Questions tagged [electromagnetism]
For questions on Classical Electromagnetism from a mathematical standpoint. This tag should not be the sole tag on a question.
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Interpreting the cohomology class of the Maxwell tensor.
In the introduction to Bott and Tu, “Differential forms in algebraic topology” there is the motivating example of a stationary point charge in $3$-space. The electromagnetic field $\omega$ is a $2$-...
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An improper integral from Jackson's book involving the modified Bessel function
When deriving the angular distribution of energy for synchrotron radiation one has to evaluate two tricky improper integrals (see [1] below):
$$
I_1 \equiv \int_{0}^{\infty} x^2 [K_{2/3}(x)]^2 \, \...
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Analytically solving PDEs on irregular domains in Physics
In many Physics courses you solve PDEs like heat or wave on square, circular, or spherical domains with separation of variables. Are there ways to solve PDEs and Boundary value problems on irregular ...
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Calculate Electric Field on the Z-axis from a finite charge wire
I've been trying to find the electric Field on the Z-axis from a non-uniform charge density line charge. The wire is placed on the z-axis from $z=0$ to $z=1$, $E=?$ at $z>1$ and $z<0$
$$
\rho =...
- 1
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I was trying to find field due uniformly charged sheet at a distance h from centre of the square sheet
I assumed the square(side a) sheet to be made up of wires.$$dE=Kdq/r^2$$
The field due to a wire is : Reference
$$\frac{K\lambda}{d}\left[\frac{x}{\sqrt{d^2+x^2}}\right]^{(a/2)}_{(-a/2)}=\frac{K\...
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Integrals for the the localized pyramid basis functions in Galerkin Method
I tried to show the following relations for the localized pyramid basis function $\phi_{i j}(x, y)=(1-|x| /$ $h)(1-|y| / h),|x|<h,|y|<h$, where $x$ and $y$ are measured from the site $(i, j)$. ...
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Flux of a vector field on a non-smooth surface? (in terms of electromagnetism)
While studying the famous Ampere's law, I came up with the following vector field $F$ and a surface $S$ lying in $R^3$. (In terms of physics, $F$ is the current density of some current in a circuit, ...
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Vector Line Integral For Biot Savart Law
How would one go about computing the vector line integral presented in the Biot-Savart law: $$\vec{B}=\int_c\frac{\mu_0I}{4\pi} \frac{d\vec{l}\times\hat{r}}{r^2}$$
I know how to compute vector line ...
- 33
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Stokes theorem not holding
I have a vector field $\vec{H} = (8z,0,-4x^3)$
Naturally, $\nabla \times \vec{H} = (0,8+12x^2,0)$
Stokes theorem says:
$$
\int_s{\nabla \times \vec{H}} \cdot \vec{dS} = \oint_l{\vec{H} \cdot dl}
$$
...
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Stokes theorem 2 sides not matching with Magnetic waves
We have been asked to verify stokes theorem for a magnetic field.
We know Stokes theorem states, for any vector field $\vec{H}$:
$$\int_S{(\nabla \times \vec{H}) \cdot \vec{dS}} = \oint_L{\vec{H} \...
- 123
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Pseudo-vector formal definition
I have a question about the formalization of pseudovectors. Wikipedia (and my electromagnetism professor and all the electromagnetism books) only state that a vector $v$ transforms as $v' = Rv$, while ...
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Solving $2\frac{\partial S}{\partial z}+\left(\frac{\partial S}{\partial r}\right)^2=0$
I have been trying to solve this PDE $$2\frac{\partial S}{\partial z}+\left(\frac{\partial S}{\partial r}\right)^2=0$$ The solution of this equation corresponding to a spherical wave of radius of ...
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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 ...
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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)=...
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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 ...
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