All Questions
Tagged with electromagnetism wave-equation
11
questions
1
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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
2
votes
0
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45
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How to apply phasor transformation with multiple sinusoidal functions
I am seeing some questions in my textbook involving phasor transformation with multiple functions of cosine or sine in multiplication with each other but they didn't exactly showed how to do it and I ...
- 123
1
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1
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153
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Variable separation method for solving wave equation
In variable separable method we assume the solution to be the product of such functions each of which is function of only one variable. What is the basis for that assumption? What allows us to assume ...
1
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2
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Find the time period ($T$) for an electric field wave: $E=E_0\sin{m t}\sin{2mt}$
Find the time period ($T$) for an electric field wave: $E=E_0\sin{m t}\sin{2mt}$
I thought $T$ is such that, $E(T+t) = E(t)$. As period of given sinusoidal function $E$ is 2$\pi$,
$$ \Rightarrow 2\pi ...
- 326
0
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221
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Deriving the wave equation
Given:
$$\nabla \times \mathbf H = \frac{4\pi}{c} \mathbf j \ \ \ \ \ \ \ \ \ (1)$$
$$\nabla \times \mathbf E = -\frac{1}{c} \frac{\partial \mathbf H}{\partial t} \ \ \ (2)$$
$$\...
- 1,139
0
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0
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459
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Deriving the wave equation out of $\nabla \times \vec H = \frac{4\pi}{c} \vec J$
I am trying to derive the wave equation presented by Alfven in his 1942 paper
Based on the electrodynamic equations:
$$\nabla \times H = \frac{4\pi}{c}J$$
$$\nabla \times E = -\frac{1}{c} ...
- 1,139
-1
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1
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1
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Proof: Any function of the form $f \left(t - \mathbf{a}_n \cdot \dfrac{\mathbf{r}}{c} \right)$ is a solution to the $n$-dimensional wave equation
My electromagnetism (Maxwell's equations) textbook gives the following wave equation for free space:
$$\nabla^2 \mathbf{h}(\mathbf{r}, t) - \dfrac{1}{c^2} \dfrac{\partial^2{\mathbf{h}(\mathbf{r}, t)}}...
- 4,322
3
votes
1
answer
336
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Wave propagation with a complex coefficient $\beta$ in a Robin boundary condition. How does this affect scattering from the boundary?
Can anyone give me an idea of what happens in the following situation involving Robin boundary conditions with a complex coefficient.
Lets say we have an incident electromagnetic plane wave $u(x) = e^...
- 3,695
2
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1
answer
543
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$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 ...
- 2,614
0
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2
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36
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Is the reach of the E- and B-field in an EM-wavefront infinite?
In my textbook, the wave-equation for EM waves was derived by using Maxwells' equations in integral form on a EM propgagation in $x$-direction (in vacuum), with E-field in $y$-direction and B-field in ...
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