用latex排版电磁场课程报告

一、预览结果

二、处理一些细节

1.使用tikz绘图

\usepackage{tikz}\begin{tikzpicture} \draw[dashed] (0,0) circle [radius&＃61;1.5];\draw[thick] (0,0) circle [radius&＃61;2.5];\draw[dash dot dot] (-4,0) -- (4,0);\draw[-latex][very thick] (0,0) node[below] {$O$} -- node[above] {$a$} (-1,0) node[above] {$q$} ;\fill (-1,0) circle[radius&＃61;2pt]; \draw[-latex][very thick] (0,0) -- node[above left] {$b$} (1.061,1.061); \draw[latex-latex][very thick] (1.061,1.061) -- node[above left] {$b$} (1.768,1.768); \coordinate (S1) at (-1.768,-1.768); \draw[thick] (S1) -- (-1.768,-3.2328);\draw[thick] (-2.068,-3.2328) -- (-1.468,-3.2328);\draw[thick] (-1.968,-3.3328) -- (-1.568,-3.3328);\draw[thick] (-1.868,-3.4328) -- (-1.668,-3.4328);
\end{tikzpicture}


如图所示&＃xff1a;

\begin{tikzpicture}%插入分割线\draw[dashed][very thick] (0,0)--(14.64,0);
\end{tikzpicture}


2.插入emoji表情

The emoji package allows user to typeset emoji in a LaTeX document. It requires LuaHBTeX: in TEX Live 2020, lualatex will base on this new engine; but in TEX Live 2019, only lualatex-dev can be used to compile.

选项->设置TexStudio…

\usepackage{emoji}\emoji{&＃43;1}
\emoji{joy}


三、完整代码

\documentclass[a4paper,12pt]{article}\usepackage{ctex}
\usepackage{tikz}
\usepackage{geometry}
\usepackage{emoji}
\geometry{left&＃61;3.18cm,right&＃61;3.18cm,top&＃61;2.54cm,bottom&＃61;2.54cm}
\title{2021秋《电磁场》课程EE2003课程报告}
\author{姓名&＃xff1a;猫九 学号:11111111 19级搬砖类}\begin{document}
\maketitle
\begin{center}\begin{tikzpicture}\draw[dashed][very thick] (0,0)--(14.64,0);\end{tikzpicture}
\end{center}
\noindent \textbf{例1-13}一点电荷$q$放置在内表面半径为$b$&＃xff0c;厚度为$c$的导体球壳内&＃xff0c;点电荷与球心的距离为$a$。分别求在球壳接地和不接地的两种情况下点电荷所受的力。\noindent \textbf{解&＃xff1a;} \noindent &＃xff08;1&＃xff09; 当球壳接地时&＃xff0c;如图所示:\begin{center}\begin{tikzpicture} \draw[dashed] (0,0) circle [radius&＃61;1.5];\draw[thick] (0,0) circle [radius&＃61;2.5];\draw[dash dot dot] (-4,0) -- (4,0);\draw[-latex][very thick] (0,0) node[below] {$O$} -- node[above] {$a$} (-1,0) node[above] {$q$} ;\fill (-1,0) circle[radius&＃61;2pt]; \draw[-latex][very thick] (0,0) -- node[above left] {$b$} (1.061,1.061); \draw[latex-latex][very thick] (1.061,1.061) -- node[above left] {$b$} (1.768,1.768); \coordinate (S1) at (-1.768,-1.768); \draw[thick] (S1) -- (-1.768,-3.2328);\draw[thick] (-2.068,-3.2328) -- (-1.468,-3.2328);\draw[thick] (-1.968,-3.3328) -- (-1.568,-3.3328);\draw[thick] (-1.868,-3.4328) -- (-1.668,-3.4328); \end{tikzpicture}
\end{center}\noindent 由于球壳接地&＃xff0c;所以球壳外的电场$E&＃61;0$ ,求点电荷所受的力时&＃xff0c;可以使用镜像法。由教材42页的例题可知&＃xff0c;点电荷附近接地导体球的影响&＃xff0c;可以由位于距离球心$b$处的镜像电荷$(-q^{&＃39;})$的来表示。\noindent 在本题中&＃xff0c;只需要求球壳内的电场强度。球壳的厚度$c$不产生影响。在球壳外距离球心$$d&＃61;\frac{R^2}{a}&＃61;\frac{b^2}{a}$$
处放置一个电荷&＃xff0c;如图所示$$
q^{\prime}&＃61;-\frac{d}{b}q&＃61;-\frac{b}{a}q
$$\begin{center}\begin{tikzpicture} \draw[dashed] (0,0) circle [radius&＃61;1.5];\draw[thick] (0,0) circle [radius&＃61;2.5];\draw[dash dot dot] (-4,0) -- (4,0);\draw[-latex][very thick] (0,0) node[below] {$O$} -- node[above] {$a$} (-1,0) node[above] {$q$} ;\fill (-1,0) circle[radius&＃61;2pt]; \draw[-latex][very thick] (0,0) -- node[above left] {$b$} (1.061,1.061); \draw[latex-latex][very thick] (1.061,1.061) -- node[above left] {$b$} (1.768,1.768); \coordinate (S1) at (-1.768,-1.768); \draw[thick] (S1) -- (-1.768,-3.2328);\draw[thick] (-2.068,-3.2328) -- (-1.468,-3.2328);\draw[thick] (-1.968,-3.3328) -- (-1.568,-3.3328);\draw[thick] (-1.868,-3.4328) -- (-1.668,-3.4328);\draw[red] (0,0) -- (0,-0.8); \fill (3,0) circle[radius&＃61;2pt]; \draw[red] (3,0) node[above][black] {$q^{&＃39;}$} -- (3,-0.8);\draw[latex-latex][very thick][red] (0,-0.5) -- node[below][black] {$d$} (3,-0.5); \end{tikzpicture}
\end{center}\noindent 该电荷位于球心和点电荷$q$的连线上。它对点电荷$q$的作用力就是球壳对点电荷$q$的作用力&＃xff0c;大小为
$$
F&＃61;\frac{q^{\prime}q}{4\pi \varepsilon _0\left( d-a \right) ^2}&＃61;-\frac{abq^2}{4\pi \varepsilon _0\left( b^2-a^2 \right) ^2}
$$
\noindent 其中负号表示两个电荷之间是异种电荷&＃xff0c;是吸引力。~\\
\noindent&＃xff08;2&＃xff09; 对于球壳不接地的情况&＃xff0c;球壳外表面产生的感应电荷在球壳内不产生电场&＃xff0c;球壳表面的感应电荷也可以用$(-q^{&＃39;})$来代替&＃xff0c;球壳内电场强度的分布不变。点电荷$q$受到的力和球壳接地时受到的力相同。~\\
\noindent \textbf{本题目考查知识点&＃xff1a;}
\begin{enumerate}\item[1.] \textbf{镜像法}求导体球面问题&＃xff0c;教材P42&＃xff0c;公式&＃xff08;1-78&＃xff09;\item[2.] 静电场的\textbf{唯一性定理}&＃xff0c;教材P28\item[3.] \textbf{库仑定律}
\end{enumerate}~\\\noindent \textbf{对本学期《 电磁场》课程及授课教师的意见和建议:}由老师上的《 电磁场》课程非常好&＃xff0c;由老师讲很课细致&＃xff0c;而且上课的过程中还讲述与课程相关的故事和自己的经历&＃xff0c;双语教学也让我们体验到了不一样的上课方式&＃xff0c;从电磁场这门课程中不仅学到了专业知识&＃xff0c;也领会到了其他的方方面面。由老师yyds&＃xff01;\emoji{&＃43;1}唯一遗憾的是最后几节课没有能在线下听由老师讲课&＃xff0c;以及之后不确定能不能在深圳再见到由老师。对于课程的建议&＃xff1a;希望教务部在排课程的时候不要一周排三节课&＃xff0c;感觉没开学几天就结课了,\emoji{joy},而且周五上两节电磁场课程比较难顶。\end{document}