a hypothetical North Pole when it is in range of a magnetic field of a magnet, it is clear that the direction of hypothetical North Pole would be from North Pole to South Pole of a magnet no... | Take a large number of small magnets, all pointing in the same direction, and glue them together. You get something like:
This is a pretty good model for a typical bar magnet. The individual small magnets are individual atoms. Now place your hypothetical north pole inside this larger magnet, and you can see which way ... | {
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Gravitational lenses and two slit experiment When an image of a distant galaxy is split by a gravitational lens are the photons from the two images capable of displaying interference? This may not be possible in real conditions because of magnetic fields/polarization/intervening matter etc. but in an ideal case it is ... | There is no interference in this situation. You need coherent light for interference. The distant galaxy is not a source of coherent light. It is an extended source emitting incoherent light.
| {
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Does photon behave both wave like and particle like at the same time? As we all know, photons show dual character, but do they behave both ways at the same time? Then how do they propagate just like other particles do and combined with wave motion?
| Well, according to Heisenberg in his essay named "The physical principles of the quantum theory", the answer is more complicated that it looks. He wrote, and I agree, that our language is conditioned by our macroscopic experience. In this scale the concepts of wave and particle are perfectly defined. In the quantum wor... | {
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If electron carries negative charge, why bother looking for it's electric dipole moment? I got confused after reading about spherical electron, would there really be some type of unknown particles popping in and out of existence within the virtual particle cloud around the electron that give electron it's property? Why... | If you have two classical static electric charges and wish to compute potentials and electric field, you can approximate with multipole expansion.
Because, you can have separately charged particles. Contrast to magnetism, there is no such thing as magnetic monopole.
| {
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How the current moves in the battery and outside the battery? Does it move again to the negative terminal or stays at the positive terminal until the electrons all come .so the voltage will.be zero and current flow .I want simple clear explanation because i am confused .when I see a circuit that has two batteries one c... | Generally charge (negative) moves from anode to cathode and the chemical reaction in the battery is mediated by a salt bridge (may be different for various battery types). The salt bridge keeps the charge of the total system from separating completely and, in effect, slows down the electro-chemical reaction so that the... | {
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Continuum mechanical analogous of Maxwell stress tensor Maxwell stress tensor $\bar{\bar{\mathbf{T}}}$ in the static case can be used to determine the total force $\mathbf{f}$ acting on a system of charges contanined in the volume bounded by $S$
$$ \int_{S} \bar{\bar{\mathbf{T}}} \cdot \mathbf n \,\,d S=\mathbf{f}= \f... | The classical-physics analog of the Maxwell stress tensor is the Cauchy stress tensor. It is a linear operator that inputs a unit vector at a point and outputs the stress density vector across an infinitesimal area normal to the unit vector at that point.
| {
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Expectation value of position of eigenstate of position Consider a quantum system in an eigenstate $|x\rangle$ of the position operator $\hat{x}$, which means that $\hat{x}|x\rangle=x|x\rangle$. I hope that the expected value of $\hat{x}$ will be $x$, since the state $|x\rangle$ is the one in which the system is locat... | The formula for the expectation value $\langle A\rangle=\langle\psi|\hat{A}|\psi\rangle$ is given for the normalized states $\langle\psi|\psi\rangle=1$. You can generalize it as
\begin{equation}
\langle A\rangle=\frac{\langle\psi|\hat{A}|\psi\rangle}{\langle\psi|\psi\rangle}
\end{equation}
Of course this expression wou... | {
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What's the difference between muons and electrons in experiment? In the lecture note Track Reconstruction and Pattern Recongnition in High-Energy Physics written by Prof. Ivan Kisel, there is a figure (in page 7), which describes the different pieces of modern detectors.
He explained, Electromagnetic Calorimeter meas... | Muons can more easily penetrate more material. Typically in most detectors there is a distinguishable pattern between muons and electrons. A clear example would be data from the Super Kamiokande detector where one detects Cerenkov light coming from electrons/muons.
The "fuzzines" of the right circle means that the lig... | {
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Gravitational Deflection of light I'm looking for an expression for the deflection of light in a static gravitational field. Referring to 'deflection of star light past the sun' in Sean Carroll's "Spacetime and Geometry" - equation 7.80 for the "transverse gradient":
$$
\nabla\perp\Phi = \frac{GM}{(b^2 + x^2)^{3/2}}\v... | As far as I can understand if you want a "general solution" you have to integrate to obtain the solutions for a null geodesic. That cannot be done in general and each static gravitational field will produce a different answer.
| {
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Why does the spectrum of blue LEDs appear to have two peaks? Due to having poor distance vision and thus strong corrective lenses, I'm "blessed" with the ability to see the spectrum of a light source whenever I look at it from an angle. One thing I've particularly noticed is that blue LEDs in appliances and such seem t... | The second image is probably the same colour, but due to internal reflection of the lens (off the near face and back off the far face).
I'm sorry to say that your blessing (which I share, btw) is not limited to chromatic abberation.
| {
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Applying force on centre of mass of a body which lies outside the body The center of mass of a uniform ring lies at its geometrical center i.e.
outside the body. But we generally define center of mass as a point in which if we apply a force, the whole body will move in the same way as if the whole of the mass is assume... | If you apply a force to a point not on the body, there will be no effect, obviously.
Perhaps an important clarification on the whole center of mass thing: if for example you're dealing with gravity, you aren't saying "well it's as if there's a force $mg$ applied at the center of mass"! What you're saying instead is "it... | {
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How much time will it take to move an object whose length is equal to one light year? Suppose there's a stick whose length is one light year and I push it from one side by one centimeter. How much time would it take for its other side to move by one centimeter and why?
| The answer to this depends on the material properties of the stick. If it were a mythical "rigid body," the entire stick would move all at once, but that "rigid body" is an approximation that isn't valid in situations like this. The rigid body assumptions assume that you can transmit information about movement instan... | {
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Why are photons not involved in $\beta -$ decay? Theory of $\beta -$ emission exclusively considers participation of one $W -$ boson, one electron and one electron-antineutrino, but no photons. However Maxwell's electrodynamics require that during any change of an electromagnetic field, EM-radiation (photons) must be ... | It has been reported, predicted, and even used to place an upper bound on the neutrino mass. My background is condensed matter so I may be very wrong about these sorts of particle-physics topics: but I believe the presence of a large nucleus nearby probably breaks your expectation of pairwise emission. (Pairwise emissi... | {
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Does the density parameter alone determine the fate of the universe? According to this: http://astronomy.swin.edu.au/cosmos/D/Density+Parameter
The density parameter alone determines the fate of the universe (if its less than 1 expands forever, etc.). But according to wikipedia that's not exactly the case because of da... | The first of your two sources is incorrect. The fate of the universe depends on the total density parameter and the contribution of dark energy to that total density.
Universes can be open, closed or flat and these will occur for cases where the total density parameter is $<1$, $1$ or $>1$ respectively. However, this j... | {
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What does Enthalpy mean? What is meant by enthalpy? My professor tells me "heat content". That literally makes no sense. Heat content, to me, means internal energy. But clearly, that is not what enthalpy is, considering: $H=U+PV$ (and either way, they would not have had two words mean the same thing). Then, I understan... | A brilliant analogy by Daniel Schroeder:
*
*To summon a rabbit the magician must "build" it with all the energy it consists of. He must provide its internal energy $U$.
*But first he must push away all the air that is in the way. This requires some work, $W=pV$. In total, the energy he must spend is $U+pV$. Let's ... | {
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Does entropy decrease if time is reversed? Entropy increases if we let newton's equation work its magic.
Since newton's equation is time reversible, I would assume that in a closed isolated system, solving the differential equation and running time backwards would increase (and NOT decrease) the entropy of the system.... | Simple answer: in our universe, definitely no.
You're hitting here on an idea known as Loschmidt's Paradox[1]: given that microscopic laws are time reversible, entropy should have the same tendency to increase whether we run a system forwards or backwards in time, exactly as you understand.
The fact that this understa... | {
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How can energy of oscillators be quantised but they can still vibrate at all frequencies? In Black Body radiation, Planck's law has a postulate saying
The wall of black body contains oscillators of all possible frequencies,ν.
There is one more postulate which says
The energy of these oscillators is not continuous ... | I think the source of confusion is relative sizes of the cavity and typical wavelengths of standing waves in the cavity. In the Plank's law derivation the size of the cavity is considered to be much bigger than the wavelengths, that is why the oscillator frequency spectrum is considered to be continuous.
| {
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Do frame fields (tetrads) satisfy orthonormality vector field condition if orthogonal? Referencing https://en.wikipedia.org/wiki/Frame_fields_in_general_relativity#Relationship_with_metric_tensor.2C_in_a_coordinate_basis :
Suppose we start directly from $g^{\mu \nu}= e^{\mu}_{\ a} e^{\nu}_{\ b} \eta^{ab} \,$ (eq 1), wh... | Let $g,e,\eta$ denote the corresponding matrices. Equation is $$ g^{-1}=e\eta^{-1}e^T. $$
Invert everything here: $$ g=(e^T)^{-1}\eta e^{-1}. $$ Now express $\eta$: $$ e^Tge=\eta\Leftrightarrow e^\mu_ag_{\mu\nu}e^\nu_b=\eta_{ab}. $$ There's your ortonormality condition.
| {
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Confusion regarding gravity not being a force In high school, it was taught that formula for describing circular orbital velocity around a central body is derived by equating Newton's law of gravity with the centripetal force formula (under the logic that the inwards centeipetal force required is provided by the gravit... | You cannot longer use Newton's formalism $F = m a = -GMm/r^2$ if you introduce the fact that the geometry of space time is changed by the presence of the central body $M$.
It is true that the test mass $m$ still moves around $M$ because of gravity, but you should think of gravity not as a force any more, but as an eme... | {
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Aliens from antimatter region If we established a radio contact with an extraterrestrial civilization, assuming the signal latency permits, what question would we ask them to know if they are made of matter or anti-matter? I realize that there may not be anti-matter regions in the universe. However, my question is not ... | The question would be fairly simple. Anti-matter aliens would have nuclear physics with anti-protons and anti-neutrons. Weak interactions would produce then produce what would appear to be right handed CP violations. The question to ask is what is the parity violation in the beta decay of cobalt-60 nuclei found by by C... | {
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Quantum Mechanics and Schur's lemma Today i was studying on a textbook and i crossed a paragraph that confused me a little.
Suppose you have an algebra generated by $\hat{X}$ and $\hat{P}$ and a function $f(\hat{X},\hat{P})$ that commutes with $\hat{X}$ and $\hat{P}$. Then you can prove that this function is proportion... | Let $\psi(x)$ be any wave function, and assume $f$ can be formally expanded:$f=\sum_{km} a_{km} x^k p^m$. Then
\begin{align}
[x,f]\psi(x)&=x\left(\sum_{km} a_{km} x^k p^m\right)\psi(x)- \left(\sum_{km} a_{km} x^k p^m x\right)\psi(x)\, ,\\
&=\left(\left(\sum_{km} a_{km} x^{k} xp^m\right)- \left(\sum_k a_{km} x^k p^m x\r... | {
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Tensor in different coordinate system I have the tensors $F_{\mu\nu}$, $F^{\mu\nu}$ in coordinate system $(t,x,y,z)$ and want to transform these to coordinate system $(t',x',y',z')$ just by multiplicating matrices.
My idea was to calculate the Jacobians $J=(\frac{\partial x^i}{\partial x'^j})_{ij}$ and $J'=(\frac{\pa... | By definition, under a change in coordinate system a tensor's components transform(s)
$$F_{\mu'\nu'}=\frac{\partial x^{\mu'}}{\partial x^{\mu}}\frac{\partial x^{\nu'}}{\partial x^{\nu}}F_{\mu'\nu'}$$
So you could prove your statement by showing
$$F_{\mu'\nu'}F^{\mu'\nu'}=F_{\mu\nu}F^{\mu\nu}$$
by using the metric $\eta... | {
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QFT: Range of 'collision' If two particles approach each other, they can [provided that their properties add to those of other particle(s)] interact and go from, say, $$e + \bar e \to \gamma + \gamma$$
My question is how would one estimate the range of this? What distance is needed between $e$ and $\bar e$, is it less ... | My understanding is as follows: "in" and "out" states are fully delocalized states with exact momentum (plane waves) whose history starts at time $-\infty$ and ends in $+\infty$. Everything in between is not a state but so-called "S-matrix evolution". So: how is you question truly answered in nature? My answer: I do no... | {
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Can I achieve BEC with electrons only? Suppose I traps some free electrons using magnetic field and cool them to subzero temperature, can I get a super-electron this way? and does it violate the exclusion principle?
| No because electrons are fermions not bosons.
It is possible for fermions to form a BEC if they can pair up with spins opposed to form a bosonic particle. For example this is what happens in superconductivity and superfluid helium-3. However this requires some attractive force to bind the particles together. In superco... | {
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What is the scientific term for the photon emission caused by electrons jumping orbitals? Suppose an electron in an atom at the K-orbital is sufficiently energized (excited) that it jumps to the L-orbital. When this electron returns to its ground electronic state (it jumps back to the K-orbital), in order to respect th... | Excitation of electrons to higher orbitals give spectral absorption lines. The consequent deexcitations give spectral emission lines.
The term is spectral lines, to contrast with the continuum produced by other emissions.
| {
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What is the hydrodynamical explanation for the 'footprint' of a diving whale? When a whale dives it leaves behind a so called 'footprint'. The water seems to be calmer or the surface is at least more smooth an shows less wrinkles.
Image source
I read some text which were talking about a 'wake of the diving whale' but ... | The whale creates a vortex ring with its tail, which moves upwards and creates an oval patch of outward current on the surface: short surface waves can't propagate (well) against the current, and that's why the patch is smoother than the ocean around it.
Source: The flow induced by a mock whale : origin of flukeprint f... | {
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Torque and its origin What's the origin of the definition of torque, that is, the moment of force about the point in consideration? - (1)
Is there a proof?
Why should torque be r x F, and not r² or r³ x F for that matter? I have tried searching many books but none gave the proof as to why torque should be r x F only,... | By definition a moment in physics is the product of a physical quantity and a position. So the quantity $\vec{r}\times\vec{F}$ could by definition be considered a moment of force. The utility of this moment is found when we consider the moment of momentum, $\vec{L}=\vec{r}\times \vec{p}$ ($\vec{p}$ is momentum), also ... | {
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Calculations in the Relativity of Simultaneity Train Thought Experiment I have some confusions about proper time and the calculations involved in Einstein's famous thought experiment where two lightning strikes occur simultaneously at the ends of a train for an observer observing the train to be moving at velocity v (O... | We have two events here :
\begin{align}
&\text{event f : A light pulse from the train front}
\tag{01}\\
&\text{event b: A light pulse from the train back}
\tag{02}
\end{align}
Let these two events have the following space-time coordinates
For Observer 1:
\begin{align}
\text{event f : } &\left(x^{f}_{1},t^{f}_{1}\right)... | {
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Thoriated Tungsten filaments I have a question about doping a tungsten wire with thorium to improve the thermionic emission. I have found that the doping lowers the work function of the system, resulting in a thermionic current greater than the one produced from a pure W filament. The point is, WHY this happens? What a... | This seems to be well described here, which, in turn contains a reference to L.W. Turner,(ed), Electronics Engineer's Reference Book, 4th ed. Newnes-Butterworth, London 1976. I just might have a copy of that somewhere, but not to hand.
The mechanism agrees with what I remember being told it was: Thorium is added to th... | {
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Charged particles emiting radiation I tried to find the reason by couldn't get the right answer. I wished to know that if both proton and electron have same acceleration, do they radiate same amount/amplitude of EM radiation. Also, since quarks have electric charge, do they radiate photons along with gluons (which I ha... | Proton and electron have exactly the same charge so they would radiate the same amount of EM radiation as per Larmor Formula. Relativistic generalization of it could be calculated through Liénard–Wiechert potential, but it is still going to be independent of the mass.
Quarks are charged particles with a charges equal t... | {
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What feature of the Beryllium nucleus makes it such a good source of neutrons when hit with alpha radiation Be is often used as the neutron gun to supply neutrons to initiate nuclear reactions, particularly nuclear chain reactions. I always presumed the nucleus of lighter elements to be more stable than the heavier on... | As noted, the (sole) stable isotope of Be is $^{9}$Be, with 4 protons and 5 neutrons. $^{8}$Be spontaneously dissociates into two $\alpha$ particles since it is more favorable energetically (this was the basis for the first human-controlled nuclear reaction, $^{7}$Li(p,$\alpha$)$\alpha$ by Cockroft and Walton in 1932 w... | {
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Inducing emf in a circular coil Magnetic field lines from a moving magnet induces emf in a circular coil.What does the velocity of the magnet have to do with the emf induced?Increasing the velocity of the magnet doesn't increase the amount of field lines entering the coil right?
| According to Faraday's Law (ignoring Lenz's law, which isn't relevant here):
$$\epsilon = \frac{\Delta N\phi}{\Delta t}$$
Therefore, the EMF ($\epsilon$) is proportional to the rate of change of magnetic flux linkage ($N\phi)$. Magnetic flux ($\phi$) is just the number of field lines (imaginary lines denoting the stren... | {
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Notion of anisotropic Fermi surface I would like to check something.
I know that the Fermi energy is the maximum energy occupied by a Fermion at $T=0$ (if I have $N$ fermion it will be the energy of the Fermion that has the highest single particle energy).
I would like to check something about the anisotropy of the Fer... | Like you said, Fermi energy corresponds to the highest energy occupied by an electron at $ T = 0 $. For the free electron gas, $E = 1/(2m)\times\left(k_x^2+k_y^2+k_z^2\right)$. If you plot the momenta on the Cartesian axes, the constant energy will be a spherical shell.
Here's a more intuitive way of seeing this. Take ... | {
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How may sound waves behave inside the human body? in Vibroacoustic Therapy (VAT) sound is transferred to skin surface via transducers that are in direct contact with the skin. This means no energy loss to surrounding air. We are mostly using sinusoidal frequences between 30 Hz and 120 Hz. The different organs inside th... | sound waves of that low frequency will not be affected by the position or density or size of the internal organs. for organs to be targeted, the wavelength of the sound must be smaller than the dimensions of the organ. Note also that individual cells in the body that make up those organs are extremely small compared to... | {
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Gravity and centrifugal force Assuming the radius of Earth as $6.36\cdot10^6\:\mathrm m$. Then i get for the centrifugal force of an object with the mass of $m=10,000\:\mathrm{kg}$:
$$r\cdot\omega^2 \cdot m = 6.36\:\mathrm m \cdot \left(\frac{1}{24\cdot3600\:\mathrm s} \right)^2\cdot 10,000\:\mathrm{kg} = 8.52\:\mathrm... | The centrifugal force does have an effect on the weight of objects on the Earth.
It is about half the reason things are lighter at the equator than the poles, the other being that they are further from the center of the Earth, owing to its oblate shape (itself a result of the centrifugal force). The reason you got s... | {
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} |
Why do radio waves spread out while higher frequency waves travel in beams? Why is it that radio waves spread out in proportion to the square of the distance, while higher frequency electromagnetic waves, like microwaves, infrared waves, light, etc are able to propagate as beams? What fundamental property allows highe... | Due to diffraction, wave effects become more important as the size of the wave source becomes comparable to the length of the wave. Visible light has micrometer-scale wavelengths, so a millimeter-sized light source is thousands of wavelengths across and diffraction isn't a very big deal. But radio wavelengths can be ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/361055",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 4,
"answer_id": 0
} |
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