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.
6,106 questions
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Mathematically precise statement and proof of Maxwell relations?
This question asks about the "mathematical background" of the Maxwell relations, e.g.,
$$\left(\frac{\partial x}{\partial y}\right)_{z} \left(\frac{\partial y}{\partial z}\right)_{x} \left(\...
- 7,233
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Max height definition in projectile motions [closed]
I have recently thought about this earlier when I was solving alot of problems about projectile motions or to be specific "vertical motion due to gravity (FREE FALL)"
In some of the problems ...
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determinant of the Jacobian of a "physical" map
Let's considere a physical domain $\mathcal{D}$ of dimension $D$ (generally 2 or 3, but whatever).
In fluid mechanics for instance, one can define a mapping function $M:D\mapsto D$ that maps ...
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Moment of inertia of a part of a fractal
A physics problem that I was solving recently went as follows:
Take a square plate of side l , and remove the “middle” square (1/9 of the area). Then
remove the “middle” square from each of the ...
3
votes
1
answer
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Parameter Second Derivative of Solution to Coupled ODEs
Problem Statement
I am treating a system of ordinary differential equations (ODE) that can be written as
$$
\frac{\mathrm d\vec{x}(t)}{\mathrm dt} = A \, \vec{\theta}(\vec{x}(t), u(t), t),
$$
with ...
- 77
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Help in ensuring divergence of electric field of a cubic body in free space is zero after finding the electric field : Part 2
The background to this question is here.
In the expression:
$2 \tan^{-1} \left[ \dfrac{a-20}{c-20}. \dfrac{\sqrt{(a-20)^2+(b-20)^2}-\sqrt{(a-20)^2+(b-20)^2+(c-20)^2}}{\sqrt{(a-20)^2+(b-20)^2}-(b-20)}...
- 587
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In which sense does the 2D critical Ising lattice converge towards a conformally invariant field?
When presenting the 2D Ising model, physicists often claim that, at the critical temperature, the continuous limit of the lattice is a conformally invariant field.
However, they don't give a rigorous ...
- 843
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Given $\frac{\partial^2 F}{\partial x \partial y} \neq \frac{\partial^2 F}{\partial y \partial x}$ How to determine if $F$ is a potential function?
Given: $$F(x,y) =
\begin{cases}
xy \dfrac{x^2 - y^2}{x^2 + y^2} & \text{if } (x,y) \ne (0,0) \\
0 & \text{if } (x,y) = (0,0)
\end{cases}$$
the order 2 mixed derivatives on the Cartesian ...
- 1,109
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Deriving formula for distribution from recursive formula
I've been working on a physics model for my Extended Essay and I am troubled by it.
The gist is that there is a platform oscillating like a sine wave with very high frequency. If you drop a ball on it,...
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Are all transformations that preserve intervals of time and distance between simultaneous events necessarily affine? [closed]
I am reading Mathematical Methods of Classical Mechanics (Arnold, 2nd ed.).
On page 6 it states that galilean tranformations are affine transformations that preserve intervals of time and distance ...
- 493
3
votes
1
answer
453
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Is there a way to meaningfully choose a unique, finite average of a function whose graph matches the description in Wood’s quote?
Motivation:
In a magazine article on problems and progress in quantum field theory, Wood writes of Feynman path integrals, “No known mathematical procedure can meaningfully average an infinite number ...
- 53
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1
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Find the maximum value of k so that the cube topples at D?
The diagram shows a central cross section $CDEF$ of a uniform solid cube of weight $kW$ with edges of length $4a$. The cube rests on a rough horizontal floor. One of the vertical faces is parallel to ...
4
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1
answer
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Help in ensuring divergence of electric field of a cubic body in free space is zero after finding the electric field
MAIN OBJECTIVE : To find the electric field due to a cubic body at free space points (except few) and then ensure that the divergence of its electric field in free space is zero
GIVEN : Charge density ...
- 587
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votes
1
answer
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Final position and velocities as linear combination of forces
In exercise 2.3 in Boyd & Vandenberghe's Introduction to Applied Linear Algebra, one is asked to express the final position and velocities of a unit mass after suffering a series of piecewise ...
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Arranging 8 positive and 8 negative charges to produce $1/r^5$ potential in 3D
Short version of the problem:
Given 8 +Q charges and 8 -Q charges in 3D, can I find an arrangement in which their potential has its leading non-zero term proportional to $1/r^5$?
Step by step ...
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