29 lines
776 B
TeX
29 lines
776 B
TeX
\documentclass[../main.tex]{subfiles}
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\graphicspath{{\subfix{../images/}}}
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\begin{document}
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\section{Equations of electrodynamics and classical mechanics}\label{sec:appendix_a}
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Newton's second law
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\begin{equation}\label{eq:newton_second}
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m \ddot{\mathbf{r}} = \sum_{i} \mathbf{F}_{i}
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\end{equation}%
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%
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Lorentz force
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\begin{equation}\label{eq:lorentz_force}
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\mathbf{F} = q \mathbf{E} + q \mathbf{v} \times \mathbf{B},
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\end{equation}%
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%
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Electric field
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\begin{equation}\label{eq:e_field_potential}
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\mathbf{E} = - \nabla V
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\end{equation} %
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%
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Electric field at a point $\mathbf{r}$
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\begin{equation}\label{eq:e_field_point}
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\mathbf{E} = k_{e} \sum_{j=1}^{n} q_j \frac{\mathbf{r} - \mathbf{r}_{j}}{|\mathbf{r} - \mathbf{r}_{j}|^{3}}
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\end{equation}
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\end{document} |