Questions tagged [electromagnetism]
For questions on Classical Electromagnetism from a mathematical standpoint. This tag should not be the sole tag on a question.
407
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Finding $\int_{-\infty}^{\infty}\frac{\sin(ax)}{\sqrt{(b-x)^2+c^2}}dx$ [closed]
How do we find
$$\int_{-\infty}^{\infty}\dfrac{\sin(ax)}{\sqrt{(b-x)^2+c^2}}dx$$
I have no idea on how to even begin approaching this. Can I get a hint?
EDIT:
I've got to this integral from a physics ...
- 183
1
vote
1
answer
130
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Given a triple integral representing the (electric) vector field of a continuous volume charge distribution, how to obtain the potential function?
My question is about the math involved in the concept of electric potential. Though this is a physics concept, it is basically a lot of vector calculus. The derivations below are based on the content ...
- 5,021
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0
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59
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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
0
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0
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Dirac String force
Assume that the Dirac string is lying along the negative $z$-axis, and is subject to a magnetic field $B$. Assume throughout this question that we are considering a static situation. The force on the ...
- 429
1
vote
1
answer
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Potential and integral (electrodynamics)
I'm supposed to find the vector potential $A(x)$
the field generated by an infinite conducting wire of section $\pi a^2$, in which flows a constant current density $j=j \cdot \theta(a-r)\hat{z}$ ...
- 429
1
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0
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176
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Jackson's Electrodynamics, exercise 5.34, using Laplace solutions to prove a relation about mutual inductance
I've managed to solve 5.34 (a) and (b) of Jackson's electrodynamics. Right this minute I believe I know how to solve (c) but I am not certain yet and need some help on this.
It is not a trivial ...
- 581
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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
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0
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Generalization for a result on vector analysis
This is inspired in a problem from Griffths's Electromagnetism book (3th edition).
The problem asks us to construct a vector field which is both solenoidal and irrotational (div-free and curl-free) ...
- 225
2
votes
2
answers
1k
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Finding the distance from a point a distance $z$ above the center of a square to any point on the edge
I was working on an electrostatics problem that I thought I was doing correctly. However, upon reading the solution I see I was not. I will post my attempt and the solution below and then ask a few (...
- 2,220
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1
answer
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"Double" relativistic variant of the same classical mechanics equation
This question is about my curiosity about the relativistic Kepler equation of which I am reading in a recent paper. Actually, I am only interested in an introductory concept stated in paper.
Let
$$ m\...
user603537
1
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2
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239
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Examples of relativistic equations
I am posting this question here because it is just reference request and I do not need a fully detailed answer.
Attending my physics class, we introduced two relativistic equations:
$$ \frac{d}{dt}\...
user603537
1
vote
0
answers
77
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Verification of Stokes’ theorem
Consider the vector field $$\vec{F}=-\frac{y}{x^2+y^2}\hat{i}+\frac{x}{x^2+y^2}\hat{j}$$. Calculating the curl of the vector field I am getting zero. But when I am calculating the line integral along ...
3
votes
1
answer
79
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vector calculus directions
Consider a current density:
$$\vec{j}=j_0(1-\frac{r^2}{R^2})\vec{e_3}$$ if $r\le R$ and $j=0$ if $r\ge R$
where $r$ is the distance from the $x_3$ axis.
I need to use Biot-Savart law to find the ...
- 429
0
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1
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81
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Does Euler-Lagrange extremization of $L=-\frac{1}{4}F_{\mu\nu}F^{\mu\nu}$ lead to the Maxwell equations?
Suppose $F_{\mu\nu}$ and $F^{\mu\nu}$ are defined as follows:
$$F_{\mu\nu} = \begin{bmatrix} 0 & E_x & E_y & E_z \\ -E_x & 0 & -B_z & B_y \\ -E_y & B_z & 0 & -B_x \\...
- 802
0
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0
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74
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Electromagnetic field tensor in an orthonormal basis (in SI units)
Is it true?
Electromagnetic fiel tensor, defined by:
$\mathbf{F}\overset{\text{def}}=B+E\wedge \mathrm{d}t= B_1\mathrm{d}y\wedge \mathrm{d}z+ B_2\mathrm{d}z\wedge \mathrm{d}x+ B_3\mathrm{d}x\wedge \...
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