All Questions
Tagged with electromagnetism potential-theory
8
questions
1
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67
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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
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0
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41
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Electrostatic potential of a charge in a 3-torus
Consider the 3-torus which arises from taking $R^3$ and identifying two points $x\equiv x+nL$ whenever $n$ is a vector with integer components. I'm curious about finding the electrostatic potential ...
- 2,289
1
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244
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Differential equation for a vector potential
From Helmholtz’s theorem, any smooth vector field $\mathbf{F}$ that goes to zero at infinite distance can be uniquely decomposed everywhere in the sum of a divergence free component and an ...
- 41
1
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59
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References for magnetic Sobolev spaces
I am working on PDE. Recently I have been studying magnetic Sobolev spaces. While the theory is clear to me, having very little knowledge about physics, I have almost no idea how these spaces help ...
- 31
3
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Why is electric potential function in free space infinitely differentiable?
Electric potential function in free space of a continuous charge distribution $\rho'$ distributed over volume $V' \subset \mathbb{R}^3$ is denoted by:
$\psi (x,y,z): \mathbb{R}^3 \setminus{V'} \to \...
- 1,141
2
votes
1
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126
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Dirichlet problem on a wire: a co-dimension 2 boundary condition
A wire may be thought of as a smooth compact curve $C \subset \mathbb{R}^3$ with boundary two endpoints. Suppose we are given a smooth $\phi: C \to \mathbb{R}$ (a potential on the wire), then can $\...
- 1,112
0
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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
3
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Charge density of charged conductor with flat side
Given a charged conducting body with a flat side, can the charge density (and hence the normal electric field) be constant on the flat part?
According to physics lore, the charge density is greater ...
- 1,410