# 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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### Using "Maxwell's curl equations" to get $H_y = \dfrac{j}{\omega \mu} \dfrac{\partial{E_x}}{\partial{z}} = \dfrac{1}{\eta}(E^+ e^{-jkz} - E^- e^{jkz})$

I am currently studying the textbook Microwave Engineering, fourth edition, by David Pozar. Chapter 1.4 THE WAVE EQUATION AND BASIC PLANE WAVE SOLUTIONS says the following: The Helmholtz Equation In ...
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How can we compute the following triple integral (electromagnetic diffusion in a sphericall shell)? $E(\mathbf{r}) = \int_0^{2 \pi} d\phi' \int_0^{\pi} \sin \theta' d\theta' \int_R^{R+h} d r' r'^2 \... 0 votes 1 answer 30 views ### Generalizing regular polyhedra by repelling points on a sphere Find the arrangement of$N$identical point charges on a sphere. For uniqueness, assume one charge sits on the north pole and another one lies on a fixed latitude of the sphere Given a circumference ... 2 votes 2 answers 33 views ### Numerical Solution of nonlinear P-B Equation in unbounded domain for determining the EDL potential distributions around a spherical particle For my project I am studying a paper, namely "Perturbation solutions for the nonlinear Poisson–Boltzmann equation with a higher order-accuracy Debye–Huckel approximation" by Cunlu Zhao, ... 1 vote 0 answers 36 views ### Complex integral of$\int_{-\pi}^{\pi}\frac{\cos\theta\,d\theta}{\csc \alpha+\cos\theta}$[closed] A current$I_1$flows in a circular circuit of radius a and a current$I_2$flows through a very long straight conductor in the same plane of the circular circuit (see the figure). From the laws of ... 2 votes 1 answer 113 views ### What does it mean to say that "$h$is a coordinate measured normal from the surface"? How does this work in practice? I am currently studying the textbook Microwave Engineering, fourth edition, by David Pozar. Section Fields at a General Material Interface of chapter 1.3 FIELDS IN MEDIA AND BOUNDARY CONDITIONS says ... 2 votes 1 answer 183 views ### Geometric Algebra or Differential Forms for Electromagnetism? [closed] Electromagnetism (Maxwell's equations) are most often taught using vector calculus. I have read that both geometric algebra and differential forms are ways to simplify the material. What are some ... 0 votes 0 answers 11 views ### Example of a magnetic vector field I am doing a high school level presentation about maxwells equations. For that I intend to do animations using the python library manim, but that in turn requires me to know the function for a ... 3 votes 1 answer 71 views ### 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 ... 2 votes 0 answers 25 views ### Is$0$the null space of the integral operator with kernel$G(r,r') = \frac{\exp(-ik|r-r'|)} {|r-r'|}$? Let$G(r,r') = \frac{\exp(-ik|r-r'|)} {|r-r'|} $, where$r$and$r'$are position vectors in a domain$D$of$\mathbb R^3$and$k$is a positive real constant. Suppose that$h$is a continuous real ... 0 votes 2 answers 37 views ### What is the radial direction? I'm currently in an electrostatics course; and wanting to rip my hair out. The question says: A sphere of radius 𝑎 is polarized such that the polarization at 𝒓 within the sphere is given by 𝑷 = 𝑘𝑟... 1 vote 1 answer 64 views ### What is the correspondence between gauge field terminology and bundle terminology in electromagnetism? In electromagnetism, the electromagnetic field tensor can be expressed as $$F_{\mu \nu} = \partial_\mu A_\nu - \partial_\nu A_\mu.$$ If we let$A= A_\mu dx^\mu$, since$F= \frac{1}{2} F_{\mu \nu} dx^\... 1 vote
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### Calculating the divergence of electric field in standard coordinates

Given an electric field $$\vec{E(r)} = (c/r^2 ) \hat {r}$$ I want to show that $\nabla \cdot \vec{E} = 0$ for $r \ne 0$ and do the calculation in standard coordinates. For simplicity I'll ...
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### Calculating the average of the square of the magnitude of an electric field

Let the sinusoidal electric field polarised in the $\hat{x}$ direction be $\overline{\mathcal{E}}(x, y, z, t) = \hat{x}A(x, y, z)\cos(\omega t + \phi)$, where $A$ is the amplitude, $\omega$ is the ...
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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 ...
Define $$E(z) = \sum_{n,m=-\infty}^\infty \frac{z^2}{((n^2 + m^2)z^2 + 1)^{3/2}} = \sum_{k = 0}^\infty \frac{r_2(k) z^2}{(kz^2 + 1)^{3/2}} \text{ for } z \neq 0$$ $$E(0) = \lim_{z \to 0} E(z) = 2 \pi$$...