# Questions tagged [homework-and-exercises]

Applies to questions of primarily educational value - not only questions that arise from actual homework assignments, but any question where it is preferable to guide the asker to the answer rather than giving it away outright. Please READ THE GUIDANCE IN META before asking homework-like questions.

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### How to apply the Faddeev-Popov method to a simple integral

Some time ago I was reviewing my knowledge on QFT and I came across the question of Faddeev-Popov ghosts. At the time I was studying thеse matters, I used the book of Faddeev and Slavnov, but the ...
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### Bottle stability optimization

A few days ago some friends and I played a game called "flunkeyball" where you need to upset a bottle with a ball. Then a question occurred: "How much water do we need to put into the bottle that its ...
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### The dual of a surface element in 4-space

In reading the classic text, "The Classical Theory of Fields", Third Edition, by Landau and Lifschitz, I found an "obvious" statement not so obvious to me. It is on p.19, the statement of the ...
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### Simple argument for unexpected behavior in SUSY model

Consider a supersymmetric theory with 3 chiral superfields, $X, \Phi_1$ and $\Phi_2,$ with canonical Kahler potential and superpotential $$W= \frac12 h_1 X\Phi_1^2 +\frac12 h_2 \Phi_2\Phi_1^2 + fX.$$ ...
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### Can spheres leaking charge be assumed to be in equilibrium?

I am struggling with the following problem (Irodov 3.3): Two small equally charged spheres, each of mass $m$, are suspended from the same point by silk threads of length $l$. The distance between ...
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### Magnetic scalar potential far above a magnetic film

The situation I am looking at is a magneto-static problem of a finite magnetic film with magnetization $\bf{M}$. I would like to find the the magnetic field far above the plate. My expectation is that ...
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### How to prove that Weyl tensor is invariant under conformal transformations?

I need to verify that the solution for vanishing Weyl tensor is conformally flat metric $g_{\mu\nu} = e^{2\varphi}\eta_{\mu\nu}$. The most convenient way to show this is to prove that Weyl tensor is ...
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### Goldstone modes and Heisenberg model

The ideia is to show that, because of Goldstone modes, 2d systems are quite different from 3d ones. So, considering the Heisenberg model, I'll post here what I'm asked to and my current thoughts on ...
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### Ray tracing in General Relativity

I would like to find out what one would see at the Schwarzschild radius of a massive non-rotating black hole, if the black hole is surrounded by a bright ring. For that, I would place the observer at ...
135 views

### Taking pivot about an accelerating point

Given this question: A small ball of mass $m$ and radius $r$ rolls without slipping on the inside surface of a fixed hemispherical bowl of radius $R>r$. What is the frequency of small ...
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### Understanding conformal mapping in electrostatics

I'm trying to understand the use of conformal mapping to solve problems in electrostatics. To better understand the idea, I'm trying to learn how to solve this example (but you can propose any other ...
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### Komar mass for rotating black hole

I am trying to calculate the Komar conserved quantities for black hole having Killing vectors. I followed the standard procedure and calculated the Komar mass for Reissner-Nordstrom black hole (plz ...
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### Why does a salt water solution have a higher coefficient of thermal expansion (i.e. expands more) than distilled water?

I have found several different sources of data which show that a solution with a higher concentration of salt has a higher coefficient of volumetric thermal expansion than a lower concentration salt ...
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### Goldstein Classical Mechanics exercise 5.17 (3ed) conceptual

I am having difficulty understanding a concept in the "Heavy symmetric top" type of problems. I will include all of my efforts as to hopefully have someone easily point out what it is that I'm missing....
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### AP physics 1 rotation problem

could someone help me with this problem? the correct answers are a and d. one issue i have with it is that i just don't understand what the problem is asking. like what spool? what table? i tried ...
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We are given $ds^2 =- \frac{du\,dv}{M - uv},$ where $$v=t+x\, \qquad u= t - x\qquad -\infty < t, x < \infty$$ and $M$ is a positive constant. The Riemann curvature tensor is proportional to $\... 0answers 206 views ### Generating function of point transformation I am asked to show that the generating function corresponding to a point transformation in Lagrangian mechanics can be taken as null. The point transformation consists of $$Q_i=Q_i(q,t),$$ and ... 0answers 139 views ### Where is wrong in the derivation about adiabatic theorem There is a homework in Quantum Mechanics which is about adiabatic theorem. Let us argue where is wrong in following derivation. $$i \partial_t |\psi(t)\rangle = H(t) |\psi (t)\rangle \tag{1}$$ if$\...
After a suitable change of coordinates, the metric for the (flat) FLRW universe becomes $$ds^2 = (1 + 2 \Phi(\vec{x},t))dt^2 - (1-2\Psi(\vec{x},t))d\vec{x}^2,$$ where  \Phi(\vec{x},t) = -\frac{1}...