From: Andrew Lorimer Date: Mon, 18 Jun 2018 11:25:18 +0000 (+1000) Subject: finish fields notes X-Git-Tag: yr11~94 X-Git-Url: https://git.lorimer.id.au/notes.git/diff_plain/048a03720f2e0505042ffddc007440f3a5a46801?ds=inline finish fields notes --- diff --git a/physics/fields.aux b/physics/fields.aux new file mode 100644 index 0000000..f23e546 --- /dev/null +++ b/physics/fields.aux @@ -0,0 +1 @@ +\relax diff --git a/physics/fields.fdb_latexmk b/physics/fields.fdb_latexmk new file mode 100644 index 0000000..53e3039 --- /dev/null +++ b/physics/fields.fdb_latexmk @@ -0,0 +1,64 @@ +# Fdb version 3 +["pdflatex"] 1529320655 "fields.tex" "fields.pdf" "fields" 1529320656 + "/mnt/andrew/graphics/ac-generator.png" 1529320281 28991 f74a831edcaed66632e709a6b2e2ebfd "" + "/mnt/andrew/graphics/ac-motor.png" 1529313736 18626 d0f4943be26fdce44a4ce45ccb01633c "" + "/mnt/andrew/graphics/dc-motor-2.png" 1529320688 53769 fc78422983cc0333d421ae3c4a8e8e14 "" + "/mnt/andrew/graphics/field-lines.png" 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5000i,500n,10000p,200000b,80000s + +Output written on fields.pdf (1 page, 212033 bytes). +PDF statistics: + 51 PDF objects out of 1000 (max. 8388607) + 32 compressed objects within 1 object stream + 0 named destinations out of 1000 (max. 500000) + 21 words of extra memory for PDF output out of 10000 (max. 10000000) + diff --git a/physics/fields.pdf b/physics/fields.pdf new file mode 100644 index 0000000..8f1fe4b Binary files /dev/null and b/physics/fields.pdf differ diff --git a/physics/fields.tex b/physics/fields.tex new file mode 100644 index 0000000..67d0bc0 --- /dev/null +++ b/physics/fields.tex @@ -0,0 +1,136 @@ + + +\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}