# All Questions

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### Link between photon helicity and polarization of $A^\mu$ electromagnetic potential

From Wigner theorem we know that the irreducible unitary representation of the Poincarè group for massless and spin 1 particle is labelled by the momentum $p_\mu$ and the two possible helicity $+1,-1$ ...
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1 vote
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### Larmor frequency in NMR for nucleus with spin greater than 1/2

I'm reading the theory about NMR and in most textbooks I can see that the Larmor frequency achived as follow: on the one hand from QM we know that $$\Delta E = \hbar \omega$$ on the other hand, if ...
• 555
44 views

### Do conductors have bound charges?

In Griffiths, the total charge density of a dielectric is: $\rho$ =$\rho_b +\rho_f$. I have several questions: Can the total charge density of a conductor be written as the equation above? Do the ...
1 vote
33 views

### Vertical Circular Motion ($u$ minimum)

In vertical circular motion, when we consider motion of a pendulum bob, while finding minimum velocity to complete VCM, we take Tension=0 at highest point and velocity at highest point is not equal to ...
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### $i\epsilon$ prescription for finite systems [closed]

What is physical interpretation of path integral for finite time and finite epsilon (i.e without taking limits time->+-inf, epsilon->0)? Does it mean you are doing some finite temperature qft ...
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### How to derive Smarr formula for Kerr Black Hole?

Following is the Smarr formula for Kerr Black Hole $$M=\frac{\kappa A}{4\pi}+2 \Omega J$$ where $\kappa, \Omega$, $J$ and $A$ are surface gravity, angular velocity, angular momentum and surface area ...
17 views

### Granular Material Piles on an Inclined Plane

Consider a conical pile of sand (or any other granular material) that is placed on a flat surface. This conical pile has a given radius and height (r and h, respectively). What would the effect be on ...
• 1
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### Ampere's law on solenoid, using a circular loop

Suppose we take a long and tightly wound solenoid with current I going in it. We can find the field inside, by ampere's law, taking a rectangular loop and assuming the magnetic field just outside the ...
• 428
19 views

### Need help with SMRs and nuclear reactors [closed]

I'm writing my IB extended essay on SMRs and how they might be useful for energy generation in Singapore but I don't quite understand a couple things. How do their passive safety systems work and ...
14 views

### Bayesian distribution for the rotated qubit example

If say we consider a spin-up qubit having undergone some Pauli-Y rotation $\theta \in [0, \pi]$, and further consider discretizing the rotation range $[0, \pi]$ such that $\theta_j \in [0, \pi]$ where ...
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### Different coupling to different kinds of sources?

Context: 1+1 dimensional scalar field coupled to a background electromagnetic field generated by two charges, q and -q situated at the points 0, a, respectively. This article studies the effect of the ...
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1 vote
28 views

### On time arrow and coordinate change in General relativity

This may be a silly question but I would like to have things cleared up once and for all in my head. I will take the example of a Schwarzschild black hole as a solution to vacuum Einstein Field ...
• 2,593
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### Physical meaning of symmetric and antisymmetric wavefunction

On describing Bosons and Fermions, the symmetry of wavefunction is introduced first. Here, If two particles a and b, are in two states n and k respectively, we get the wavefunction individually. On ...
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1 vote
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### Conservation of linear vs. angular momentum in two similar cases

I have a question that eludes my understanding: Imagine we have a bullet of mass $m$ and a rigid pendulum with a bob of mass $M$ hanging from a rigid rod of negligible mass hanging from the ceiling ...
12 views

### Two cylinders rolling without slipping on planks

I am struggling with the following setup. This setup consists of three massless planks and two massive cylinders, as can be seen from the figure. The lower plank is pulled with a force $F$ that ...
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1 vote
45 views

### Lagrangian of a multi-dimensional scalar field

We know that the Lagrangian has to be a scalar. Would it be possible if this scalar is multi-dimensional (for example $m\times m$)? Let's say a field $\phi$ is represented with an $m\times m$ matrix ...
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1 vote
20 views

### Thermal flunctuations of density in thermal equlibrium? [closed]

According to physics a fluid or gas in thermal equilibrium is not exactly homogeneous. Locally its density undergoes random fluctuations which are small compared to the corresponding equilibrium value....
44 views

### Are there any experiments that examine Hamilton's Principle directly?

Or can it be examined? I 'd glad if you can share some ideas about "principles" in general.
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1 vote
61 views

### Necessity of Singularity in General Relativity

The Schwarzschild solution is the standard example used to describe a black hole, its important points being the event horizon and the central singularity. But this solution is derived by assuming an ...
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### A Force Perpendicular to the Velocity changes only the direction of motion?

Why does a force that remains perpendicular to velocity alaways only change the direction of the motion(circular) and not induce a velocity in the perpendicular direction???
51 views

### How to understand gyroscopes by using vectors?

I’ve seen plenty of videos explaining how gyroscopes work, but almost non of them why they are constrained to work in such way. From seeing only angular momentum vectors, how could one predict ...
25 views

### Is the energy spectrum of molecules of an ideal gas at equilibrium in an isolated system the Maxwell-Boltzmann distribution? [closed]

The energy spectrum of an ideal gas at equilibrium in a closed system at thermal equilibrium with its surroundings is described by the Maxwell-Boltzmann distribution. If the system is then isolated ...
1 vote
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### How quickly can you reduce temperature of content in a jar by running cold water over it? [closed]

If I have a glass jar with a metal lid that contains 24floz of water @ 70F and I continuously run 45F water over the top of the closed jar, how long will it take for the 24fl oz to reach 45F?
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### Does detailed balance apply if electrons and ions have different temperatures

Suppose I have a plasma where the ion temperature $T_i$ is different from the electron temperature $T_e$. Does detailed balance still exist between recombination and ionization?
341 views

### Jellium Hamiltonian in the thermodynamic limit

In Fundamentals of Many-body Physics by W. Nolting, 1e, the author arrives at the following formula for the electron-electron contribution to the Hamiltonian of Jellium:  \hat{\mathcal{H}}_{ee}=\...
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1 vote
62 views

### Discovery of a Formula for Geostationary Orbit Distance: Seeking Expert Feedback [closed]

I’m an amateur enthusiast without a formal academic background in mathematics or science. Recently, I stumbled upon an idea and derived a formula that I believe calculates the distance traveled along ...
26 views

### Energy in Dielectric Medium as a Sea of Dipoles

Simply, why is the energy density in a dielectric medium = $\frac{1}{2}K\epsilon_oE^2$ where K is the dielectric constant of the dielectric medium? Working proof Consider a capacitor that is charged ...
81 views

### The usage of temperature in quantum mechanics

This is a follow up question for my previous question, because now I am more confused than I was before. In a regular quantum mechanics course, temperature plays no role as it does not appear in the ...
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### The total horizontal distance traveled by a bouncing ball nudged off a table of height $H$ [closed]

Suppose a ball gently rolls off a flat surface of height $H$ and free falls to the ground subject only to the law of gravity. Once the ball hits the ground, it rebounds as shown in the figure. When ...
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### How to count simple resistor circuit configurations? [closed]

Really stumped by this one (I'm not an EE!). Suppose we are given 1, 2, 3, 4, 5, and 6 one-ohm resistors. They can be arranged in series, parallel, bridge, and so forth circuits. No dangling resistors ...