Questions tagged [electromagnetism]
For questions on Classical Electromagnetism from a mathematical standpoint. This tag should not be the sole tag on a question.
407
questions
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A calculus problem from electrostatics
Since this problem consists of multiple parts and one needs to see all of them to understand the problem i'm going to list out all of them:
Consider a uniformly charged spherical shell of radius $R$ ...
- 429
6
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1
answer
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What is the value of $\frac{1}{2}\int_B\int_B\frac{\rho(x,y,z)\rho(x',y',z')}{4\pi\epsilon_0\sqrt{(x-x')^2+(y-y')^2+(z-z')^2}}dxdydzdx'dy'dz'$?
I am reading a book about electromagnetism by Yousuke Nagaoka.
Suppose $R$ is a positive real number.
Suppose $Q$ is a positive real number.
Let $B:=\{(x,y,z)\in\mathbb{R}^3:\sqrt{x^2+y^2+z^2}\leq R\}...
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0
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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:
$$
\begin{align}
& \square f(\underline{x}, t) = g(\underline{x},t), \hspace{3mm} \underline{x} \...
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votes
1
answer
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Linear system $Ax=y$ with partially known $x,y$ and non singular $A$
PHYSICAL INTUITION
While proving the equivalence between the Dirichlet problem (i.e. the potential is known on the surface of every conductor) and the mixed problem (i.e. the potential is known on ...
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0
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1
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Why does $\boldsymbol{\nabla} \times \textbf{E}=\textbf{0}$ imply $\boldsymbol{E_2}^{\parallel}=\boldsymbol{E_1}^{\parallel}$?
I am currently studying 'Introduction to Electromagnetism' by David Griffiths, and I was reading about the electric displacement $\boldsymbol{D}$. I decided to try to extract eq. 4.27, which states:
$\...
- 289
0
votes
2
answers
110
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Convergence of the infinite series $\sum_{n\in\text{odd}}^{\infty}\frac{z^n}{n}$
This is a follow-up on a previous question I have asked, but since I have made some improvements, I wanted to make a new post.
I was studying 'Introduction to Electromagnetism' by David Griffiths and ...
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2
votes
0
answers
67
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Evaluation of Fourier series $\sum_{n=1,3,5...} \left[\frac{1}{n}\text{e}^{-\frac{n \pi x}{a}} \text{sin}(\frac{n \pi y}{a}) \right]$
I was studying electromagnetism and followed 'Introduction to Electromagnetism' by David Griffiths. During his derivation of the solution to Laplace's equation in ch. 3.3, he derives the equation $$V(...
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1
vote
1
answer
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Evaluating an Integral with a Dot Product
Lets say I have
$\int{ \overrightarrow{B} \cdot\ \overrightarrow{dA} }$
is that equal to
$ \int{ B \cdot dA } \cdot\cos(\theta)$
or
$\int{(B \cdot\cos(\theta)) \cdot dA} $
For example: a ...
- 113
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0
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Finding the change of basis matrix for a type (0,1) tensor
I am considering a tensor (in particular, the electric field), defined by
$$E_m = g_{ij}^k c_{k\ell}^{ij}S_{\ell m} $$
Ultimately, this means that the tensor E is a rank 1, type (0,1) tensor, ...
6
votes
1
answer
162
views
Effective resistance in finite grid of resistors
Consider a $m\times n$ grid of one-Ohm resistors. What is the effective resistance of any given edge? I understand how to do the case $m=2$ inductively using the series and parallel laws, but I get ...
- 1,147
0
votes
0
answers
46
views
How do scalars like currrent or amplitude add vectorially and give correct results?
I have seen in alternating current that values of current and potential difference in different circuits like LR, CR or LCR circuits are found by adding them like vectors.
It also happens with ...
- 471
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vote
0
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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
2
votes
2
answers
251
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Why can't math software solve the integral $\int\limits_{-a/2}^{a/2}\int\limits_{-a/2}^{a/2}\frac{1}{\sqrt{x^2+y^2+z^2}}dxdy$?
Consider the task of finding the electric field at a height $z$ above the center of a square sheet of side a carrying uniform charge $\sigma$.
I am asking this in the math stack exchange because ...
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1
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1
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Absorbing constants when determining them through boundary conditions
I am working through example $3.3$ in Griffiths Electrodynamics in section $3.3$ on Separation of Variables. The example involves solving the $2$-dimensional version of Laplace's Equation for the ...
- 2,220
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0
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Lorenz condition and uncoupling pde - general name for techniques of pde uncoupling
I'm reading Jackson's Electrodynamics chapter 6.2.
It is possible to reduce Maxwell's equations to
$\nabla^2 \phi + \frac{\partial}{\partial t} (\nabla \cdot A) = - \frac{\rho}{\epsilon_0}$ (6.10)
$\...
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