# 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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### 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 ...
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### Finding smooth behaviour of infinite sum

Define $$E(z) = \sum_{n,m=-\infty}^\infty \frac{z^2}{((n^2 + m^2)z^2 + 1)^{3/2}} = \sum_{k = 0}^\infty \frac{r_2(k) z^2}{(kz^2 + 1)^{3/2}} \text{ for } z \neq 0$$ $$E(0) = \lim_{z \to 0} E(z) = 2 \pi$$...
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### Is there a way to represent electrostatics tensors in tensor (possibly tensor product) way?

I'm working with electrostatic interaction tensors, which are defined as follows: \begin{align} T &= \frac{1}{r} \\ T^\alpha &\equiv \nabla T = -\frac{r^\alpha}{r^3} \\ T^{\alpha\...
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### What is the biharmonic operator of a vector ($\nabla^4 \vec{A}$)?

I'm trying to implement a new term into a code that solves electromagnetism, and it is equal to $$\frac{\partial \vec{B}}{\partial t} = \nu \nabla^4 \vec{B}$$ I gather that $\nabla^4$ is called the ...
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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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### Maxwell equation and divergence theorem contradict?

In my engineering mathematics class, I learned about Gauss' law and form of one Maxwell equation. I learned that $∇∙E=ρ/ε$ in Maxwell's equation $∇∙E=0$ in process of proving Gauss' law. force of ...
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### Integral involving the module of a vector

While working on a proof in electrodynamics, I found the following integral: $\int_{0}^{R} \frac{r^{2}}{|\vec{r}-\vec{a}|^{3}}dr$, where $\vec{a}$ is a constant vector whose module is less than $r$. ...