All Questions
Tagged with electromagnetism greens-function
10
questions
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Fourier decomposition of functions that have blowups at the origin
I had a question about the following. Consider the function $\frac{i}{4}H_{0}^{(1)}(\tilde{k}\rho)$ where $H_{n}^{(1)}$ is the Hankel function of the first kind of order $n.$ For context, it is a ...
- 131
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75
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Non-vanishing bondary terms of the inhomogenous wave equation
I'm trying to follow a derivation of the solution to the inhomogeneous wave equation
$$
\bigg[ \nabla^2 - \frac{1}{c^2} \frac{\partial^2}{\partial t^2} \bigg] \psi(\vec{r},t) = - f(\vec{r},t),
$$
...
- 165
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Integrate $\frac{ e^{i k | \mathbf{r} - \mathbf{r'} |} }{|\mathbf{r} - \mathbf{r'} |}$ in a spherical shell
How can we compute the following triple integral (electromagnetic diffusion in a sphericall shell)?
$ E(\mathbf{r}) = \int_0^{2 \pi} d\phi' \int_0^{\pi} \sin \theta' d\theta' \int_R^{R+h} d r' r'^2 \...
- 191
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56
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Is $0$ the null space of the integral operator with kernel $G(r,r') = \frac{\exp(-ik|r-r'|)} {|r-r'|}$?
Let $G(r,r') = \frac{\exp(-ik|r-r'|)} {|r-r'|} $, where $r$ and $r'$ are position vectors in a domain $D$ of $\mathbb R^3$ and $k$ is a positive real constant. Suppose that $h$ is a continuous real ...
- 21
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82
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Do these two Green's functions satisfy the Lorenz gauge condition?
I posted this question on Stack Exchange Physics (https://physics.stackexchange.com/questions/679845/do-these-greens-functions-satisfy-the-lorenz-gauge-condition), but repost it here since I didn't ...
- 514
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43
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Integral over Green's function of wave equation
the following paper says if $f(\vec{x})=f(x)$ does only depend on $x$ then we have
$\int d^3x' \frac{e^{\pm ik_{\phi}|\vec{x}-\vec{x}'|}}{|\vec{x}-\vec{x}'|} f(\vec{x}')= \frac{2\pi i}{k_{\phi}} e^{ ...
- 123
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105
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Finding vector potential from a given magnetic field
I want to find the vector potential from a given magnetic field in three-dimension in cartesian coordinates for two cases.
1) Where the magnetic field is in any analytical form and
2) When the ...
- 11
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2
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239
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Evaluate $\int_0^{2\pi}\ln(1+a^2-2a\cos(x))dx\text{ ,with }a>0$ [duplicate]
$$\int_0^{2\pi}\ln(1+a^2-2a\cos(x))dx,\;\;\;\;\text{with }a>0$$
How to evaluate Integral of $\ln(1+a^2-2a\cos x) dx$? where $x$ from $0$ to $2\pi$ and $a>0$, $\ln$ is the natural logarithm.
- 422
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440
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Prove Property of Green Function Solution to Laplace Equation in a 2D-square
Let's consider a 2D-square with 4 euqal subsquares containing different dielectrics.
Inside the square domain, the unkown potential function $\Phi$ satisfies the Laplace equation:
$\nabla^2\Phi=0$
...
- 21
2
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1
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543
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$u = 0$ is the only solution to the homogeneous Helmholtz equation $\Delta u + k^2 u = 0$?
We have that the solution to the inhomogeneous Helmholtz equation
$$\Delta u + k^2 u = f$$
can be represented by
$$u(x) = \int_{\mathbb{R}^3}G(x - y) f(y) dy$$
where $G$ is the fundamental ...
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