All Questions
Tagged with electromagnetism complex-analysis
10
questions
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 ...
- 289
1
vote
0
answers
59
views
Kramers-Kronig computation for real susceptibility
i am trying to get the real part of electric susceptibility using the imaginary part with Kramers-Kronig relation for a Lorentz-Drude model.I chose to ask this question in math stack exchange as im ...
- 11
4
votes
5
answers
216
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How to calculate $\int_0^{2\pi}\frac{\cos(\phi)-R}{1-2R\cos(\phi)+R^2}\cos(n\phi)~d\phi$?
I wish to calculate
$$I(R)=\int_0^{2\pi}\frac{\cos(\phi)-R}{1-2R\cos(\phi)+R^2}~\cos(n\phi)~d\phi,$$
where $n\in\mathbb{N}$, $R\in[0,1)$.
Based on trial and error from plugging numbers into Wolfram ...
- 1,027
1
vote
1
answer
89
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How to calculate the leading order solution to $\sum_{n=-\infty}^\infty\frac{1}{[(x+n\epsilon)^2+1]^{3/2}}$?
I wish to calculate a series solution to the following sum,
$$S(x)=\sum_{n=-\infty}^\infty\frac{1}{[(x+n\epsilon)^2+1]^{3/2}},$$
where $x$, $\epsilon$ $\in$ $\mathbb{R}$ and $\epsilon \ll 1$.
Do you ...
- 1,027
0
votes
1
answer
45
views
Perpendicular complex-valued vectors
I'm reading an E&M Textbook and somewhat confused about how to find perpendicular vectors that satisfy the right hand rule, when the coefficients are complex. For example, if $E$ has direction $(\...
4
votes
0
answers
128
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How to solve $\sum_{n=-\infty}^\infty\frac{y^2}{[(x-n\pi)^2+y^2]^{3/2}}$?
I need to solve this sum:
$$\sum_{n=-\infty}^\infty\frac{y^2}{[(x-n\pi)^2+y^2]^{3/2}}.$$
Do you have any ideas for how I could do this?
I know that this sum:
$$\sum_{n=-\infty}^\infty\frac{y}{(x-n\pi)^...
- 1,027
1
vote
1
answer
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 ...
0
votes
1
answer
249
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Author's derivation of time-independent form of Maxwell's equations
Laser Electronics, 3rd edition, by Joseph T. Verdeyen, gives the following:
To describe an electromagnetic wave, we need two field-intensity vectors, $\mathbf{e}$ and $\mathbf{h}$, which are related ...
- 4,322
0
votes
1
answer
96
views
How to integrate Fresnel Integrals? $\int_0^y e^\frac{-j\beta(z)^2}\rho dz$
I am having trouble solving this integration of a spherical fresnel zone with radius y
$\displaystyle\int_0^y e^\frac{-j\beta(z)^2}\rho dz$
, where j is complex and $\beta$ and $\rho$ are constants.
...
0
votes
0
answers
43
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Complex Electric Flux Integral
I am working through Gamelin and am having trouble understanding the following:
The electric field is given by $\textbf{E} = \frac{1}{r} e_r$ where $e_r$ is the unit radial vector. Through each ...
- 1,104