All Questions
Tagged with electromagnetism multivariable-calculus
54
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 ...
2
votes
2
answers
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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1
answer
75
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What integral is used to calculate the electric field generated by a continuous charged curve?
I'm studying Multivariable Mathematics, by Ted Shifrin, in which one reads that ''the gravitational force exerted by a continuous mass distribution $\Omega$ with density function $\delta$ is
$$\mathbf{...
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34
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Boundary Conditions on the Magnetic Flux Density (B-field)
My question is similar to this one (Boundary conditions magnetic field) in that it is related to the boundary conditions of the magnetic field (B-field). However, my question focuses on mathematically ...
- 665
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2
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What does $\vec{\nabla}^2 \vec{E} = \vec{\nabla}^2 \left[ f(\vec{k} \cdot \vec{r} - \omega t) \vec{E}_0 \right]$ mean?
$\vec{E} = f(\vec{k} \cdot \vec{r} - \omega t) \vec{E}_0$ with the constant vector field $\vec{E}_0$
I only know the case if I apply the Laplacian operator on a scalar field, in this case it is a ...
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63
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Vector Line Integral For Biot Savart Law
How would one go about computing the vector line integral presented in the Biot-Savart law: $$\vec{B}=\int_c\frac{\mu_0I}{4\pi} \frac{d\vec{l}\times\hat{r}}{r^2}$$
I know how to compute vector line ...
- 33
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124
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Stokes theorem not holding
I have a vector field $\vec{H} = (8z,0,-4x^3)$
Naturally, $\nabla \times \vec{H} = (0,8+12x^2,0)$
Stokes theorem says:
$$
\int_s{\nabla \times \vec{H}} \cdot \vec{dS} = \oint_l{\vec{H} \cdot dl}
$$
...
- 123
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89
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Divergence theorem with normal component of a curl to a surface
Let $\mathbf{A}$ be a vector function in $\mathbf{R}^3$ and we want to find the normal and tangent components of $\nabla \times \mathbf{A}$ on a smooth and closed surface $\Gamma$. $\mathbf{n}$ is the ...
8
votes
1
answer
711
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A calculus problem from electrostatics
Since this problem consists of multiple parts and one needs to see all of them to understand the problem i'm going to list out all of them:
Consider a uniformly charged spherical shell of radius $R$ ...
- 429
1
vote
1
answer
212
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Evaluating an Integral with a Dot Product
Lets say I have
$\int{ \overrightarrow{B} \cdot\ \overrightarrow{dA} }$
is that equal to
$ \int{ B \cdot dA } \cdot\cos(\theta)$
or
$\int{(B \cdot\cos(\theta)) \cdot dA} $
For example: a ...
- 113
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0
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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
votes
3
answers
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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1
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134
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Formalizing some items in an electrostatics computation
Consider the question attached (Example 3.4 from Zangwill's Modern Electrodynamics, Ch 3). I can follow the solution quite easily using "physics math" but, having just recently finished ...
- 1,143
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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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Electric potential due to dipole layer
In Classical Electrodynamics, Jackson derives the electric potential for a surface with a dipole charge.
Here is his derivation. I will omit constants for brevity.
Letting $D(\textbf{x}) := \lim_{d(\...
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