Questions tagged [physics]
Questions on the mathematics required to solve problems in physics. For questions from the field of mathematical physics use (mathematical-physics) tag instead.
6,141 questions
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Energy of a torus vortex at $R/r =\sqrt2$ in an incompressible inviscid fluid
I'm looking for the total hydrodynamic energy of a steady vortex torus in an unbounded, incompressible, inviscid 3D fluid, where the ratio of major radius $R$ to minor (tube) radius $r$ is exactly $\...
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How to prove that $\sum_j \delta_{ij} \cdot \delta_{jk} = \delta_{ik} $ [duplicate]
My Mathematical Methods in Physics course has just begun, and we have been introduced to functions such as the Kronecker-Delta and Levi-Civita symbols.
We were assigned a problem asking us to prove ...
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Analytic proof of value of integral arising in electrostatics
The following triple integral arises in electrostatics, when trying to find the electric flux of a uniformly charged hemispherical shell through its flat circular base:
$$
I = \int_{x=0}^1 \int_{\...
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Purely mathematical solution to a physics question: finding the period of a particle moving in uniform circular motion. [closed]
This will seem like a primitive and rather uninteresting conclusion, but I was messing around with questions in James Stewart's Multivariable Calculus 5e. Particularly Chapter 14, Problems Plus 1(b):
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Newtons second law with NSA - why is this logical inference illegal when applying Newtons second law to infinitesimal elements?
I am thinking about some physics applications of nonstandard analysis (NSA). In particular, I am considering what happens to a weak version of Newtons second law as we try to apply the Newtonian ...
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Why is the jerk equal to the velocity in orbital mechanics?
In Sec. 1.4.2 of BWE, item 3 gives the cross product. The second term should be
$\mathbf{r\times \dddot{r}}$ (which I learned is called the jerk) and then it is equal to $\mathbf{r\times \dot{r}}$. ...
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How does the delta-function identity work when defining retarded time in Liénard–Wiechert potentials?
In the derivation of the Lienard-Weichert electric potential, I am up to the point where we have
$$
\Phi(\mathbf{r},t)=\frac{q}{4\pi\epsilon_0}\int\frac{\delta(t'-t_R)dt'}{|\mathbf{r}-\mathbf{w}(t')|},...
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Using nonstandard analysis to solve fluid dynamics physics problem
I am currently taking a course in fluid dynamics and was wondering if one might apply non-standard analysis to prove a certain result. I will try to provide all necessary prerequisite knowledge such ...
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Why is there little mathematical research in Nuclear Physics? [closed]
Mathematics and Physics have always been very close.
Even though everyone has a different definition of what Mathematical Physics (or even Physical Mathematics, whatever that means) really studies, we ...
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"Portals" in $\mathbb{C}$: branch cuts that translate function arguments
First some background and motivation.
I recently came across a YouTube video where the creator tried to calculate the effects of portals on the gravitational field (although electrostatics should work ...
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Definition for plane wave equations term
I am working on Exercise 3.4 from a book by Douglas Abraham which is given in the scan below, and a wave equation type problem. I have a result but I believe I am not sure what a term means, namely $\...
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Counting sign factors in the Majorana condition without choosing a gamma-matrix representation
I am considering Majorana spinors. My aim is to develop an explanation of spinor theory without using any specific representation of the gamma matrices. I present my setup and the problem below.
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First variational formula for non volume forms.
Setup
In field theory, one usually is given a Lagrangian volume form which depends on some fields (and finitely many of their derivatives) which are differential forms. The equations of motion of such ...
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Confusion about contour integration of a single pole in time ordered Green's function.
I am trying to integrate the following term with contour integration
\begin{align*}
\int_{-\infty}^\infty dk\int_{-\infty}^\infty d\omega \frac{1}{k}\frac{\cos(kx-\omega t)}{\omega+vk-\text{sgn}(k)i\...
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Understanding distributions in "An Introduction to Quantum Field Theory" by George Sterman
I am doing some work in quantum field theory, and am working my way through Chapter 14 of Sterman's An Introduction to Quantum Field Theory. On the following pages:
a "distribution" is ...
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