From 6bf4b90c90f15f4ab60833bddf5b5756d1a6b1f6 Mon Sep 17 00:00:00 2001
From: Elizabeth Alexander Hunt <me@liz.coffee>
Date: Thu, 2 Jul 2026 11:55:17 -0700
Subject: Init

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 Homework/phys2210/Physics-II-Lab/eq.tex | 87 +++++++++++++++++++++++++++++++++
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+% Created 2023-03-22 Wed 13:37
+% Intended LaTeX compiler: pdflatex
+\documentclass[11pt]{article}
+\usepackage[utf8]{inputenc}
+\usepackage[T1]{fontenc}
+\usepackage{graphicx}
+\usepackage{longtable}
+\usepackage{wrapfig}
+\usepackage{rotating}
+\usepackage[normalem]{ulem}
+\usepackage{amsmath}
+\usepackage{amssymb}
+\usepackage{capt-of}
+\usepackage{hyperref}
+\usepackage{ dsfont } \usepackage{amsmath} \usepackage[a4paper,margin=1in,portrait]{geometry}
+\date{\today}
+\title{}
+\hypersetup{
+ pdfauthor={},
+ pdftitle={},
+ pdfkeywords={},
+ pdfsubject={},
+ pdfcreator={Emacs 28.2 (Org mode 9.6.1)}, 
+ pdflang={English}}
+\begin{document}
+
+
+
+\section{26}
+\label{sec:orgf4c4750}
+\subsection{B from x\textsubscript{dist} On axis of a current loop of radius a}
+\label{sec:org00b53ee}
+\(B = \frac{\mu_0 I a^2}{2(x_{dist}_{}^2 + a^2)^{3/2}}\)
+
+
+\subsection{B on axis from magnetic dipole}
+\label{sec:org6813b5a}
+\(B = \frac{\mu_0}{2 \pi} \frac{\mu}{x^3}\)
+
+
+\subsection{Net Torque on closed loop with area A at orientation \(\theta\)}
+\label{sec:org0128423}
+\(\tau = I A B \text{sin}(\theta)\)
+
+
+\subsection{Field outside, inside any current distribution with line symmetry}
+\label{sec:orge95f90c}
+\(B = \frac{\mu_0 I}{2 \pi r}\)
+
+\(B = \frac{\mu_0 I r_{inside}}{2 \pi R_{outside}^2}\)
+
+\subsection{Sheet with uniform current density J}
+\label{sec:orge9e2a8c}
+\subsection{Solenoid with turns n per unit length}
+\label{sec:org1db4f9c}
+
+\section{27}
+\label{sec:org95cec61}
+\subsection{Flux through solenoid with n turns per unit length}
+\label{sec:orgdb8f31e}
+\(\phi_B = BA = \mu_0 n I \pi R^2\)
+
+
+\subsection{Flux through rectangular loop with \(l\) parallel to wire at distance \(a\)}
+\label{sec:org046d4b3}
+
+\(\phi_B = \int B dA = \int_{a}^{a+w} \frac{\mu_0 I}{2 \pi r} l dr = \frac{\mu_0 I l}{2 \pi} \text{ln}(\frac{a+w}{a})\)
+
+
+\subsection{Induced current through circuit with bars at distance \(l\) and moving bar velocity \(v\)}
+\label{sec:org865a9be}
+\(I = \frac{Blv} {r}\)
+
+\subsection{Flux through coil with \(N\) turns turning at frequency \(f\) in field \(B\)}
+\label{sec:org252abf7}
+\(\phi_B = N B \pi r^2 \text{cos}(2 \pi f t)\)
+
+\(E = - \frac{d \phi_B}{dt}\)
+
+\subsection{Inductance of a solenoid}
+\label{sec:orgf5ed5cf}
+\(L = \frac{\phi_B}{I} = \mu_0 n^2 A l\)
+
+\subsection{Electric field of a solenoid of radius \(R\) at loop radius \(r\) with \(B = bt\)}
+\label{sec:org5396fcb}
+\(E = \frac{R^2 b}{2r}\)
+\end{document}
\ No newline at end of file
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