# 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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### 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]: $$\nabla \cdot \textbf{g}(r)=\textbf{g}^{\prime}\cdot \mathbf{\hat{r}},$$ where ...
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Define $$E(z) = \sum_{n,m=-\infty}^\infty \frac{z^2}{((n^2 + m^2)z^2 + 1)^{3/2}} = \sum_{k = 0}^\infty \frac{r_2(k) z^2}{(kz^2 + 1)^{3/2}} \text{ for } z \neq 0$$ $$E(0) = \lim_{z \to 0} E(z) = 2 \pi$$...