All Questions
Tagged with electromagnetism mathematical-physics
34
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103
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The reason for curl free
I wonder about the reason for the idea of this, would you mind explain for me this can happen in mathematics. Thank you !
- 1
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1
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What is the correct sign for the four-vector potential gauge transform; $A_\mu\to A_\mu\pm\partial_\mu\lambda$ and where does this gauge originate? [closed]
I have three questions regarding the following extract(s), I have marked red the parts for which I do not understand for later reference. The convention followed for the Minkowski metric in these ...
- 419
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43
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Analytically solving PDEs on irregular domains in Physics
In many Physics courses you solve PDEs like heat or wave on square, circular, or spherical domains with separation of variables. Are there ways to solve PDEs and Boundary value problems on irregular ...
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Calculate Electric Field on the Z-axis from a finite charge wire
I've been trying to find the electric Field on the Z-axis from a non-uniform charge density line charge. The wire is placed on the z-axis from $z=0$ to $z=1$, $E=?$ at $z>1$ and $z<0$
$$
\rho =...
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Non-homogeneous wave equation, retarded potentials and causality
Consider the non-homogeneous wave equation in three dimensions with homogeneous initial conditions:
$$
\begin{align}
& \square f(\underline{x}, t) = g(\underline{x},t), \hspace{3mm} \underline{x} \...
- 1,179
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2
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110
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Convergence of the infinite series $\sum_{n\in\text{odd}}^{\infty}\frac{z^n}{n}$
This is a follow-up on a previous question I have asked, but since I have made some improvements, I wanted to make a new post.
I was studying 'Introduction to Electromagnetism' by David Griffiths and ...
- 289
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55
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Equilibrium position of $ n $ free charges as polynomials roots
I asked the same question on here but received no answer.
The classic problem of the electrostatic equilibrium positions of a linear system of $ n $ free unit charges between two fixed charges is well ...
- 923
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2
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239
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Examples of relativistic equations
I am posting this question here because it is just reference request and I do not need a fully detailed answer.
Attending my physics class, we introduced two relativistic equations:
$$ \frac{d}{dt}\...
user603537
2
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131
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casting electromagnetism for exterior differential calculus
I am trying to understand curved spacetime Maxwell's equations in terms of exterior differential calculus. I am surfacing this topic due to working with a flat, but non-constant metric and I am ...
- 101
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1
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871
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How do we compute Hodge duals?
The motivation for this question is to try to come up with a general expression for $(\star F)_{\mu\nu}$, the $\mu,\nu$ component of the Hodge dual of the Field strength tensor, which is of great ...
- 12.5k
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218
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Wave equation under Galilean transformation
In Jackson's book on classical electrodynamics (3rd ed, ch 11, p. 516), he mentions how a wave equation for a field $\psi(\bf{x}^{'},t^{'})$ is transformed under Galilean shift, defined as $\mathbf{x}^...
- 1,309
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Electric field with $\nabla \times \vec{E} = 0$ and $\nabla \cdot \vec{E} = 0$ outside of a conductor circulates a constant electric current
Q: suppose that I know that outside of some conductor circulates a constant electric current , I have $\nabla \times \vec{E} = 0$ and $\nabla \cdot \vec{E} = 0$. How do I prove that $\vec{E} = 0 $ ...
- 95
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Representing flux tubes as a pair of level surfaces in R^3
I am trying to see if Vector fields(I am thinking of electric and magnetic fields) without sources(divergence less) can be represented by a pair of functions f and g such that the level surfaces of ...
- 341
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2
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112
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Electric potential : numerical value for the triple Integral
The function $\phi:L\to\mathbb{R}$ where $L={\{(x,y)\in\mathbb{R}^2:x^2+y^2=4\}}$ is defined as,
\begin{align*}&\phi(x,y)=\\
&\int_{0}^{\pi}\!\!\!\!\int_{0}^{2\pi}\!\!\!\!\int_{1}^{2}\!\!\frac{...
- 992
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Can someone find $\vec{A}$ for this example [found in my TB : Griffith] with this method?
Example 10.2 of 3rd edition Griffith [electrodynamics]
click here to read this question
So I thought to convert I into $\vec{J}$ as follows :
$$\vec{J}(\vec{r},t)= I_o\theta(t)\delta(x)\delta(y)\hat{z}...
