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Expanding the discussion in Thermal conductivity from the mass distribution of an object
Is it possible to have asymmetric heat flow with linear materials with temperature independent thermal resistivity? For example, in a frustum cone?
To give a numerical example, I did a simulation of a frustum cone surrounded by a h... |
Can anyone tell me if the angular momentum completeness relation is given by
$$
\sum_{l=0}^{\infty} \sum_{m=-l}^{l} (2l + 1) |l,m\rangle\langle l,m| = I
$$
or
$$
\sum_{l=0}^{\infty} \sum_{m=-l}^{l} |l,m\rangle\langle l,m| = I
$$
Because I remember the first one but I see a lot of places use the second one. Can someone ... |
Consider a two level atom where the two levels of the atom are seperated by energy $\hbar\omega_{0}$ and are coupled via the dipole interaction induced by interaction with a laser of fluctuating frequency, $\omega$. The probability distribution of this laser frequency could be given by a Lorentzian distribution:
$$P(\o... |
My question is whether there is any known method, which doesn't use calculus, to find the speed of ball C, given that the speeds of balls A and B are given at a certain moment in time. Suppose that in the figure below the triangle is equilateral, the balls have equal masses and the rods are rigid and ideal.
|
For a spacecraft travelling at 0.9 c for 5 seconds, only 5 seconds would have passed for an observer on Aircraft, while 26.31 second would pass for a stationary observer watching from Earth.
In a hypothetical scenario if a radio communication had been established between spacecraft and a stationary observer on earth, h... |
Is it:
$$
S_\mu = (I, \frac{1}{2}\vec{\sigma})\quad\text{or}\quad S_\mu = (0, \frac{1}{2}\vec{\sigma})
$$
Specifically in the "CHIRAL DYNAMICS IN NUCLEONS AND NUCLEI" Bernard,Kaiser,Meißner, commonly known as the BKM review (http://arxiv.org/abs/hep-ph/9501384v1) they state on page 142, in part A of the appendix that "... |
I've been struggling with this question.
A hemispherical bowl of inner radius $r$, density $ϕ$ and thickness $t$ is floating in a fluid of density $ρ$. The bowl is being filled with sand at a constant mass-rate $α$. What is the length of time $T$ before the bowl sinks below the surface?
The bowl is in equilibrium, I dr... |
For a general permittivity tensor, why is the imaginary part of the off-diagonal component, e.g.:
$$\epsilon_{xy}$$
equal to:
$$\frac{\epsilon_{xy} + \epsilon_{yx}^*}{2i}$$
instead of:
$$(\epsilon_{xy} + \epsilon_{xy}^*)/2i$$
|
Consider the oscillator equation
$$\ddot{x} + F(x,\dot{x}) \dot{x} + x = 0$$
where $F(x,\dot{x}) < 0$ if $r \leq a$ and $F(x,\dot{x}) > 0$ if $r \geq b$, where $r^2 = x^2 + \dot{x}^2$. What would be an example of a spring system (or other physical system) that might be modeled by such an equation? Thus far I have only ... |
I'm trying to understand how to calculate radiance ($L_{e,\nu}$), so I am using the sun/earth as a comparison as I have seen it stated that the radiance of sunlight is equal to:
$$
L_{e,\Omega} \approx 1.54\times10^7 \frac{W}{sr \cdot m^2}
$$
My understanding of radiance is:
Radiance is the radiant flux ($\Phi_e$) emi... |
I came across this problem for an exam preparation question, which I am struggling to answer.
Consider a sphere made of thin metal, with a radius of 1 m, at 20 km distance from an AM transmitter operating at 1 MHz. The alternating current in the transmitter tower flows vertically. The amplitudes of the E- and H-fields ... |
For $SU(2)$, we can contract two spin-1/2 indices and they break apart into two irreducible representation as (math notation) -
$$
2\otimes2 = 3\oplus 1
$$
that is the triplet and the singlet sector. The triplet and singlet projection operators are given as
$$
P_t = \vec{S}_1.\vec{S}_2 + \frac{3}{4}\mathbb{I}\\
P_s = -... |
When we learn about atmospheric pressure in physics class, there's this classic experiment with a straw (second drawing above). So i wanted to ask about the hydrostatic pressure in that particular experiment.
Is the total pressure at point 1' equal to Patm + ρgh ?
So is the total pressure at point 1' essentially the s... |
I understood where the expression of the entropy
$S=-k_B\sum p\log p$ comes from. Now I am trying to take this expression to its continuum limit and I want to get the form
$$S=-k_B\int\rho \log\rho$$
I imagined that we were in a 6N dimensional phase space so that I replace $p$ into $\rho \delta\Gamma$ where $\delta\Gam... |
In my Intro to Astronomy ("intro" is very important, please keep responses as simple as possible) course, we're currently learning about light and electron orbitals and such, and I came across this in the textbook about emissions spectra and element composition of the Sun:
Let us now apply what we know about spectra t... |
Wikipedia says
The effective aperture of an antenna is given by $$A_{\mathrm{e}}(\theta, \phi)=\eta A \cos \theta \cos \phi ,$$
where, $(\theta, \phi)$ are the azimuth and elevation angles relative to the array normal, $\eta$ is the radiation efficiency, $A$ is the physical aperture area of the antenna.
My confusion is... |
I'm reading the capacity chapter of Serway's book, and I had a question about the charging of a parallel plate capacitor.
Let's assume the following situation with a modification of the circuit in the figure: we connect the negative terminal of the battery and one of the capacitor plates to ground. The positive termina... |
I learned that thermal energy is just the kinetic energy of the individual particles of a substance. What if I give the ice cube kinetic energy, not by heating it, but rather by making it move very fast? Then the ice particles will gain kinetic energy because they are now moving very quickly, translationally through sp... |
I’ve been watching videos: Like this about magnetic levitation. They have a copper plate, normally quite thick, a smaller disk magnet under, and a larger disk magnet on top. Upon movement of the smaller magnet, eddy currents are induced and so the top magnet is levitated. How would the thickness of the copper plate aff... |
I'm studying Polarization, but I don't understand how i can solve the Gauss's law for vector D.
This is an example from the book. . The author chooses a surface such that the magnitude, direction, and orientation of the vector D are constant on that surface allowing them to pull D out of the integral. But how can I do ... |
In a lesson about the introduction of classical field theory it was mentioned the Klein-Gordon equation
$$(\Box + m^2) \phi(x) = 0. \tag{1}$$
But before we got this equation, we studied the Hamiltonian density that we obtained from the Lagrangian density and defined as
$$\mathcal{H}=\frac{1}{2} \left(\dot\phi^2+|\nabla... |
A candle creates an upward draft of hot air, without which the flame would be spherical. The buoyancy generated is proportional to the density difference as well as the strength of gravity.
Suppose a candle was placed on a "planet" with an Earth-like atmosphere at "sea level" but with 1000 times Earths gravity. Such an... |
It seems that alkali atoms are often used in cold atom experiments. The first BEC was formed with alkali atoms, and many modern experiments used Alkalis. What is special about having a single electron in the outer most orbital that is useful for cold atom experiments?
|
Problem
In this particular case of a dynamic skating motion combining translation and rotation, I consider the question of determining the appropriate torques and applying the correct rotational version of Newtons 2.nd law. To me this seems to involve some ambiguity which I would like to have resolved by someone capabl... |
I was reading a paper on cosmological perturbation in modified $f(R)$ gravity link https://arxiv.org/abs/0802.2999. From eqn 34 in the paper, they plot $\delta$ vs $1+z$ in figure 1. How to set the initial condition for $\dot{\delta}$ and $\delta$?
|
Wick rotation is formally described by the transformation
$$t \mapsto it.$$
In many place it is stated more rigorously as an analytic continuation into imaginary time. I understand why we do it but now how we do it. When someone says analytic continuation I think taking a function defined in some domain in $\mathbb{C}^... |
Say they both decelerate at the same rate also. If clock A sees clock B as slower than itself and clock B see clock A as slower than itself due to relativity isn't this a paradox because when they meet (as far as my understanding is concerned) they will each see the other as being slower? Obviously I am missing someth... |
So, I came across a very exciting paper on arXiv today. Here, they talk about the Hubble Space Telescope (HST) imaging of the host galaxy of the very first known quasar- 3C 273. My question is related to the 'tail' seen in the current and earlier optical images of this object.
From my understanding, synchrotron emissi... |
I know how to calculate the force applied to either or both ends of a lever system, but I would like to know how to calculate the force applied over the fulcrum of a lever.
|
I have a differential equation describing a resonator that looks like this:
$$ \frac{d\alpha(t)}{dt} = [j a - b]\alpha(t) + \sqrt b e^{jct}$$ where I can solve it putting: $$\alpha(t) = \alpha e^{jct}$$
in the above eqn. leading to:
$$\alpha = \frac{\sqrt b}{j[a-c]-b}$$
Now, I want to replace $a$ in the first eqn. with... |
For an equilateral triangle formed by 3 point masses which has a circumradius 'a' there are 4 null points: The centroid and 3 other points on the angular bisectors of the three sides.
On calculation we can find out that they are at 0.285a distance from the centroid/circumcenter.
Now if we calculate the number of gravi... |
I'm having some trouble solving an electrodynamics problem.
There is a wire inside a coaxial cylindrical conductor of radius $a$.
An alternating current $I=I_0 cos(\omega t)$ flows in the wire and returns through the outer cylindrical conductor.
We suppose both the wire and the cylyndrical conductor have infinite lengh... |
The outer product between a bra-ket $|a\rangle\langle a|$ where if $|a\rangle\in\mathcal{H}$ and $\langle a|\in\mathcal{H}_{dual}$ is a vector in the tensor vector space formed by the Hilbert space and its dual. Then it can be related to a linear operator due to the isomorphism
with the space of all endomorphism of the... |
I'm reading a paper (https://arxiv.org/abs/1507.05030) on a proposed form for the relativistic heat equation derived by optimal transport from a relativistic cost function. In particular, the paper they reference shows how the heat equation follows from the usual kinetic energy $E_\mathrm{kin}=\frac{1}{2}mv^2$ and how ... |
If a particle is subject to a constant acceleration $a$, the position of the particle after a certain time is given by the formula $s(t)=\frac{1}{2}at^2$. This immediately results in the formula $v(t)=at$ for the velocity as function of time. However, it is also possible to specify the velocity as a function of the pos... |
It all started with this question.
There are three different ways to solve this but one way is using kepler's second law. $\frac{dA}{dt}=\frac{L}{2m}.$ This applies because angular momentum is conserved about the origin since net net torque about that point is zero. So this turns into basic integration problem. $\int_... |
Let's have following scenario:
A spaceship departs from the Earth and constantly accelerates in a straight line for 60 000 000 seconds at 1g (10 m/s^2), then immediately starts decelerating at 1g for another 60 000 000 seconds, coming to a halt relative to the Earth (edit: time measured by the traveler).
When I do a "c... |
It is often written that the simulation hypothesis cannot be proven or disproved.
There is also a lot of talk about the fact that the simulation hypothesis is not science.
But the people also write that future experiments on the Planck scale will be able to prove the simulation hypothesis. Quantum space and time or qua... |
Regarding moment of inertia (MOI) of a solid cyclinder, I want to calculate the MOI through the horizontal axis (central diameter) which is the 2nd diagram in the figure:
I want to do so by using the perpendicular axis theorem.
If I assume it to be '$I_\text{horizontal axis}$' then by the perpendicular axis theorem
$$... |
I'm currently trying to solve the DE that defines charge in a circuit containing an Inductor, Capacitor, Resistor and (crucially) a Memristor. This needs to be able to work for any variable values and ends up being of the form:
$k_1 \cdot y'' + k_2 \cdot y' + k_3 \cdot yy' + k_4 \cdot y = k_5 \cdot \cos(k_6 \cdot x)$
(... |
The Quantum Regression Theorem states that if the time evolution of single-operator expectation values is known, then this determines the time evolution of higher-order correlations.Mathematically we can show that (See Carmichael 1991)
$\langle \dot{\textbf{A}}\rangle={\textbf{M}}\langle{\textbf{A}}\rangle$
where $\tex... |
In real life, we can have a pencil of length 2 cm. Can we have pencil of length $\sqrt{2}$ cm?
My answer to that was no , we cannot even make 2 cm pencil.
My argument was that when are working theoretically in mathematics we have axioms and certain assumptions. In real life we approximate things, therefore every length... |
I searched online that there is no 'neutral point' in the electric field of two charges of opposite signs, unlike the electric field of two positive charges.
However my question is when you put 2 charges of opposite signs on the x axis, is there a point where the E strength is equal to zero?
The two charges carry the s... |
In a problem I am doing, it boiled down to an integral that resulted in $$\ln(x+1\text{ m})\Big|_{x=0\text{ m}}^{x=3\text{ m}}$$
this is basically just $${\color{red}{\ln(4\text{ m}) - \ln(1\text{ m})}} = {\color{blue}{\ln\left(\frac{4\text{ m}}{1\text{ m}}\right)}} = \ln(4)$$
Obviously, when you you do use logarithm p... |
I had a question about the charging of a parallel plate capacitor. Let's assume the following situation: we connect the negative terminal of the battery and one of the capacitor plates to ground. The positive terminal connects directly to the plate as in the figure. I understand that the negative terminal and the plate... |
I would like to determine the brightness of the light source at twilight based upon its apparent magnitude.
In the question here:
What are the average wavelengths and brightnesses of sunlight across the stages of twilight?
we can find the query referring to the brightness of sunlight at different stages of twilight. In... |
Can someone please explain simply how we determine how many times we have to consider reflection and refraction to obtain final image.
Example a:
Here they only considered refraction twice to obtain final image.
Example b:
But over here, they did refraction, reflection and refraction again for final image formation.
... |
I've been trying to model some single qubit gates via Rabi oscillations for a project. In this we have some Hamiltonian (in this case it's due to an oscillating electromagnetic field) that when applied for a specific time and with the right parameters produces the desired unitary evolution of the initial state.
However... |
If two perpendicular magnetic fields(one in x-axis and one in y-axis) are interacting on a ferromagnetic material then if one of the magnetic field (x-axis)has magnetically saturated ferromagnetic material which decreases magnetic permeability of ferromagnetic material then will it also change magnetic permeability in ... |
(Newton's first law states that every object will remain at rest or in uniform motion in a straight line unless compelled to change its state by the action of an external force. This tendency to "resist" changes in a state of motion is inertia.)
How to calculate the time an motionless object will "resist" to changes wh... |
During the derivation of velocity of efflux
Bernoulli's principle is used,
$$P_A + \rho gH + \frac{1}{2}\rho V_A^2 = P_B + \rho gh+ \frac{1}{2}\rho V_B^2$$
My question is why $P_A=P_B=P_0$ = atmospheric pressure? Definitely the pressure of fluid at points $A$ and $B$ are different. Also, during derivation of Bernoulli... |
Are there any physically realistic situations described by a Schrodinger equation
$$-\frac{\hbar^2}{2m}\frac{d^2}{dx^2} \psi + V \psi = E\psi$$
where $V$ depends on $\hbar$?
I know the total energies $E$ often or always depend on $\hbar$. I'm really asking about the non-constant part of $V$.
|
According to definition group action, it is required that action of a group $G$ on a set $X$ must satisfy the compatibility condition:
\begin{equation}
g \cdot (h \cdot x) = (gh) \cdot x \text{ for any } g,h \in G \text{ and} x \in X.
\end{equation}
Now, let $G$ be a typical gauge group such as $SU(2)$ or $SU(3)$ and $... |
Imagine we are talking about electric potential (e.g. gravitational potential or electric potential or whatever, it doesn't matter), then we have:
\begin{equation}
dV = \textbf{E} \cdot d\textbf{l},
\end{equation}
where $dV$ is the infinitesimal change in the electric potential, $\textbf{E}$ is the electric field and $... |
Consider the following spectrum
This spectrum represents the evolution of the energy levels of a certain molecule in its ro-vibrational ground state as a function of the magnetic field.
Such graphs are very common in physics.
When producing such graphs, one needs to diagonalize the relevant Hamiltonian then plot its e... |
I want to understand $1/N$ contributions to quark bilinear operators $J(x)$ in large $N$, for instance, operators of the form $q\bar{q}$ or $\bar{q}\gamma^\mu q$. As pointed out by E. Witten, in the large $N$ limit leading Feynman diagrams are planar diagrams with the minimum number of quark loops. When considering qua... |
Since current can be calculated as $I = q/t$, the original definition of 1 Coulomb in SI unit system was that it is such amount of charge which flows through wire cross-section having current of $1 A$ in $1 s$ of duration, i.e. $$\tag 1 1C=1A\cdot 1s$$.
Now it is simply stated that $1 C \approx 6~241~509~074~460~762~6... |
It is very simple to show that an isolated charged particle cannot completely absorb a photon, since that would contradict the conservation of linear momentum or energy: consider a system where the charged particle of mass $m$ is at rest and a photon impinging on it with energy $E_\gamma$, the conservation of linear mo... |
For a non-interacting massive scalar field $\phi$
in an $n+1$ dimensional minkowskian spacetime,
the field commutator between two event points is
$$
[\phi(x),\phi(y)] = \int
\frac{\mathrm{d}^n p}{(2\pi)^n} \frac{1}{2\sqrt{p^2+m^2}}
\left(
\mathrm{e}^{-\mathrm{i}p\cdot(x-y)}
-\mathrm{e}^{-\mathrm{i}p\cdot(y... |
As far as I know, if one wishes to consider quark self energy diagrams inserted on external legs of a scattering amplitude, they cancel with the crossterm diagrams in the on-shell scheme. For this reason, it is not necessary to calculate these specific terms.
Can the same thing be said if one chooses to work in the MS-... |
As is well known, the photoelectric effect is an experimental phenomenon that had enormous historical importance for the emergence of the concept of photons and quantum mechanics itself. As is well known, when a light source radiates the surface of the metal (we could think of photons described by a wave function or in... |
I do computational fluid dynamics for a living. I have recently been working on a case in which I simulate the flow (assumed 2D) of a compressible gas from a large chamber at pressure $P_1$, through a small orifice which is $d$ meters wide, and then once again into a large chamber at pressure $P_2$. The physical quanti... |
The polytropic index is the index $n$ that characterizes a polytropic process, a process that obeys the relation:
$$pV^n=C.$$
I am looking for various methods for evaluating the value of this index.
I found the following formula:
$$n=\frac{ln\left( \frac{p_2}{p_1}\right)}{ln\left( \frac{p_2}{p_1}\right) - ln\left( \fra... |
The 2d Ising model has a row-to-row transfer matrix that can be written suggestively as
$$T = e^{\tau \sum_i \sigma^z_i \sigma^z_{i+1}} e^{ \lambda \tau \sum_i \sigma^x_i}$$
where $\tau$ and $\lambda$ are functions of $K_x$ and $\bar{K}_y$ (coupling in the $x$ direction and dual coupling in the $y$ direction).
$\tau$ ... |
I understand that the Quantum Heisenberg XXZ model in 1D has the form:
$$\hat H = \frac{1}{2} \sum_{j=1}^{N} (J_x \sigma_j^x \sigma_{j+1}^x + J_y \sigma_j^y \sigma_{j+1}^y + J_z \sigma_j^z \sigma_{j+1}^z + h\sigma_j^{z})$$
with the term $J_z \sigma_j^z \sigma_{j+1}^z$ disfavoring/favoring nearby aligned spins depends o... |
Let $\Lambda$ be a Lorentz transformation represented as $4 \times 4$ matrix.
Then, following What does it mean to transform as a scalar or vector? , it seems that a vector field $f : \mathbb{R}^4 \to \mathbb{R}^4$ should satisfy the transformation property
\begin{equation}
[\Lambda^\mu_\nu f^\nu](x) = f^\mu ( \Lambda... |
I've noticed that on a really tinted window, when looking from farther (and even pretty close just not touching the window), you cannot look inside, but when you put your head so close to the window, that your face is very close (almost touching), then you gain the ability to see inside the window.
I am not asking why ... |
Suppose that there are two points in an empty space A and B and observers at A and B having clocks:
If A were to be traveling near speed of light, when clock at A passes 1 hour, observer at A observes that clock at B passes more than 1 hour, say 5 hours.
If B were to be traveling near speed of light, then when clock a... |
Imagine you have a cylindrical lens of power $C$ and of angle $\theta$ relative to some neutral 0 axis.
I want to know, if you took a normal 2D image and shown it through that lens, what would the distortion look like? For example, suppose we shined a projector through that lens.
What would the equations be to distort ... |
I was looking at an info table for radionuclides, and it said that for F-18, the 511keV gamma rays have a 1st half-value layer of 7mm, and a 2nd half-value layer of around 4mm (Edit: in lead). Why is there a first and second HVL? I thought electromagnetic waves follow the Beer Lambert law (I ~ exp(-x/L)), and so no m... |
In Plasma Astrophysics, Part 1, Equation (4.7)
the dimensionless non-relativistic energy of fast particles ($m$) in a plasma with electrons ($m_e$) and protons ($m_p$) is defined as,
$$
x = \frac{m v^2}{2 k_B T} \bigg( \frac{m_e}{m} \bigg)
$$
Why is it defined like this? This is just
$$
\frac{m_e v^2 / 2}{k_B T}
$$
whi... |
Is it possible for the phenomenon of turbulence – eddys and vortices on many scales – to occur in spacetime in the context of General Relativity? For example near a Kerr black hole.
If not, what is different about the governing equations of GR, vs those of fluid dynamics, that determines this?
|
When considering interactions, the free propagator $S_0(p)$ of fermions for example gets "dressed" due to the self-energy of the fermion. The complete propagator then becomes
$$
S(p)=\frac{/\!\!\!p}{p^2-m_0^2-\Sigma(p)}
$$
where $m_0$ is the bare mass, and $\Sigma(p)$ is the self-energy of the fermion. Independently of... |
I understand that the moon causes a tidal bulge on Earth, and this tidal bulge moves slightly ahead of the moon due to Earth's rotation.
When reading about why the moon is moving away from the Earth, the most common explanation given is that the tidal bulge slows Earth's rotation and the moon must speed up due to the c... |
When I think of white light, I'm imagining a combination of all 7 colors of light but I believe that since light has wave nature I can say that at some point that the probability density of red light is more than that of violet light and vice versa right? My doubt is that since both have different probability densities... |
We have a liquid at $X^{\circ}$ Celsius , we want to convert it to $Y^{\circ}$ Celsius gas
1: $X^{\circ}$ Celsius liquid absorb latent heat of vaporisation, turn into $X^{\circ}$ Celsius gas, and then absorb specific heat capacity to turn into $Y^{\circ}$ Celsius gas
2: $X^{\circ}$ Celsius liquid absorb specific heat c... |
Refrence:- If there is a weight force $Mg$ on a box of area $A$ then pressure on box will be $Mg/A$. In another case box is on ground in equilibrium, so there will be two equal and opposite forces on box. In that case pressure would be 2Mg/A. Similarly in a container of height 'H' and area '1 m² which is full of fluid ... |
Physicists struggling to explain too-fast spinning galaxies with standard models of gravity is weird to me.
If we can accept that normal physics don't apply on a quantum level why shouldn't the same not be a thing on an astronomical level?
|
Question:
Someone is washing their car, using a nozzle similar to the one sketched in the figure. The nozzle is 9.91 cm long, with an inlet diameter of 1.07 cm and an outlet diameter of 0.460 cm. The volume flow rate through the garden hose (and through the nozzle) is V = 0.0530 L/s, and the flow is steady. Estimate th... |
Hi I was wondering about the following setup. Let’s say we have a radioactive atom which decays via beta decay which produces a $W$ boson. The $W$ boson has a chance of turning into an electron or a muon or other particles. However let’s say that the atom is surrounding by a barrier on all sides such that the radius of... |
Let's say a block is moving on a rough ground with a velocity v and it is not rotating. I understand that about the centre of mass (C), for rotational equilibrium, the torque produced due to friction is balanced by the torque produced by the normal hence the block doesn't rotate.
However My doubt is that since the bloc... |
Suppose there's a Magnetic field in vertical direction and we hold and release a superconductor cube so experimentally it is seen that the cube floats/hovers in the same orientation as it was released but how can we prove it on paper by calculating the force on surface currents?
And if we release a rotating ball superc... |
Following Warren Siegel's book on Field theory (pg. 223), one might derive the action of Lorentz generators $S_{ab}$ on an antisymmetric 2-tensor field strength $F_{cd}$ which arises for example in Maxwell field theory.
$$(S_{ab} F)^{cd}=\delta_{[a}{}^{[c}F_{b]}{}^{d]}$$
Now, using a generic free field equation $$(S_a^... |
I am trying to find the the equation earth's orbit using Kepler's Scheme. After every 1.88 years Mars returns to its initial position in the sky.
With reference to the diagram and data below find the equation for the orbit of the earth taking average earth-sun distance as 1.
Data:
$$\begin{array}{c|c|c|}
& \text{D... |
In equation 4.1.4 Wald describes the metric in pre-relativistic physics as,
$$h_{ab} = \sum_{\mu, \nu} h_{\mu\nu}(\mathrm{d}x^{\mu})_a (\mathrm{d}x^{\nu})_b\tag{4.1.4}$$
with $h_{\mu\nu} = \mathrm{diag}(1,1,1)$.
My confusion is to what exactly is meant by $(\mathrm{d}x^{\mu})_a$ here?
|
My search for a book with extremely hard physics problems(conceptual or a problem to solve) had led me to a couple books like "Pathfinder for Olympiad and JEE (Advanced) Physics", "I.E Irodov", "S.S Krotov" and the "200 Puzzling Problems in Physics" series over the past couple months and other books that I had seen on ... |
There is something about output power of battery in circuits that bothering me.
I hope you help me.
So we know the formula for power in electrical circuits is (current x voltage) or:
$$
P=IV
$$
and the voltage of a battery while there is a current running through it is:
$$
V = \varepsilon - Ir
$$
where $\varepsilon$ is... |
One statement of the Clausius inequality is
$$dS \geq \frac{\delta q}{T}$$
where $\delta q$ is the exchanged heat. My understanding is that $T$ refers to the temperature of the surroundings rather than the temperature of the system itself. This is because when deriving the Clausius inequality, we use
$$dS = dS_\text{pr... |
Let $\phi_1$ and $\phi_2$ be quantum field operators of certain spin on $\mathbb{R}^4$. Then, the principle of locality dictates that if $x$ and $y$ are space-like separated, we have
\begin{equation}
\phi_1(x) \phi_2(y)=\phi_2(y) \phi_1(x) \text{ if at least one of } \phi_1, \phi_2 \text{ is Bosonic}
\end{equation}
or
... |
The dependence of the electric potential can be obtained from Poisson equation and in one dimension is,
$$
\nabla^2 V(x)=-\frac{\partial \mathrm{E}}{\partial x}=-\frac{\rho(x)}{\epsilon \epsilon_0},
$$
where $\nabla^2$ is the Laplace operator, $V$ is the voltage, $E$ is the electric field, $\rho$ is the charge density,... |
Consider the following Green function:
$$G_{2}(x,t,x',t') = \langle \Omega_{0}, e^{itH_{0}}a_{x}e^{-itH_{0}}e^{it' H_{0}}a_{x'}^{*}e^{-it' H_{0}}\Omega_{0}\rangle$$
for $t' > t$. Here, $a_{x}^{*}$ and $a_{x}$ ($x \in \mathbb{R}^{3}$) denote the creation and annihilation operators on a fermionic Fock space and $\Omega_{... |
Considering two (significantly large) containers with equal volumes, one thin and tall, the other wide and short, both filled with water. If pipes with identical cross-sectional areas are used to empty them simultaneously, which container will empty faster? Or will they empty at the same time? Is pressure a factor?
|
Is it right to assume that in 4-dimensional spacetime the speed of any object is constant?
I mean a stationary object travels straight to the future but any spatial movement simply means that the direction of the speed vector doesn't point straight to the future. Because that's how I roughly understand what happens wit... |
I have determined a quadrupole tensor for a hollow sphere with radius $R$ and charge density $\rho(\theta)$. The tensor has the following form:$$Q=\left(\begin{array}{ccc}Q_{11} & 0 & 0 \\ 0 & Q_{11} & 0 \\ 0 & 0 & -2 Q_{11}\end{array}\right)$$ Why are only the diagonal elements non-zero? I have found this through calc... |
First assume there is no beam splitter. An apparatus emits (unmeasured electromagnetic waves corresponding to) single photons. It is directed towards a measurement device, suited to measure practically all the photons heading its way.
Then, instead, assume there is a beam splitter, and two measurement devices, similar ... |
In particle physics, it is usually no problem to determine the momentum of a charged particle such as electron, by using something like a pixel detector. This relies on ionization. There is also accompanying energy loss. This measurement is only approximate.
Question1: how do we measure the momentum of a very slow movi... |
Suppose, I have 20 data for the velocity components Vx, Vy and Vz with 5 minutes interval of time, how to find the angular frequency and wave vector using minimum variance method for those data? What is the Physics/Mathematics behind that? Thanks!
What else method we can follow to find the angular frequency and wave ve... |
I have a simple question: you can think of a charged particle as a particle with mass, and hence there will be an electric field surrounding the charge, which causes electric potential energy (if there is a charged particle within its field). However, how does this work within a circuit? How can a battery have electric... |
I'm writing a code to calculate the maximum optimal angle for motion under linear drag and how it's affected by mass. It appears that for the most part this angle is independent of mass and not of initial velocity, which makes sense to me. However, i found that when i put very small masses into my range <1E-7 kg, the a... |
My question involves sample problem 9-8 of the book "Physics" by Halliday, Resnick and Krane, 5th edition. So I could understand the answer given but there is something that is not explicitly explained that I'm having some trouble understanding or at least I don't think it was clearly explained.
But first some backgrou... |
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