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I came across a scenario in which a coil having a radius $r$ is placed co axially to another coil having radius $R$. They have some non zero finite distance between their centers. If some finite current is passed through the coil of radius $r$,(provided that $r<<R$) what is the magnetic flux linked with the larger coil... |
We are also given the following hint:
Equate the energies and sectorial velocities at the apogee and perigee of an elliptic orbit to express the area of the ellipse in terms of E.
For some background info:
Energy is: $E = \frac{-GMm}{2a}$ where m is the mass of satellite, M is mass of object in center, a is the semi ... |
This question came up during discussions with my friends in QM, and they asked me this question I couldn't answer.
Mathematically, the dual vector space $V^*$ of a vector space $V$ is defined as the set of linear functions $f:V\to F$.
Let us consider only Hilbert spaces now. Then, by the Riesz Representation Theorem, a... |
According to this and this, both posts describe the fact that the earth and the moon are attracting each other due to gravitation.
The gravitation force is $\frac{GMm}{r^2}$.
However, I am not able to understand why this is equal to $\frac{mv^2}{r}$, this force describes the centripetal force needed to keep an object t... |
Resistance is explained by collision of electrons with ions. In the same way could someone please explain how a battery allows electrons to flow through the circuit. I think of it as the repulsion by the negative terminal. The electrons flowing cause the constant speed. I would appreciate an answer.
|
Does the presence of the Aharonov-Bohm (AB) effect break Time-reversal symmetry (TRS) for spinless systems in a topological square lattice? As we know that TRS protects the edge states in Topological insulators. So TRS is somewhat essential to have non-trivial topological phases (always true?). Or there may be some poi... |
It is know that the symmetry operators can be applied to operators like
$$
\hat{O} \stackrel{g}{\rightarrow} \widehat{g O}
$$
demand the matrix element to be invariant under symmetry, we have
$$
\langle g \psi|\widehat{g O}| g \phi\rangle=\langle\psi|\hat{O}| \phi\rangle
$$
if the symmetry operator is unitary, we get
$... |
I have been measuring the voltage response to current of an LED. It's a point source LED with an oval emission area of 40x150um (link to datasheet https://www.daido.co.jp/en/products/point_source_led/pdf/med7p4_e.pdf). I have done the same measurements for a range of temperatures from 10°C-70°C. I expected the decrease... |
Wolfram Physics project https://www.wolframphysics.org/ demonstrates how complex structures emerge from the simple graph-like structures and rules. Graphs can be used as the microstructure, in fact - entire Wolfram universa in just graph. My question is - what math tools, structures are used for the modelling of the em... |
For the damped harmonic oscillator equation
$$\frac{d^2x}{dt^2}+\frac{c}{m}\frac{dx}{dt}+\frac{k}{m}x=0$$
we get that the general solution is
$$x(t)=Ae^{-\gamma t}e^{i\omega_d t}+Be^{-\gamma t}e^{-i\omega_d t}$$
where $\gamma = \frac{c}{2m}$ and $ \omega_d=\sqrt{\omega^2-\gamma ^2}$.Using Eulers equation, we can expan... |
So I started with the antiferromagnetic Heisenberg Hamiltonian with $J =-1 $: $H = -(-1) \sum_{NN}\sigma_i\cdot\sigma_j$.
I wrote the Pauli-matrices as their matrix-representation and got for eg. the first NN-interaction: $\sigma_x\otimes \sigma_x \otimes \mathbb{1}\otimes \mathbb{1} + \sigma_y\otimes \sigma_y \otimes ... |
In the Schrödinger equation we can see an operator associated with the position This operator is used in the expression for the kinetic energy $T$, being part of the quantum mechanical Hamiltonian.
Why isn't an operator for $V$ to be seen in the equation? $V$ being the potential energy in the Hamiltonian?
The potential... |
Given a wave-function of a single particle we can calculate probability density for positions. We can also calculate probability density for momenta. Are these probability densities assumed to be always independent?
Or, in other words, if we measure position and momentum of a particle (for example electron in hydrogen ... |
Recently, I was studying about the various different paths which we can go through in thermodynamics, and, I wish to ask how exactly we can achieve a process such as a constant temperature or constant volume process.
And, by the way, aren't all processes constant volume? because we define volume as the size of contai... |
In articles I've read, evidence of dark matter (rotation of galaxies / gravitational lensing / galaxy collisions etc) is presented at galactic scales.
Are there examples of dark matter at smaller scales than this?
One possibility I could think of, would be a misidentified 'silent' black hole vs a cold dark matter clump... |
If we take volume of a system, then it's often defined as volume of container and is an extensive property but it's often said that molar volume is an intensive property. How exactly does dividing the volume by number of moles turn an extensive property into an intensive one?
reference: 21:36 of this of this video
|
Given that we assume the force acting on a coin as well as the distance the which force acts on the coin is constant, would it be possible to determine the linear impulse on the coin with only that information?
|
The Measure Problem of eternal inflation cosmology is to determine the correct probability measure over the theoretically infinitely many individuals (or civilizations or worlds) for self-locating belief. Ultimately we want to know what credence we should we assign to being in a world with property P, according to a ... |
I remember reading in Richard Feynman's QED about this unknown physics mechanism which possibly involves information propagating instantly and it blew my mind:
The probability of photon to reflect or refract on a slide of glass depends on the thickness of the slide. Feynman said that we don't know how the photon is "aw... |
A snowball rolls from the roof of a large barn that has a downward slope of 20 °. The roof end is 15.0 m above the ground and the snowball has a speed of 6.00 m / s when abandoned from the roof. At the same moment, a man of 1.90 m tall is 12.0 m from the barn running towards it with speed v, of constant modulus. What m... |
Two pendulums of masses $m_1$ and $m_2$ ($m_1>m_2$) and strings of same length are taken. The densities of the both the bobs are the same ($d_1=d_2$), if we compare the time period of the two pendulums then:
(A) $T_1>T_2$
(B) $T_1=T_2$
(C) $T_1<T_2$
(D) Can't say
|
I'm trying to understand each of the terms in this equation intuitively
but I'm having a little trouble. I know that we can represent the equation in the following way:
$G_{\mu\nu}= \kappa T_{\mu\nu}$
where $\kappa=\cfrac{8\pi G}{c^4}$
But my question is: How can I remove the value of $\kappa$ from the equation to veri... |
In this clip we can see a model of a car-boat with a sail.
(Explicit links. Whole version: https://www.youtube.com/watch?v=zp1KzGQdouI. Parts: https://www.youtube.com/watch?v=jhem8Z9ujPE, https://www.youtube.com/watch?v=7g1Gz-62dHQ)
Facts are (for the first video):
sail is flat (thus both sides are equally long)
sail ... |
So in the Wikipedia Page of Dirac equation we are presented with this equation
$$\nabla^2 - \frac{1}{c^2}\frac{\partial^2}{\partial t^2} = \left(A \partial_x + B \partial_y + C \partial_z + \frac{i}{c}D \partial_t\right)\left(A \partial_x + B \partial_y + C \partial_z + \frac{i}{c}D \partial_t\right).$$
My question is:... |
Given our extensive use of wireless/wired technology (mobile phones, chargers, etc.), how dangerous is it to use these amidst a thunderstorm? Is it dangerous enough to consider avoiding? Is there a distinction between wireless (i.e. mobile phone) and wired (i.e. charging laptop)?
Is lightning dangerous enough for us to... |
In gravitational field, the things are usually different from those in flat spacetime. For instance, sometimes you have to use covariant derivative $\nabla$ instead of ordinary differential $\partial$, or one may find the volume element is $d^4x \sqrt{g}$, not $d^4x$, ect.
I am looking for notes/book having very detail... |
$\vec F$ = force vector,
$\vec A$ = area vector,
$P$ = pressure
Mathematically $\vec F = P \vec A$. By product rule we get,
$$
{\rm d}\vec F = P {\rm d}\vec A + \vec A {\rm d}P
$$
Why do we often compute Force over a surface as $\vec F = \int P {\rm d}\vec A$ whilst ignoring the term $\int \vec A {\rm d}P$ ?
|
Why is momentum defined as mass times velocity? I asked this question because everywhere people try to answer this by saying that $F=ma$ and if we integrate it with respect to ${\rm d}t$ we can get $p=mv$. But that's not true.
Originally, Newton put forth the second law as $F={\rm d}p/{\rm d}t$ and then using $p=mv$ we... |
There's an estimate from the recent detection of intermediate-mass black hole mergers that there are roughly $0.13^{+0.3}_{-0.11} Gpc^{-3} yr^{-1}$ similar events a year.
I'm wondering how to convert this merger rate into a number density of these intermediate-mass black holes, and preferably an estimate for the amount... |
Following my book I came to know the following expressions for the position and momentum operators ($\hat{x},\hat{p}$):
\begin{align}&\langle x|\hat{x}|\psi\rangle=x\psi(x) \ \ \ \ \ &(1)\\[1.5ex]
&\langle x|\hat{p}|\psi \rangle=-i\hbar\frac{d}{dx}\psi(x) \ \ \ \ \ &(2)\\[1.5ex]
&\langle p|\hat{x}|\psi\rangle=i\hbar\fr... |
New theories must in some approximation must reduce to older approximately correct theories.
In what approximation exactly does the angular momentum quantization condition from Schroedinger's equation reduce to that of Bohr?
According to wave mechanics,
$$L=\sqrt{\langle\hat{L}^2\rangle}=\sqrt{\ell(\ell+1)}\hbar$$
Acco... |
A rigid square of mass $M$ rests on a horizontal plane where it is free to move with no friction. Inside it lies a point mass $m$, also free to move with no friction. Assuming that the square is initially still and the particle has a velocity $v_0$ which makes an angle $\theta$ with one of the sides of the square and t... |
In this video lecture , at 39:37, The professor describes that if we do the process slowly then the system moves through a set of equilibrium states but why exactly does the speed of doing the process effect reversibility ?
For an analogy, take that video itself, if I play it at 1x or 2x speed by changing the Youtube s... |
At 43:40 of this video lecture, the instructor interprets the path along $p$-$V$ curve as cooling and I don't exactly understand how he inferred this.
It's quite obvious if you introduce in the gas law, $pV=nRT$ but the context was about general gases, so what is the general way of arguing that it would be cooling with... |
Can someone please explain to me why the following statement is true:
"Neutrino mixing phenomena arise from the noncoincidence of energy-propagation eigenstate and the weak (interaction) eigenstate bases"
This is a statement from an article about sterile neutrinos, but this particular statement is regarding neutrinos i... |
I started a new internship recently in a photonic devices company, I have a background in physics but not that much in optics (I know the basics). So there are a lot of terms that I don't understand such as "passive/active optical alignment". I searched online for lectures to get an introduction for photonic devices as... |
I'm looking for a list of explicit expressions of Wigner distributions of notable functions (e.g., Fock states, Gaussian states, thermal states, etc).
Is there a paper, book, or other online source featuring something like this?
|
What causes the Coandă effect? Here's my understanding of it:
When a fluid flows around a curved surface it has high velocity and so low pressure its pressure will be lower than the atmospheric pressure and so it will be forced to follow the curve by the higher pressure of the atmosphere.
If this above explanation is c... |
As is widely known, non-square-integrable wavefunctions don't belong to the Hilbert space, and therefore cannot represent physical states.
This is the case for e.g. oscillating wavefunctions and generally wavefunctions that do not vanish sufficiently rapidly at infinity (see however Normalizable wavefunction that does ... |
In his book on group theory, Wu-Ki Tung seems to utilize a few peculiar conventions regarding the placement of indices on vector and matrix symbols. For instance, if $|x\rangle=\sum_{i=1}^n|e_i\rangle x^i$ and $|y\rangle=\sum_{i=1}^n|e_i\rangle y^i$, he writes: $$\langle x|y\rangle=\sum_i x^\dagger_{\phantom{\dagger}i}... |
I am working through Kleppner and Kolenkow's An Introduction to Mechanics on my own and have a question about the solution of the mentioned problem.
Problem Statement: An inverted garbage can of weight $W$ is suspended in air by water from a geyser. The water shoots up from the ground with a speed of $v_0$ at a consta... |
For an adiabatic transformation between state A and B $\delta q = 0$ and consequently from the first law of thermodynamics $dU = \delta w$, since $U$ is a state function its variation should be the same whether the process is reversible or irreversible.
The possibility to go via an irreversible or irreversible path bet... |
I would like to know how to analyze the dynamics of a ball on a curved surface (lower part of a sphere), which can move in the xy plane. To be clear, the surface does not rotate, only translates. The interaction between the ball and the surface is due to gravity and normal force, and friction. My main goal it to find a... |
To maintain the current in the purely inductive circuit why is the applied alternating voltage is equal and opposite to the induced e.m.f in an inductor .
I'm unable to understand this point
Why isn't the net e.m.f of the circuit becomes zero
What is meant by to maintain the flow of current in the circuit
In what condi... |
In Zeidler's book on QFT, page 94 there is a definition for a Laplace transform that reads
\begin{equation}
(\mathcal{L} f)(\mathcal{E}) = \int_0^\infty e^{i\mathcal{E}t/\hbar}f(t) dt,
\end{equation}
where $\mathcal{E}_0=E_0-i\Gamma_0=E_0-i\hbar \gamma_0$ and $\mathcal{E}=E-i\Gamma$. Consider a model for a "truncated" ... |
I'm having some trouble in computing the spherical harmonic's expansion of a general wave function $\psi(\textbf{x})$ where $\textbf{x}$ is a vector in 3D .
The result on the article I'm working on is the following:
$$\psi_{lm}(r) = r\int d\Omega Z_{lm}(\theta,\phi)\psi(\textbf{x})$$
where $r=|\textbf{x}|$, and $Z_{lm}... |
Usually when we talk about the Michelson Morley experiment the ether wind is parallel to the light travelling path P-Mirror 1, and perpendicular to the light travelling path P-Mirror 2.
However, I want to show that the ether wind can be any arbitrary angle theta. My understanding is that the speed of light travelling ... |
To talk about this topic let's use a concrete example:
Suppose I have a one-dimensional system subjected to a linear potential, such as the hamiltonian of the system is:
$$H=\frac{\hat{p}^2}{2m}-F\hat{x}, \qquad \hat{x}=i\hbar\frac{\partial}{\partial p},$$
then I might want to find the eigenfunctions of the hamiltonian... |
On Earth, our arms feel pain if we put them upwards due to the gravitational force downwards. Is this also true when I find myself in empty space (without gravitation)?
|
The discovery of a black-hole pair with "forbidden" masses has gotten me trying to understand pair-instability supernovae. A well-crafted sentence from a recent paper gives the explanation
Population III stars above $65 M_\text{sun}$ encounter the pair instability after central carbon burning, when thermal energy cre... |
When I was learning about indeterminacy, my teacher wasn't quite clear on why the trajectories of electrons were indeterministic. He made mention of the fact that we cannot know both the position and velocity simultaneously and they are needed in order to calculate trajectories. After that, he just said something brief... |
i'm working on a paper about quantum entropy and i'm stuck on an analytical step about computing a matrix exponential.
I have the following Hamiltonian $$H=\frac{1}{2}\sum_ip_i^2+\frac{1}{2}\sum_{i,j}x_iK_{ij}x_j$$
so that i get the following wave function $$\psi_0(x_1,x_2,...,x_N)=\frac{1}{2}(\det\Omega)^{1/4}\exp(-x... |
This morning, in our little backyard, I heard an airplane that was flying above the clouds, which were completely and uniformly covering the blue sky, as if they formed one big homogeneous grey mass. The wind was sleeping. It was a deep, heavy, roaring sound that seemed to last forever and it wasn't precisely clear whe... |
Problem
I am locked in a room with no windows and I need to tell if the room is moving, I only have a lamp.
According to my professor I cannot tell if the room is moving because of the Special Relativity Theory.
My thought
What if the room moves to a speed very close to the speed of the light and I can see that the bea... |
I am currently reading Schwartz's book on QFT and the Standard Model and I'm stuck on the beginning of the proof he gives for the LSZ reduction formula. Let the initial and final states of a scattering process be
$$|i\rangle= \sqrt{2\omega_1}\sqrt{2\omega_2} \, a_{p_1}^\dagger(-\infty)a_{p_2}^\dagger(-\infty)|\Omega\ra... |
As there is the tidal force of the Moon exerted on the Ocean water I supose there must be some force acting to the Earth's atmosphere. So when the atmosphere starts falling down as the Moon is travelling away does this effect causes winds oriented away from the point that is closest to the Moon?
|
I would like to understand the mathematical content of Kochen-Specker theorem. This theorem states the following:
If the dimension of a Hilbert space $\mathcal{H}$ is $>2$ then there is no valuation $\lambda:\mathcal{B}(\mathcal{H}) \to \mathbb{C}$.
Recall that a valuation is the function with the following propertie... |
Assume the following, simple, 1D system: a particle on a spring, next to a wall, in a heat bath. Now, let's say that we implement a Monte Carlo scheme (Metropolis or other) for the position of the particle. The wall is hard, so whenever there is an attempt to pass it, the attempt will be rejected. My question is, is th... |
Is it possible to find the ground state of interacting $\phi^4$ theory with quartic interaction analytically?
|
I'm trying to understand the air flow within a melodica.
A melodica is a wind instrument that has a piano-like keyboard. Pressing on a key opens an airway so that air entering the melodica's air chamber can flow past a brass reed and exit the system. Low note reeds are bigger than high note reeds and the opening throug... |
I was wondering how the electromagnetic force would behave in a Gallilean transformation universe. Would the magnetic force be non-existent?
We know that Gallilean transformations are Lorentz transformations as $c\rightarrow \infty$. How does taking this limit affect the behavior of the electromagnetic force (i.e. Maxw... |
https://youtu.be/M8aZoM9p43k
This YouTube link shows a experiment I quickly made. Two resonant lc circuits that use magnetic fields to wirelessly light up a led. I manually found the best frequency after finding the inductance using a LCR meter. Its low frequency, so like 200kHz. No impedance matching. My two main que... |
I was reading Spivak book on mechanics, and in the first chapter he reproduces with modern day mathematics Newton's proof of proportionality between mass and weight.
He proceeds to explain the equations of motion of a simple pendulum with radius $l$.
And then he states the following: for any $\alpha > 0$ the path
$$\... |
I'm having fun learning about the physics of optical networks at a new job. It's fun connecting elementary physics learned so many years ago with how they're leveraged today in practical application.
My question is about the concept of chromatic dispersion. I've read chromatic dispersion defined thus:
[T]he differenti... |
Most lenses are spherical, but...
Are there elliptical, parabolic or hyperbolic microscope lenses?
(I asked a similar question, about telescopes, on Astronomy S.E.; I hope this is not considered 'double-posting').
|
The question is as follows:
A ball is thrown from a point $O$ towards a vertical wall in such a way that, after rebounding from the wall, it returns to $O$ without striking the ground. The ball’s initial velocity has magnitude $U$ and is at an angle $θ$ above the horizontal. When the ball strikes the wall, the horizon... |
Question:
What is the direction of the flow of electrons during an electric shock?
I was studying electrostatic force, suddenly a question struck my mind “What will be the direction of flow of electrons when I touch a live bare wire standing barefoot on the ground?” (Obviously I am not going to do that). Assuming tha... |
Refer to this image showing the temperature of a metal pipe at the inlet and the outlet:
The temperature $T(z,t)$ is a function of the length $z$ and time $t$. Let the average temperature be
$$T_\mathrm{avg}(t)=\frac{1}{2}\big(T(a,t)+T(b,t)\big).$$
Integrating the partial derivative of $T$ with respect to $t$, $\frac{... |
It seems to me that we encounter first-order equations of motion in some very special situations in physics. It is not clear to me what the connection is, and I am hoping to get some insight into what is underlying this.
I have a few examples in mind where "equations of motion" are first order in time, corresponding to... |
In the book Quantum Field Theory and the Standard Model by M. D. Schwartz, the author has used negative kinetic term in most of the Lagrangians. See equation (7.91) at page 97, for example. (Focus on the first term on the right side of equal sign.)
$${\cal L}=-\frac{1}{2}\phi\Box\phi-\frac{1}{2}m^{2}\phi^{2}+\frac{g}{3... |
According to this source, "An isochronous curve of Leibniz is a curve such that if a particle comes down along it by the pull of gravity, the vertical component of the speed is constant, when the gravitational field is supposed to be uniform."
Suppose the curve is given by $(x(t),y(t))$. I am attempting to for solve ... |
Question: The sphere of radius a was filled with positive charge at uniform density $\rho$. Then a smaller sphere of radius $\frac{a}2$ was carved out, as shown in the figure, and left empty. What are the direction and magnitude of electric field at A? At B?
How do I solve this question? The hint given for this questi... |
In hyperphysics website it's shown
$$\frac{A}{B} = 8πh\frac{\nu^3}{c^3}.$$
But in many famous textbook like Quantum Mechanics: Concepts and Applications Textbook by Nouredine Zettili the formula is written down
$$\frac{A}{B} = 8πħ\frac{ν^3}{c^3}.$$
And more surprisingly I got 2 different Questions where I had applied t... |
From this Wikipedia article:
Dark matter is a form of matter thought to account for approximately 85% of the matter in the Universe and about a quarter of its total mass-energy density or about $2.241×10^{-27}\frac {kg}{m^3}$.
Vera Rubin, Kent Ford, and Ken Freeman's work in the 1960s and 1970s provided further strong... |
Einstein's thought of a person under free-fall and when suspended in free space with no forces acting, will feel the same way.
On Walter lewin's lecture on free fall he told free fall is when only gravity force is acting on a body (Newtonian Mechanics).
How is these two thoughts connect, how both the conditions are sam... |
$\rm Spin(10)$ unifies all left-handed fermions and anti-fermions, and all right-handed fermions and anti-fermions. And its Pati-Salam subgroup unifies quarks with leptons (SU(4)) and complements SU(2)L with SU(2)R.
And $\rm Spin(10)$ includes $\rm SU(5)$'s $u_L^α\to \bar{u}_L^{\bar β}+X^{\bar γ}$ and even introduces ... |
What are the differences between using x-rays and ultrasounds for medical diagnosis?
From a physical point of view I am aware that x-rays are able to reach deeper into the material - but I think this is just a matter of power in case of ultrasounds, or? As it is for x-rays as well.
The physics behind both principles is... |
If we have such a clock and we use it to travel to a back hole and stay there for say 24 universal hours and we come back to the earth, is the passed time exactly the same on earth according to that clock?
I am trying to understand whether the time we refer to in physics is somehow related to the life/vibration/movemen... |
I think the title is pretty self explanatory: If $\psi(x, t)$ is an unknown wavefunction of a wave traveling at a known speed $v$, how does one find $\psi(x, 0)$ given $\psi(0, t)$? I know that $\psi(x, t) = f(x - vt)$.
|
Full question
Does a moving charge create a magnetic field or does a changing electric field create magnetic field or are they same? and a moving charge always creates a changing electric field?
Here is a thought experiment to show what I mean :
Imagine a conductor thats an infinite line of charge on a Z-axis in some... |
I took a picture in the mirror with a flash (and in a flash). This was the result:
After a comment made below by @SuperfastJellyfish (indeed widening occurs), I made another picture (this time in the length of the mirror, which shows orientation doesn't matter):
I'm very curious about how this pattern came to be. Dif... |
How can the speed of oscillation of a harmonic oscillator be affected if somehow it got accelerated to a relativistic speed perpendicular to its oscillation? Can this be compared with the effect on relativistic laser clock?
|
If we measure position of a quantum particle, we force its wavefunction to collapse into a wavefunction whose probability density is given by a Dirac delta function (all the probability density of position is "squeezed" into one point in space).
Immediately after the measurement the wavefunction starts to delocalise (s... |
Let us assume we live on Euclidean $\mathbb{R}^d$ and consider the normalized partition function
\begin{equation}
\begin{aligned}
Z : D &\to \mathbb{R} \\
J &\mapsto \frac{\int \exp \left[ -S \left( \psi \right) + \left \langle J, \psi \right \rangle\right] \mathcal{D} \psi}{\int \exp \left[ -S \left( \psi \right) \rig... |
So as I understand it, the mechanism for the strong force is that quarks emit/exchange gluons. Similarly, quark-anti-quark pairs are what pass between nucleons in an atom causing them to stick to each other.
But how does this cause quarks, protons and neutrons to stick? What is it about the exchange which creates the s... |
I had a doubt today (this is not my homework question, I made it up). Suppose in a LCR circuit at resonance we take out power loss as $P=VI \cos\phi$ (power factor and $\cos\phi$ becomes 1) and in another condition when there is no resonance we take out power loss as $P'= VI\cos\phi$ (and $\cos\phi = R/Z$) .....now i... |
My teacher said that velocity of separation is $V_1$- $V_2$ where $V_1$ is greater than $V_2$ and said same for velocity of approach. The problem is how would you determine which velocity is greater if the question requires you to find an unknown velocity . We can make mistakes in writing correct equations.
Hope you go... |
Before I ask my question, I want to make it clear that I am aware that the field strength is the property of the field while the acceleration of free fall is a property of a mass falling in a vacuum under gravity.
I originally thought that the acceleration of free fall is defined as the (net) acceleration of an object ... |
At 2:22 of this video , the prof. Moungi bowendi motivates the ideal gas law by saying that
$$ \lim_{ p \to 0} p \overline{V} = f(T)$$
That is if we drop pressure and see how it changes the volume, keep multiplying the two quantities and find the limit, we would find that it always converges to some constant dependent ... |
I am working out some details in a SciFi novel. I'm thinking of having spec ops who would use a device that could manipulate carbon atoms to form and maintain large, rigid, one-atom thick carbon sheets as wings. They would then be able to glide for great distances, or even fly like birds.
Situation
Let's say said spec ... |
Given the far-field vector potential...
$$\vec A_{\text{ff}}(\vec r) = \left(\frac{\mu_0I}{2\pi kr}e^{-jkr}\frac{\cos\left(\frac{\pi}{2}\cos(\theta)\right)}{\sin^2(\theta)}\right)\hat z$$
I need to find the magnetic far-field; I tried by doing the following...
$$\vec H_{\text{ff}}(\vec r) = \frac{1}{\mu_0}\boldsymbol\n... |
In the provided figure, pistons seal the top and bottom of a cylinder of cross sectional area $A$ containing solution, which is split into two chambers via a semi-permeable barrier. The initial number densities of each chamber are the same, equal to $n_0$. After a weight $W$ is added on the top piston, the bottom and ... |
In this article the Boltzmann equation for the sterile
neutrinos is simpified to this form:
$$\frac{\partial}{\partial t} f_s (p,t) -H p \frac{\partial}{\partial p} f_s (p,t) \approx \frac{\Gamma_\alpha (p) }{2} \sin ^2 2\theta \left[ 1+ \left( \frac{\Gamma_\alpha (p) l_m}{2} \right)^2\right]^{-1} [f_\alpha (p,t) - f_s... |
I know that Einstein introduced his cosmological constant assuming it as an independent parameter, something characteristic of the Universe, in itself, but the term of it in the field equations can be moved "to the other side" of equality, written as a component of the energy-tension tensor $T$ for vacuum:
$$T_{\mu\nu}... |
In Weinberg's QFT Volume 1 Chapter2, he "derives" the Lie algebra from the Lie group as follows
[...] a connected Lie group [...is a...] group of transformations ($\theta$) that are described by a finite set of real continuous parameters, say $^a$, with each element of the group connected to the identity by a path wit... |
I have seen documentaries, news, and general public reports among other things, that express the conclusion of particles like electrons super position can be at two places at the same time, but i haven't been able to find the details of the experiment and the tools used to reach to this conclusion.
My hypothesis is th... |
We have been given the initial speed of 2 particles. They have a constant speed. At any point of time $t\geq0$, their positions are given by $i+v\cdot t$ where $i$ is the initial position of the particle. So what is the condition that these 2 particles will collide?
Example: let's say position of the first particle is ... |
This is related to Taylor series for unitary operator in Weinberg and Weinberg derivation of Lie Algebra.
$\textbf{The first question}$
On page 54 of Weinberg's QFT I, he says that an element $T(\theta)$ of a connected Lie group can be represented by a unitary operator $U(T(\theta))$ acting on the physical Hilbert spa... |
If a system is in thermodynamic equilibrium then the properties of that system are uniform throughout space and time. As in, over time the properties do not show much bulk evolution. Under this definition, how is a thermodynamic reversible process possible? if a system is truly uniform throughout then it would be impo... |
How are the dimensions of a cassegrain telescope configured? In particular the distance of the secondary hyperbolic mirror from the primary mirror and also the diameter of the secondary mirror. Any equations or diagrams will be a massive help.
I also read that the back focus of the hyperbolic secondary mirror must coin... |
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