All Questions
Tagged with electromagnetism vectors
30
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if divergence of a vector is zero, how to find the spherical coordinate of the vector?
The perturbed part of magnetic field is $\mathbf{\delta B}$ where $\mathbf{\delta B} = \delta B_x(x,y), \delta B_y(x,y)$ and
$\nabla \cdot \mathbf{\delta B} = 0$.
To prove $\mathbf{\delta B} = \delta ...
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-1
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1
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116
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Polar coordinates: What unit vectors span the $(r,\theta)$ space? [closed]
Polar coordinates: What unit vectors span the $(r,\theta)$ space?
I am thoroughly confused. If in the Cartesian system, the associated orthonormal polar vectors at different points on a circle keep ...
- 419
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2
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Book Recommendation: One that has a lot of problems and theory associated with polar coordinates and spherical polar coordinates
I would like to "master" polar coordinates and spherical polar coordinates. In the sense, I would like to become as well versed with them as I am with cartesian coordinates.
I have gone ...
- 419
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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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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
2
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2
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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 (...
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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
3
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1
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223
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Calculation of a vector by taking the gradient of the integral of its divergence
I have encountered several times of a special way of calculating a vector from the divergence of the vector. It has at least appeared in the theories of elasticity and electrodynamics.
If I define the ...
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165
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Irrotational implies conservative without using the path-connection
Let's consider a simply-connected domain $V$ in $\mathbb{R}^{3}$ and a smooth vector field $\mathbf{F}$ in $V$ (please don't answer considering other scenarios). Under this assumption, let's consider ...
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1
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102
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Can we have vectors with vectors as components?
I was working on my course on Electrodynamics earlier today, when I was tasked with computing the eletric field of a non-trivial charge distribution, and it struck me that I had a field with ...
- 487
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132
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A laplacian working on an equation containing a laplacian and a gradient
I have an equation as follows:
$$a \Delta \mathbf{u} + \mathbf{\nabla}(\mathbf{\nabla} \cdot \mathbf{u}) = 0$$
in which $a$ is a constant, $\mathbf{u}$ is a vector, $\Delta$ is the Laplacian operator, ...
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1
vote
1
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73
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Volume Integral : $\int \mathrm d^3\mathbf{r}' \frac{\nabla \cdot \mathbf{M}(\mathbf{r'})}{|\mathbf{r'}-\mathbf{r'}|}$
I am trying to understand the following claims. I would appreciate if you could help me, as I am still unable to understand it.
The problem asks us to find the following integral:
$$I = \int \mathrm d^...
- 187
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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1
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58
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Where does this matrix, $\begin{pmatrix}0 & \mathcal{B}_{z} \\-\mathcal{B}_{z} & 0\end{pmatrix}$ come from in the Lorentz force law?
The anisotropic conductivity of the Hall configuration.
We will only explore the case of perpendicular electric and magnetic fields, throughout the course, with the convention that: $\boldsymbol{\...
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83
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Vector Analysis cross product and dot product
Three vectors $\vec A,\vec B,\vec C$ Compare the value of these 4 questions.(use the parallelepiped)
a) $(\vec A\times \vec C)\cdot\vec B$
b) $\vec A\cdot(\vec C\times\vec B)$
c) $(\vec A\times\vec B)\...
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