blob: 2db754890d53a49647885c0024d18941e88260fb (
plain) (
blame)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
|
% 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}
|
