All Questions
Tagged with electromagnetism taylor-expansion
9
questions
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2
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155
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Taylor Expansion for a configuration of $2$ point charges on a line
Was getting back into physics and reading a chapter on electrostatics which sets up the following situation. We have a configuration of point charges - one $-q$ at the point ($-d,0,0$) and one $+q$ at ...
- 2,220
2
votes
1
answer
853
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Electric potential due to dipole layer
In Classical Electrodynamics, Jackson derives the electric potential for a surface with a dipole charge.
Here is his derivation. I will omit constants for brevity.
Letting $D(\textbf{x}) := \lim_{d(\...
- 613
2
votes
0
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60
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Approximate value of hyperbolic tangent in certain case
I am reading Thé Nature of Magnetism. While reading, I came across a particular approximation of hyperbolic tangent
while in first case $T>T_c$ , it is just Taylor series,
in case $T < T_c$ ( ...
- 21
12
votes
3
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397
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Finding smooth behaviour of infinite sum
Define
$$E(z) = \sum_{n,m=-\infty}^\infty \frac{z^2}{((n^2 + m^2)z^2 + 1)^{3/2}} = \sum_{k = 0}^\infty \frac{r_2(k) z^2}{(kz^2 + 1)^{3/2}} \text{ for } z \neq 0$$
$$E(0) = \lim_{z \to 0} E(z) = 2 \pi$$...
- 2,339
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1
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553
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Taylor expansion of $\frac {1}{|x-y|}$with x and y two vectors
This equation comes from a physics script on electrodynamics, saying that this equation comes from a Taylor series expansion.
I understand the first equality, but not the second one. It is really not ...
- 147
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2
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621
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How should I get the relations eq 3.36 into eq 3.37 in griffiths?
enter image description here
How to get this relations...?? Please give me answers.
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2
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172
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Binomial series expansion of a trinomial?
In electrostatics, the potential of a charge $q$ placed on the $z$-axis at $z=a$ is
\begin{equation}
\phi=\frac{1}{4\pi \epsilon_0}\frac{q}{r_1}
\end{equation}
where $r_1$ is the distance from the ...
- 343
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1
answer
198
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Electric potential in the far region?
I have the electric potential
$$\Phi(\vec{x})=\frac{\lambda}{2\varepsilon_0}\log\left(\frac{R+\sqrt{R^2+z^2}}{|z|}\right),$$
whose behavior I have to study in the far and near region, i.e. expand ...
- 187
2
votes
1
answer
420
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Expansion of 1/R
My problem is the following, I have ${1}/{R}={1}/{|\vec{r}-\vec{r}'(t)|}$ which can be expanded as
$1/R=1/r+\vec{r}\cdot\vec{r}'(t)/r^3+...$
How do I do this expansion? This was a part of a ...
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