Andrew's git - notes.git/blob - physics/fields.tex

   1
   2
   3\documentclass[a4paper,landscape]{article}
   4
   5\usepackage[a4paper,landscape]{geometry}
   6\usepackage{multicol}
   7\usepackage[cm]{fullpage}
   8\usepackage{amsmath}
   9\setlength{\parindent}{0cm}
  10\usepackage[nodisplayskipstretch]{setspace}
  11\setstretch{1.5}
  12\usepackage{graphicx}
  13\usepackage{wrapfig}
  14
  15
  16\begin{document}
  17
  18\pagenumbering{gobble}
  19\begin{multicols}{3}
  20
  21  {\huge Fields}\hfill Andrew Lorimer\hspace{2em}
  22
  23\section*{Non-contact forces}
  24\begin{itemize}
  25\item electric fields (dipoles \& monopoles)
  26\item magnetic fields (dipoles only)
  27\item gravitational fields (monopoles only)
  28\end{itemize}
  29
  30\begin{itemize}
  31\item monopoles: field lines radiate towards central object
  32\item dipoles - field lines go from + to -, or N to S
  33\item closer field lines means larger force
  34\item dot means out of page, cross means into page
  35\end{itemize}
  36
  37\section*{Gravity}
  38\[
  39F_g=G{{m_1m_2}\over r^2}\tag{grav. force}
  40\]
  41
  42\[
  43g={F_g \over m}=G{M_{\operatorname{planet}} \over r^2}\tag{grav. acceleration}
  44\]
  45
  46\[
  47E_g = mg \Delta h\tag{grav. potential energy}
  48\]
  49
  50\[
  51W = \Delta E_g = Fx\tag{work}
  52\]
  53
  54Area under force-distance graph = $\Delta G.P.E$
  55
  56Area under field-distance graph = $\Delta G.P.E / \operatorname{kg}$
  57
  58% \columnbreak
  59
  60\section*{Magnetic fields}
  61% \begin{itemize}
  62% \item field strength $B$ measured in tesla
  63% \item magnetic flux $\Phi$ measured in weber
  64% \item charge $q$ measured in coulombs
  65% \item emf $\mathcal{E}$ measured in volts
  66% \end{itemize}
  67
  68% \[
  69% {E_1 \over E_2}={r_1 \over r_2}^2
  70% \]
  71
  72\[
  73F=qvB\tag{force on moving charged particles}
  74\]
  75
  76if $B {\not \perp} A, \Phi \rightarrow 0$ \hspace{1em}, \hspace{1em} if $B \parallel A, \Phi = 0$
  77
  78
  79\includegraphics[height=3cm]{/mnt/andrew/graphics/field-lines.png}
  80
  81\section*{Electric fields}
  82
  83\begin{align*}
  84F=qE \tag{force on particle - $E$ is field strength} \\
  85W=q_{\operatorname{point}}\Delta V \tag{work in field or points} \\
  86F=k{{q_1q_2}\over r^2}\tag{Coulomb - force between particles} \\
  87E=k{Q \over r^2} \tag{field at distance from charge} \\
  88F=BInl \tag{force on a coil} \\
  89\Phi = B_{\perp}A\tag{magnetic flux} \\
  90\mathcal{E} = -N{{\Delta \Phi}\over{\Delta t}} \tag{Faraday - induced emf} \\
  91{V_p \over V_s}={N_p \over N_s}={I_s \over I_p} \tag{xfmr coil ratios} \\
  92\end{align*}
  93
  94
  95\textbf{Lenz's law:}  ``$-n$'' in Faraday - emf opposes $\Delta \Phi$
  96
  97\textbf{Eddy currents:} counter movement within a field
  98
  99\textbf{Right hand grip:} thumb points to north or $I$
 100
 101\textbf{Right hand slap:} field, current, force are $\perp$
 102
 103\textbf{Flux-time graphs:} gradient $\times n = \operatorname{emf}$
 104
 105\textbf{Transformers:} core strengthens \& focuses $\Phi$
 106
 107% \columnbreak
 108
 109\section*{Power transmission}
 110
 111\begin{align*}
 112  V_{\operatorname{rms}}={V_{\operatorname{p\rightarrow p}}\over \sqrt{2}} \tag{rms to peak $\rightarrow$ peak} \\
 113  P_{\operatorname{loss}} = \Delta V I = I^2 R = {{\Delta V^2} \over R} \tag{power loss}
 114\end{align*}
 115
 116\includegraphics[height=4cm]{/mnt/andrew/graphics/ac-generator.png}
 117
 118\section*{Motors}
 119% \begin{wrapfigure}{r}{-0.1\textwidth}
 120
 121\includegraphics[height=4cm]{/mnt/andrew/graphics/dc-motor-2.png}
 122\includegraphics[height=3cm]{/mnt/andrew/graphics/ac-motor.png} \\
 123% \end{wrapfigure}
 124\textbf{DC:} split ring (one ring split into two halves)
 125
 126% \begin{wrapfigure}{r}{0.3\textwidth}
 127
 128% \end{wrapfigure}
 129\textbf{AC:} slip ring (separate rings with constant contact)
 130
 131
 132
 133
 134
 135\end{multicols}
 136\end{document}