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+
+\documentclass[a4paper,landscape]{article}
+
+\usepackage[a4paper,landscape]{geometry}
+\usepackage{multicol}
+\usepackage[cm]{fullpage}
+\usepackage{amsmath}
+\setlength{\parindent}{0cm}
+\usepackage[nodisplayskipstretch]{setspace}
+\setstretch{1.5}
+\usepackage{graphicx}
+\usepackage{wrapfig}
+
+
+\begin{document}
+
+\pagenumbering{gobble}
+\begin{multicols}{3}
+
+ {\huge Fields}\hfill Andrew Lorimer\hspace{2em}
+
+\section*{Non-contact forces}
+\begin{itemize}
+\item electric fields (dipoles \& monopoles)
+\item magnetic fields (dipoles only)
+\item gravitational fields (monopoles only)
+\end{itemize}
+
+\begin{itemize}
+\item monopoles: field lines radiate towards central object
+\item dipoles - field lines go from + to -, or N to S
+\item closer field lines means larger force
+\item dot means out of page, cross means into page
+\end{itemize}
+
+\section*{Gravity}
+\[
+F_g=G{{m_1m_2}\over r^2}\tag{grav. force}
+\]
+
+\[
+g={F_g \over m}=G{M_{\operatorname{planet}} \over r^2}\tag{grav. acceleration}
+\]
+
+\[
+E_g = mg \Delta h\tag{grav. potential energy}
+\]
+
+\[
+W = \Delta E_g = Fx\tag{work}
+\]
+
+Area under force-distance graph = $\Delta G.P.E$
+
+Area under field-distance graph = $\Delta G.P.E / \operatorname{kg}$
+
+% \columnbreak
+
+\section*{Magnetic fields}
+% \begin{itemize}
+% \item field strength $B$ measured in tesla
+% \item magnetic flux $\Phi$ measured in weber
+% \item charge $q$ measured in coulombs
+% \item emf $\mathcal{E}$ measured in volts
+% \end{itemize}
+
+% \[
+% {E_1 \over E_2}={r_1 \over r_2}^2
+% \]
+
+\[
+F=qvB\tag{force on moving charged particles}
+\]
+
+if $B {\not \perp} A, \Phi \rightarrow 0$ \hspace{1em}, \hspace{1em} if $B \parallel A, \Phi = 0$
+
+
+\includegraphics[height=3cm]{/mnt/andrew/graphics/field-lines.png}
+
+\section*{Electric fields}
+
+\begin{align*}
+F=qE \tag{force on particle - $E$ is field strength} \\
+W=q_{\operatorname{point}}\Delta V \tag{work in field or points} \\
+F=k{{q_1q_2}\over r^2}\tag{Coulomb - force between particles} \\
+E=k{Q \over r^2} \tag{field at distance from charge} \\
+F=BInl \tag{force on a coil} \\
+\Phi = B_{\perp}A\tag{magnetic flux} \\
+\mathcal{E} = -N{{\Delta \Phi}\over{\Delta t}} \tag{Faraday - induced emf} \\
+{V_p \over V_s}={N_p \over N_s}={I_s \over I_p} \tag{xfmr coil ratios} \\
+\end{align*}
+
+
+\textbf{Lenz's law:} ``$-n$'' in Faraday - emf opposes $\Delta \Phi$
+
+\textbf{Eddy currents:} counter movement within a field
+
+\textbf{Right hand grip:} thumb points to north or $I$
+
+\textbf{Right hand slap:} field, current, force are $\perp$
+
+\textbf{Flux-time graphs:} gradient $\times n = \operatorname{emf}$
+
+\textbf{Transformers:} core strengthens \& focuses $\Phi$
+
+% \columnbreak
+
+\section*{Power transmission}
+
+\begin{align*}
+ V_{\operatorname{rms}}={V_{\operatorname{p\rightarrow p}}\over \sqrt{2}} \tag{rms to peak $\rightarrow$ peak} \\
+ P_{\operatorname{loss}} = \Delta V I = I^2 R = {{\Delta V^2} \over R} \tag{power loss}
+\end{align*}
+
+\includegraphics[height=4cm]{/mnt/andrew/graphics/ac-generator.png}
+
+\section*{Motors}
+% \begin{wrapfigure}{r}{-0.1\textwidth}
+
+\includegraphics[height=4cm]{/mnt/andrew/graphics/dc-motor-2.png}
+\includegraphics[height=3cm]{/mnt/andrew/graphics/ac-motor.png} \\
+% \end{wrapfigure}
+\textbf{DC:} split ring (one ring split into two halves)
+
+% \begin{wrapfigure}{r}{0.3\textwidth}
+
+% \end{wrapfigure}
+\textbf{AC:} slip ring (separate rings with constant contact)
+
+
+
+
+
+\end{multicols}
+\end{document}