Hoja de Ecuaciones Electricidad y Magnetismo
Author
Nelson Elias Rincon Quiñones
Last Updated
5年前
License
Creative Commons CC BY 4.0
Abstract
Herramienta para generar hojas de ayuda para Física
Herramienta para generar hojas de ayuda para Física
\documentclass{article}
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\usepackage{url}
\usepackage{multicol}
\usepackage{amsmath}
\usepackage{esint}
\usepackage{bigints}
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\usepackage{tikz}
\usetikzlibrary{calc}
\usetikzlibrary{decorations.pathmorphing}
\usepackage{amsmath,amssymb}
\usepackage{colortbl}
\usepackage{xcolor}
\usepackage{mathtools}
\usepackage{amsmath,amssymb}
\usepackage{enumitem}
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\makeatletter
\newcommand*\bigcdot{\mathpalette\bigcdot@{.5}}
\newcommand*\bigcdot@[2]{\mathbin{\vcenter{\hbox{\scalebox{#2}{$\m@th#1\bullet$}}}}}
\makeatother
\title{física eléctrica}
\usepackage[brazilian]{babel}
\usepackage[utf8]{inputenc}
%cambios de unidades (pt, mm, cm,ex,em,bp,dd,pc,sp) https://tex.stackexchange.com/questions/8260/what-are-the-various-units-ex-em-in-pt-bp-dd-pc-expressed-in-mm
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\newcommand{\nc}[2][]{%
\tikz \draw [draw=black, ultra thick, #1]
($(current page.center)-(0.5\linewidth,0)$) --
($(current page.center)+(0.5\linewidth,0)$)
node [midway, fill=white] {#2};
}% tomado de https://tex.stackexchange.com/questions/179425/a-new-command-of-the-form-tex
\begin{document}
\begin{center}{\huge{\textbf{Electricidad y Magnetismo}}}\\
\end{center}
\begin{multicols*}{3}
\tikzstyle{mybox} = [draw=black, fill=white, very thick,
rectangle, rounded corners, inner sep=10pt, inner ysep=10pt]
\tikzstyle{fancytitle} =[fill=black, text=white, font=\bfseries]
%--------------------------
\begin{tikzpicture}
\node [mybox] (box){%
\begin{minipage}{0.3\textwidth}
\begin{itemize}
\addtolength{\itemsep}{-2pt}
%\item[$g = $]
% 9.80 m s$^{-2}$
\item[$c = $]
Velocidad de la luz $ = 3.00\times 10^8$ ms$^{-1}$
\item[$k = $]
Constante de Coulomb $ = 8.9876\times 10^9$ Nm$^2C^{-2}$ %8.9875517873681764×109 N·m2/C2 (m/F).
\item[$\epsilon_o = $]
Constante dieléctrica vació $ = 8.85\times 10^{-12}$ N$^{-1}$C$^2m^{-2}$ (m/F)
\item[$\mu_o = $]
Permeabilidad del vació $ = 4\pi\times 10^{-7}$ H/m $= 1.256\times 10^{-6}$ Kgs$^{-2}$A$^{-2}$ %1.25663706 × 10-6 m kg s-2 A-2
\item[$e^{\pm} = $]
Carga del electrón-protón $ = 1.60\times10^{-19}$ C
\item[$m_e = $]
Masa del electrón $ = 9.11\times10^{-31}$ kg % \\ $ = 0.511$ MeV/$c^2$
\item[$m_n = $]
Masa de neutrón-protón $ = 1.67\times10^{-27}$ kg % \\ $ = 938$ MeV/$c^2$
\item[$N_A = $]
Número de Avogadro $ = 6.022 \times 10^{23}$ moléculas/mol
\item[$k_B = $]
Constante de Boltzmann $ = 1.38 \times 10^{-23} {\mbox{J}}/{\mbox{K}}$
%\item[$R = $]
% Constante de gases ideales$ = 8.31 \frac{\mbox{J}}{\mbox{mol K}} = 0.0821 \frac{\mbox{l atm}}{\mbox{mol K}}$
%\item[ $c_{\mbox{w}} = $]
% Calor específico agua $ = 1 {\mbox{ cal}}/({\mbox{g K}})$]
%\item[ $1 {\mbox{ cal}} $] $= 4.186 {\mbox{ J}}$]
%\item[ $\sigma = $]
% Constante Stefan-Boltzmann $ = 5.67\times 10^{-8}\>\frac{\mbox{W}}{\mbox{m}^2 \mbox{K}^4}$
\end{itemize}
\end{minipage}
};
%---------------------------------
\node[fancytitle, right=10pt] at (box.north west) {Constantes Fundamentales};
\end{tikzpicture}
%---------------------------
\begin{tikzpicture}
\node [mybox] (box){%
\begin{minipage}{0.3\textwidth}
$\Vec{F}_{ij}=k\frac{Q_iQ_j}{r^2_{ij}}\hat{r}_{ij} = \frac{1}{4\pi\epsilon_o}\frac{Q_iQ_j}{r^2_{ij}}\hat{r}_{ij}=Q_i\Vec{E}_j$\\
$\Vec{E}_i=k\frac{Q_i}{r^2_{io}}\hat{r}_{io}$ \\
$V=k\frac{Q_i}{r_{oi}}$
\end{minipage}
};
%---------------------------------
\node[fancytitle, right=10pt] at (box.north west) {Distribuciones Discretas};
\end{tikzpicture}
%---------------------------
\begin{tikzpicture}
\node [mybox] (box){%
\begin{minipage}{0.3\textwidth}
$\lambda= \frac{q}{L}=\frac{dq}{dL}$, $dq=\lambda dL$\\
$\sigma= \frac{q}{A}=\frac{dq}{dA}$, $dq=\sigma dA$\\
$\rho= \frac{q}{V}=\frac{dq}{dV}$, $dq=\rho dV$
\end{minipage}
};
%---------------------------------
\node[fancytitle, right=10pt] at (box.north west) {Densidad de Carga};
\end{tikzpicture}
%---------------------------
\begin{tikzpicture}
\node [mybox] (box){%
\begin{minipage}{0.3\textwidth}
\nc{Campo}\\
$d\vec{E} = k\frac{dq}{r^2_{do}}\hat{r}_{do}$\\
$\vec{E} = k\bigintsss \frac{\lambda dL}{r^2_{do}}\hat{r}_{do}$, $\vec{E} = k\bigintsss \frac{\sigma dA}{r^2_{do}}\hat{r}_{do}$, $\vec{E} = k\bigintssss \frac{\rho dV}{r^2_{do}}\hat{r}_{do}$\\
$\vec{E}_{linea}=\frac{1}{2\pi\epsilon_o}\frac{\lambda}{r}\hat{r}$\\ $\vec{E}_{placa}=\frac{\sigma}{2\epsilon_o}\hat{r}_{\scriptstyle{\perp}}$\\ Entre placas opuestas $\vec{E}_{placas}=\frac{\sigma}{\epsilon_o}\hat{r}_{\scriptstyle{\perp}}$\\
$E_i=-\frac{dV}{dx_i}$; $x_i=x,y,z$\\
$\vec{E}=-\vec{\nabla} V$
\end{minipage}
};
%------------ campo titulo---------------------
\node[fancytitle, right=10pt] at (box.north west) {Distribuciones Continuas};
\end{tikzpicture}
%---------------------------------
%\bigskip
%---------------------------
\begin{tikzpicture}
\node [mybox] (box){%
\begin{minipage}{0.3\textwidth}
\nc{Gauss}\\
$\Phi=\bigointsss \vec{E}\cdot d\vec{A}=\frac{q_{enc}}{\epsilon_o}$\\
\nc{Potencial}\\
$V=\frac{U}{q}$\\
$V=\vec{E}\cdot\vec{r}$\\
$V-V_o=-\bigintsss \vec{E}\cdot d\vec{l}$\\
$V=\frac{1}{4\pi\epsilon_o}\bigintsss \frac{dq}{r}$\\
$V= k\bigintsss \frac{\lambda dL}{r_{do}}$, $V= k\bigintsss \frac{\sigma dA}{r_{do}}$, $V = k\bigintssss \frac{\rho dV}{r_{do}}$\\
\nc{Energía}\\
$\Delta U=-\bigintsss_a^b\vec{F}d\vec{l}=-q\bigintsss_a^b\vec{E}d\vec{l}$\\
$\Delta U=q\Delta V=-W_{ab}=qEl$
\end{minipage}
};
%------------ potencial titulo ---------------------
\node[fancytitle, right=10pt] at (box.north west) {Distribuciones Continuas};
\end{tikzpicture}
%---------------------------
\begin{tikzpicture}
\node [mybox] (box){%
\begin{minipage}{0.3\textwidth}
$C_o\frac{q}{V}=\frac{\epsilon_oA}{d}$, con dieléctrico $C=kC_o=\frac{k\epsilon_oA}{d}$\\
$C_p=C_1+C_2+...+C_n=\sum_i^nC_i$\\
$C_s=1/C_1+1/C_2+...+1/C_n=(\sum_i^n\frac{1}{C_i})^{-1}$\\
$E_{pot-elec}=U=\frac{1}{2}qV=\frac{q^2}{2C}=\frac{1}{2}CV^2$\\
$\mu=\frac{\epsilon_oE^2}{2}=\frac{\epsilon_oV^2}{2d^2}=\frac{U}{V_{olumen}}$
\end{minipage}
};
%---------------------------------
\node[fancytitle, right=10pt] at (box.north west) {Capacitancia};
\end{tikzpicture}
%\bigskip\\
%---------------------------
\begin{tikzpicture}
\node [mybox] (box){%
\begin{minipage}{0.3\textwidth}
$I=\frac{V}{R}=\frac{\Delta q}{\Delta t}=\frac{dq}{dt}=JA=\int \vec{J}\cdot\vec{A}$\\
$v_d=\frac{I}{nAe}=\frac{J}{ne}=a\tau=\frac{eE\lambda}{m}$\\
$R=\rho\frac{L}{A}$, $\rho=\frac{E}{J}=\frac{1}{\sigma}=\frac{m_e}{ne^2\tau}$, $\vec{J}=\sigma \vec{E}=-ne\vec{v}_d$\\
$R_s=R_1+R_2+...+R_n=\sum_i^nR_i$\\
$R_p=1/R_1+1/R_2+...+1/R_n=(\sum_i^n\frac{1}{R_i})^{-1}$\\
$P=IV=I^2R=\frac{V^2}{R}=\frac{dU}{dt}$, $dU=dqV_{ab}=IdtV_{ab}$\\
\end{minipage}
};
%---------------------------------
\node[fancytitle, right=10pt] at (box.north west) {Corriente};
\end{tikzpicture}
%\bigskip\\
%---------------------------
\begin{tikzpicture}
\node [mybox] (box){%
\begin{minipage}{0.3\textwidth}
$F=\frac{\mu_o}{2\Pi}\frac{qvI}{r}$\\
$\vec{F}=q\vec{v}\times\vec{B}$,$F=qvBsen\theta$\\
$B=\frac{\mu_oI}{2\pi r}$\\
$\vec{F}=q\vec{E}+q\vec{v}\times\vec{B}$\\
$B=n\mu_oI$\\
$\vec{F}=i\vec{l}\times\vec{B}$
\end{minipage}
};
%---------------------------------
\node[fancytitle, right=10pt] at (box.north west) {Fuentes Campo Magnético};
\end{tikzpicture}
\bigskip\\
%---------------------------------
\begin{tikzpicture}
\node [mybox] (box){%
\begin{minipage}{0.3\textwidth}
\nc{Biot-Savart}
$d\vec{B}=\frac{\mu_o}{4\pi}\frac{Id\vec{l}\times\vec{r}}{r^3}$\\
$B=\frac{\mu_oI}{4\pi R^2}\Delta l_{arco}$\\
$B=\frac{\mu_oI}{4\pi R}(cos\theta_1-cos\theta_2)$\\
\nc{Cargas en Movimiento}\\
$r=\frac{mv}{qB}$\\
$a=\frac{qvB}{m}=\frac{v^2}{r}$
\end{minipage}
};
%---------------------------------
\node[fancytitle, right=10pt] at (box.north west) {Cargas en Movimiento con Presencia de Campos};
\end{tikzpicture}
\bigskip\\
\end{multicols*}
\end{document}