All Questions
Tagged with electromagnetism vector-fields
27
questions
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Electric fields and simply-connected regions
I apologize for the ignorance and the rough English in advance, I have an issue understanding how to match both what happens in physics and what I am seeing in calculus.
We learned that if a vector ...
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0
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34
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Boundary Conditions on the Magnetic Flux Density (B-field)
My question is similar to this one (Boundary conditions magnetic field) in that it is related to the boundary conditions of the magnetic field (B-field). However, my question focuses on mathematically ...
- 665
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63
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Electric field flux proportional to the field lines generated by (for example) a static charge
Suppose we have a stationary positive charge at a point in space that we call $+Q$. We know by definition that the flow of the electrostatic field is given by, in its simplified form,
$$\Phi_S(\vec E)=...
- 7,792
2
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Generalization for a result on vector analysis
This is inspired in a problem from Griffths's Electromagnetism book (3th edition).
The problem asks us to construct a vector field which is both solenoidal and irrotational (div-free and curl-free) ...
- 225
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3
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189
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Electric Field by integral method is not the same as for Gauss's Law
I'm trying to calculate the Electric Field over a thick spherical sphere with charge density $\rho = \frac{k}{r^2}$ for $a < r < b$, where $a$ is the radius of the inner surface and $b$ the ...
- 653
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82
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Electric Field felt at the origin of a hemisphere
I want to calculate the Electric Field that is felt at the origin $O$ provoked by a hemisphere of radius $R$ with uniform charge density $\sigma$.
I used spherical coordinates: $\vec{r} = -R(\sin(\phi)...
- 653
2
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134
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Line and Surface Integral with the Dot Product replaced with a Cross Product
Having recently studied magnetostatics, I came across the Biot-Savart law, which is based on the line integal over a current distribution in a curve $C$:
$$\mathbf B(\mathbf r)=\frac{\mu_0}{4\pi}\...
- 109
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answer
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When does zero divergence imply a vector potential exists?
From electrodynamics we know that $\boldsymbol{\nabla}\mathbf{B}=\mathbf 0$ hence we can introduce a vector potential such that $\mathbf{B}=[\boldsymbol \nabla\times \mathbf{A}]$.
What is the general ...
- 151
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4
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Divergence of a radial vector field
I am reading Modern Electrodynamics by Zangwill and cannot verify equation (1.61) [page 7]:
\begin{equation}
\nabla \cdot \textbf{g}(r)=\textbf{g}^{\prime}\cdot \mathbf{\hat{r}},
\end{equation}
where ...
- 51
1
vote
1
answer
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
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1
answer
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Why must the $B_\theta$ and $B_\phi$ components of the magnetic field be zero at $\theta=0\, \&\, \pi$?
I have been reading this paper and it says (see the last paragraph in the screenshot below) that 'the latter condition requires that $B_\theta$ and $B_\phi$ vanish along the axis $\mu=1,\ -1$'. Why ...
- 1,027
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1
answer
616
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Why does the electromagnetic tensor in component form coincide with the differential-geometric definition of a $2$-form?
From physics classes, I understand the electromagnetic field strength tensor to be defined as
$$F^{\mu\nu}=\partial^\mu A^\nu-\partial^\nu A^\mu \;,$$
where $\partial^\mu$ is the partial derivative (...
- 157
1
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0
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73
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Representing flux tubes as a pair of level surfaces in R^3
I am trying to see if Vector fields(I am thinking of electric and magnetic fields) without sources(divergence less) can be represented by a pair of functions f and g such that the level surfaces of ...
- 341
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1
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37
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Shifting magnetic field axis
Considering the image below, I have magnetometer readings while my magnetometer is oriented along x' and y'. Can I convert these readings to get the equivalent reading if my magnetometer was oriented ...
3
votes
1
answer
537
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Proof that the vector area is the same for all surfaces sharing the same boundary
In the book, Introduction to Electrodynamics by Griffiths (4th edition) in question 1.62 part c, we are asked to prove that the vector area is the same for all surfaces sharing the same boundary. The ...
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