All Questions
Tagged with electromagnetism vector-analysis
70
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103
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The reason for curl free
I wonder about the reason for the idea of this, would you mind explain for me this can happen in mathematics. Thank you !
- 1
2
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2
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76
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How to apply integration by parts to simplify an integral of a cross product?
I'm reading a physics paper and am trying to figure out how a certain expression is derived (If interested, see Appendix of the paper, Eq. (A7), (A8)). The authors skip a lot of derivation steps and ...
- 23
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61
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Is $\frac{\partial}{\partial{t}}(\nabla\times H) = \nabla \times \frac{\partial H}{\partial t}$?
While trying to prove a particular equation using Maxwell's equations in electromagnetic theory, there is a step in my textbook that says
$$\frac{\partial}{\partial{t}}(\nabla\times H) = \nabla \times ...
- 535
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60
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How to prove this vector identity? [closed]
I've seen this vector identity from the book[1] in page 89,
$$ (\nabla p)\times\nu =0,\ \text{on}\ \partial\Omega,$$
where $\nu $ is the outer normal vector of $\partial \Omega$, $ p \in H_0^1(\Omega)....
- 45
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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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2
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77
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What does $\vec{\nabla}^2 \vec{E} = \vec{\nabla}^2 \left[ f(\vec{k} \cdot \vec{r} - \omega t) \vec{E}_0 \right]$ mean?
$\vec{E} = f(\vec{k} \cdot \vec{r} - \omega t) \vec{E}_0$ with the constant vector field $\vec{E}_0$
I only know the case if I apply the Laplacian operator on a scalar field, in this case it is a ...
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26
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Flux of a vector field on a non-smooth surface? (in terms of electromagnetism)
While studying the famous Ampere's law, I came up with the following vector field $F$ and a surface $S$ lying in $R^3$. (In terms of physics, $F$ is the current density of some current in a circuit, ...
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1
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93
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Distance becoming equal to displacement
Consider a charged particle of charge q and mass m being projected from the origin with a velocity u in a region of uniform magnetic field $\mathbf{B} = - B \hat{\mathbf{k}} $ with a resistive force ...
- 333
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73
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Why does $\boldsymbol{\nabla} \times \textbf{E}=\textbf{0}$ imply $\boldsymbol{E_2}^{\parallel}=\boldsymbol{E_1}^{\parallel}$?
I am currently studying 'Introduction to Electromagnetism' by David Griffiths, and I was reading about the electric displacement $\boldsymbol{D}$. I decided to try to extract eq. 4.27, which states:
$\...
- 289
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46
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How do scalars like currrent or amplitude add vectorially and give correct results?
I have seen in alternating current that values of current and potential difference in different circuits like LR, CR or LCR circuits are found by adding them like vectors.
It also happens with ...
- 471
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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 ...
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60
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Huygens' principle for diffraction through an apeture
I understand that integrals are analogous to summing for continuous values, but for some reason I am still terrible at modeling continuous phenomena. Take for example calculating the diffraction of a ...
- 613
2
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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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34
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Translational invariance of sources/materials implies translational field invariance
Let's say we have an electromagnetic problem where $\epsilon = \epsilon(x,y)$, $\rho = \rho(x,y)$, and $J = J(x,y)$. The physicist argument is that by the symmetry of the problem we also have $E = E(x,...
- 613
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75
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Oersted's Law in differential form notation
I'm preparing to get chewed up on a midterm and I don't yet know how to write Oersted's Law in differential form notation.
The goal is to convert this
$\int_{\partial S} H \cdot dr = \int_{s} \nabla \...
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