All Questions
Tagged with electromagnetism fourier-transform
8
questions
1
vote
0
answers
25
views
2d Fourier Transform Using Weyl Expansion
If we have electric field as
$$
\mathbf{E}\left(\mathbf{r}_{\mathrm{d}}, t\right)=\frac{1}{\varepsilon} \int_{\mathcal{V}} d \mathbf{r}^{\prime} \mathbf{K}\left(\mathbf{r}_{\mathrm{d}}-\mathbf{r}^{\...
- 11
1
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0
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59
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Existence conditions for integral transforms
Let's take the Fourier transform of Faraday's law of induction
$$ \nabla \times E = - \partial_t B $$
$$ \mathcal{F}[\nabla \times E]\ = \mathcal{F}[- \partial_t B] $$
$$ \nabla \times \mathcal{F}[E]\ ...
- 613
10
votes
2
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4k
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Applying the Fourier transform to Maxwell's equations
I have the following Maxwell's equations:
$$\nabla \times \mathbf{h} = \mathbf{j} + \epsilon_0 \dfrac{\partial{\mathbf{e}}}{\partial{t}} + \dfrac{\partial{\mathbf{p}}}{\partial{t}},$$
$$\nabla \...
- 4,322
3
votes
1
answer
59
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Question on differential equations with $\delta(x)$
In a course of Electrodynamics I came across a function for electric susceptibility $\chi(\tau)$ given by:
$$\frac{d^2\chi}{d\tau^2}+\gamma \frac{d\chi}{d\tau}+\omega_0^2\chi=\omega_p^2\delta(\tau)$$
...
- 181
2
votes
0
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257
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What is the relation between 2d Fourier Transform and Plane Waves? [closed]
I'm not understanding how the two was related, but I was told that the 2d Fourier Transform decomposes an electromagnetic signal into plane waves. This, however, I am not understanding. I thought it ...
- 3,405
3
votes
0
answers
130
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Radial fourier transform of gaussians
In this paper is calculated the square modulus of the radial fourier transform of the function $\rho(r)$
$$\left|F(q)\right|^2=\left| \int_{\mathbb{R}^3} e^{i\mathbf{q}\cdot\mathbf{r}}\rho(\mathbf{r})...
- 275
0
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1
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60
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Link of Wave equation to Helmhotz equation
$\nabla^{2}\mathbf{E}-\frac{1}{c^{2}}\mathbf{E}_{tt}=0 \tag{1}$
is equivalent to Helmhotz equation by the Fourier transformation i.e.
$\tilde{E}_{zz}(z,w)+\epsilon(w)\frac{w^{2}}{c^{2}}\tilde{E}(z,...
1
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0
answers
100
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Convolution type integral with two variables
Is there some canonical way to approach integrals of type
$$
I(k,q) = \int {\rm d}^{3} s~ e^{i k \cdot s}
f\left(|s|\right)g\left(|q-s|^2\right),
$$
where $s$, $k$ and $q$ are momentum vectors, and ...
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