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--- /dev/null
+++ b/Homework/phys2210/Physics-II-Lab/capacitors.png
diff --git a/Homework/phys2210/Physics-II-Lab/circuit_report.org b/Homework/phys2210/Physics-II-Lab/circuit_report.org
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+#+TITLE: Building an RC Circuit
+#+AUTHOR: Lizzy Hunt
+#+STARTUP: entitiespretty fold inlineimages
+#+LATEX_HEADER:  \usepackage{ dsfont } \usepackage{amsmath} \usepackage[a4paper,margin=1in,portrait]{geometry}
+#+LATEX: 
+#+OPTIONS: toc:nil
+
+* The Experiment
+The purpose of this experiment was to gain a better understanding of the effects on the voltage over a capacitor
+as a time-valued function when put in a circuit in series with a resistor. To achieve
+this goal - and to experimentally verify laws governing the total resistance and capacitance of
+configurations of resistors and capacitors using a multimeter - we built an "RC circuit" by combining
+resistors and capacitors from respective smaller-valued components.
+
+Additionally, this lab fulfilled the requirement allowing us to play with dangerously high temperature metal equipment \smiley.
+
+** Theory
+Here we list some ideas the reader should be familiar with for reference later in the report.
+
+*** Resistors
+Consider $n$ resistors, $r_i \ni i \in [1, n]$ representing the total resistance of the i^{th} resistor,
+or sub-configuration of resistors, all in parallel. Then, the total resistance, R, of the group is:
+
+\begin{equation}
+R^{-1} = \sum_{i=1}^{n}(r_i)^{-1}
+\end{equation}
+
+Consider $n$ resistors, $r_i \ni i \in [0, n]$ representing the total resistance of the i^{th} resistor,
+or sub-configuration of resistors, all in series. Then, the total resistance, R, of the group is:
+
+\begin{equation}
+R = \sum_{i=1}^{n}(r_i)
+\end{equation}
+
+*** Capacitors
+Total capacitance of configurations of capacitors are similar to the inversion of the laws for
+resistors.
+
+Consider $n$ capacitors, $c_i \ni i \in [1, n]$ representing the total capacitor of the i^{th} capacitor,
+or sub-configuration of capacitors, all in series. Then, the total capacitance, C, of the group is:
+
+\begin{equation}
+C^{-1} = \sum_{i=1}^{n }(c_i)^{-1}
+\end{equation}
+
+Consider $n$ capacitors, $c_i \ni i \in [1, n]$ representing the total capacitor of the i^{th} capacitor,
+or sub-configuration of capacitors, all in parallel. Then, the total capacitance, C, of the group is:
+
+\begin{equation}
+C = \sum_{i=1}^{n }(c_i)
+\end{equation}
+
+*** The RC Circuit
+For a circuit with a resistor of resistance $R$ and capacitor with capacitance $C$ in series,
+we can model the voltage over the capacitor, $V_C$, given an initial voltage $V_0$ and final
+voltage $V_f$, as a function of time:
+
+\begin{equation}
+V_C(t) = (V_0 - V_f)e^{-\frac{t}{RC}} + V_f
+\end{equation}
+
+** Procedure
+
+The given procedure to exercise our knowledge of equations (1) - (4) if to build both a relatively higher-valued
+resistor, and capacitor, out of smaller-valued components - by soldering them in series / parallel configurations.
+
+Each pair of students is to produce a resistor and capacitor at a target value (and with a 10% margin for error),
+determined by seating arrangement. By happenstance, our group was chosen to build:
+
+1. A 22 kilo-ohm resistor (22 $k \Omega$)
+2. A 1.67 micro-farad capacitor ($\mu F$)
+
+out of only 10 $k \Omega$ resistors, and 1 $\mu F$ capacitors.
+
+I did not record the configuration we used for either. So, assume the following configurations throughout the rest of the lab (pretty sure
+these were pretty close to our monstrosities):
+
+*** Building a Resistor
+Assume all resistors as $10 k \Omega$
+#+attr_latex: :width 240px
+[[./resistors.png]]
+
+In theory, the total resistance measured from the leftmost point to the rightmost is 22 $k \Omega$:
+
+\begin{align*}
+R  &= 10^4 \text{ (leftmost resistor in series (2))} \\
+   &+ 10^4 \text{ (second leftmost resistor in series (2))} \\
+   &+ (\frac{5}{10^4})^{-1} \text{ (5 resistors in parallel (1))} \\
+   &= 2.20 * 10^4 \Omega
+\end{align*}
+
+*** Building a Capacitor
+#+attr_latex: :width 200px
+[[./capacitors.png]]
+
+In theory, the total capacitance measured from the leftmost point to the rightmost is 1.67 $\mu F$:
+
+\begin{align*}
+C  &= 2(\frac{3}{10^-6})^{-1} \text{ (two groups of 3 1-}\mu F \text{ capacitors in series (3) in parallel with) } \\
+   &+ 10^{-6} \text{ (another 1-} \mu F \text{ capacitor (4)) } \\
+   &\approx 1.67 * 10^{-6} F
+\end{align*}
+
+*** Determining the $RC$ constant
+
+To measure our $RC$ constant, we connected two voltage probes over $V_c$ (as shown in the diagram below) to a computer-generated
+positive square wave oscillating at 0.50 Hz with an amplitude of 5V. We then record for 1.5 seconds, polling at 1 kHz, from
+the time $V_C$ is at 4.95 V (the capacitor has charged) - allowing us to record at least half a second of discharge
+from the capacitor.
+
+#+attr_latex: :width 200px
+[[./total_circuit.png]]
+
+We expect to see that as it discharges, the measured voltage over the capacitor would follow an exponentially decreasing fit,
+according to the $-\frac{t}{RC}$ term in (5). To find the value of $RC$ we measure the voltage at each discrete time step ($\frac{1}{1000}$ of a second)
+from near the beginning of the exponential drop to where it reaches stability, and copy those values into a Magic Excel Sheet^{TM}. This
+region is somewhat shown in the figure below (some values are actually truncated):
+
+#+attr_latex: :width 200px
+[[./rc-discharge.png]]
+
+The Magic Excel Sheet^{TM} produces a good exponential fit to this data. But, it takes some manual fiddling with the $RC$ value itself
+to determine the minimum sum of residuals (gradient descent inspired guess and check). The value of $RC$
+producing the lowest error by this measure, is our result.
+
+* Results
+** Building a Resistor
+
+The measured resistance (via multimeter) we obtained from our resistor was $21.68 k \Omega$.
+
+** Building a Capacitor
+
+The measured capacitance (via multimeter) we obtained from our resistor was $1.78 \mu F$.
+
+** The Value Of $RC$
+
+ For our computer determined RC constant, we found it to be $3.72 * 10^{-2}$ s.
+
+* Discussion
+** Building a Resistor
+Our target value was $22.00 k \Omega$, and we came out with $21.68 k \Omega$ - an error of 1.45%.
+
+** Building a Capacitor
+Our target value was $1.67 \mu F$, and we came out with $1.78 \mu F$ - an error of 6.59%.
+
+** The Value of $RC$
+If our resistor and capacitor were exactly on the target value, our $RC$ constant would be $(2.20 * 10^4 \Omega)(1.67 * 10^{-6} F) = 3.67 * 10^{-2}$ s.
+
+The $RC$ constant from the measured resistance and capacitance would be $(2.17 * 10^4 \Omega)(1.78 * 10^{-6} F) = 3.86 * 10^-2$ s.
+
+But, our human-gradient-descent-plus-excel-magic-thanks-computer told us it was $3.72 * 10^{-2}$ s - a 3.62% error from the
+theoretical measured value, and 1.36% from the overall "target" value.
diff --git a/Homework/phys2210/Physics-II-Lab/circuit_report.pdf b/Homework/phys2210/Physics-II-Lab/circuit_report.pdf
new file mode 100644
index 0000000..59214ee
--- /dev/null
+++ b/Homework/phys2210/Physics-II-Lab/circuit_report.pdf
diff --git a/Homework/phys2210/Physics-II-Lab/circuit_report.tex b/Homework/phys2210/Physics-II-Lab/circuit_report.tex
new file mode 100644
index 0000000..e1007c9
--- /dev/null
+++ b/Homework/phys2210/Physics-II-Lab/circuit_report.tex
@@ -0,0 +1,198 @@
+% Created 2023-03-22 Wed 18:57
+% 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}
+\author{Lizzy Hunt}
+\date{\today}
+\title{Building an RC Circuit}
+\hypersetup{
+ pdfauthor={Lizzy Hunt},
+ pdftitle={Building an RC Circuit},
+ pdfkeywords={},
+ pdfsubject={},
+ pdfcreator={Emacs 28.2 (Org mode 9.6.1)}, 
+ pdflang={English}}
+\begin{document}
+
+\maketitle
+
+\section{The Experiment}
+\label{sec:orgd0521b4}
+The purpose of this experiment was to gain a better understanding of the effects on the voltage over a capacitor
+as a time-valued function when put in a circuit in series with a resistor. To achieve
+this goal - and to experimentally verify laws governing the total resistance and capacitance of
+configurations of resistors and capacitors using a multimeter - we built an "RC circuit" by combining
+resistors and capacitors from respective smaller-valued components.
+
+Additionally, this lab fulfilled the requirement allowing us to play with dangerously high temperature metal equipment \(\ddot\smile\).
+
+\subsection{Theory}
+\label{sec:orgcbdcb4a}
+Here we list some ideas the reader should be familiar with for reference later in the report.
+
+\subsubsection{Resistors}
+\label{sec:orga13127c}
+Consider \(n\) resistors, \(r_i \ni i \in [1, n]\) representing the total resistance of the i\textsuperscript{th} resistor,
+or sub-configuration of resistors, all in parallel. Then, the total resistance, R, of the group is:
+
+\begin{equation}
+R^{-1} = \sum_{i=1}^{n}(r_i)^{-1}
+\end{equation}
+
+Consider \(n\) resistors, \(r_i \ni i \in [0, n]\) representing the total resistance of the i\textsuperscript{th} resistor,
+or sub-configuration of resistors, all in series. Then, the total resistance, R, of the group is:
+
+\begin{equation}
+R = \sum_{i=1}^{n}(r_i)
+\end{equation}
+
+\subsubsection{Capacitors}
+\label{sec:org20ad8ce}
+Total capacitance of configurations of capacitors are similar to the inversion of the laws for
+resistors.
+
+Consider \(n\) capacitors, \(c_i \ni i \in [1, n]\) representing the total capacitor of the i\textsuperscript{th} capacitor,
+or sub-configuration of capacitors, all in series. Then, the total capacitance, C, of the group is:
+
+\begin{equation}
+C^{-1} = \sum_{i=1}^{n }(c_i)^{-1}
+\end{equation}
+
+Consider \(n\) capacitors, \(c_i \ni i \in [1, n]\) representing the total capacitor of the i\textsuperscript{th} capacitor,
+or sub-configuration of capacitors, all in parallel. Then, the total capacitance, C, of the group is:
+
+\begin{equation}
+C = \sum_{i=1}^{n }(c_i)
+\end{equation}
+
+\subsubsection{The RC Circuit}
+\label{sec:orgcf7b1ec}
+For a circuit with a resistor of resistance \(R\) and capacitor with capacitance \(C\) in series,
+we can model the voltage over the capacitor, \(V_C\), given an initial voltage \(V_0\) and final
+voltage \(V_f\), as a function of time:
+
+\begin{equation}
+V_C(t) = (V_0 - V_f)e^{-\frac{t}{RC}} + V_f
+\end{equation}
+
+\subsection{Procedure}
+\label{sec:org107e08f}
+
+The given procedure to exercise our knowledge of equations (1) - (4) if to build both a relatively higher-valued
+resistor, and capacitor, out of smaller-valued components - by soldering them in series / parallel configurations.
+
+Each pair of students is to produce a resistor and capacitor at a target value (and with a 10\% margin for error),
+determined by seating arrangement. By happenstance, our group was chosen to build:
+
+\begin{enumerate}
+\item A 22 kilo-ohm resistor (22 \(k \Omega\))
+\item A 1.67 micro-farad capacitor (\(\mu F\))
+\end{enumerate}
+
+out of only 10 \(k \Omega\) resistors, and 1 \(\mu F\) capacitors.
+
+I did not record the configuration we used for either. So, assume the following configurations throughout the rest of the lab (pretty sure
+these were pretty close to our monstrosities):
+
+\subsubsection{Building a Resistor}
+\label{sec:orga374597}
+Assume all resistors as \(10 k \Omega\)
+\begin{center}
+\includegraphics[width=240px]{./resistors.png}
+\end{center}
+
+In theory, the total resistance measured from the leftmost point to the rightmost is 22 \(k \Omega\):
+
+\begin{align*}
+R  &= 10^4 \text{ (leftmost resistor in series (2))} \\
+   &+ 10^4 \text{ (second leftmost resistor in series (2))} \\
+   &+ (\frac{5}{10^4})^{-1} \text{ (5 resistors in parallel (1))} \\
+   &= 2.20 * 10^4 \Omega
+\end{align*}
+
+\subsubsection{Building a Capacitor}
+\label{sec:orgc015c61}
+\begin{center}
+\includegraphics[width=200px]{./capacitors.png}
+\end{center}
+
+In theory, the total capacitance measured from the leftmost point to the rightmost is 1.67 \(\mu F\):
+
+\begin{align*}
+C  &= 2(\frac{3}{10^-6})^{-1} \text{ (two groups of 3 1-}\mu F \text{ capacitors in series (3) in parallel with) } \\
+   &+ 10^{-6} \text{ (another 1-} \mu F \text{ capacitor (4)) } \\
+   &\approx 1.67 * 10^{-6} F
+\end{align*}
+
+\subsubsection{Determining the \(RC\) constant}
+\label{sec:org1d0608b}
+
+To measure our \(RC\) constant, we connected two voltage probes over \(V_c\) (as shown in the diagram below) to a computer-generated
+positive square wave oscillating at 0.50 Hz with an amplitude of 5V. We then record for 1.5 seconds, polling at 1 kHz, from
+the time \(V_C\) is at 4.95 V (the capacitor has charged) - allowing us to record at least half a second of discharge
+from the capacitor.
+
+\begin{center}
+\includegraphics[width=200px]{./total_circuit.png}
+\end{center}
+
+We expect to see that as it discharges, the measured voltage over the capacitor would follow an exponentially decreasing fit,
+according to the \(-\frac{t}{RC}\) term in (5). To find the value of \(RC\) we measure the voltage at each discrete time step (\(\frac{1}{1000}\) of a second)
+from near the beginning of the exponential drop to where it reaches stability, and copy those values into a Magic Excel Sheet\textsuperscript{TM}. This
+region is somewhat shown in the figure below (some values are actually truncated):
+
+\begin{center}
+\includegraphics[width=200px]{./rc-discharge.png}
+\end{center}
+
+The Magic Excel Sheet\textsuperscript{TM} produces a good exponential fit to this data. But, it takes some manual fiddling with the \(RC\) value itself
+to determine the minimum sum of residuals (gradient descent inspired guess and check). The value of \(RC\)
+producing the lowest error by this measure, is our result.
+
+\section{Results}
+\label{sec:orgf43daaa}
+\subsection{Building a Resistor}
+\label{sec:org99028c5}
+
+The measured resistance (via multimeter) we obtained from our resistor was \(21.68 k \Omega\).
+
+\subsection{Building a Capacitor}
+\label{sec:org21807f6}
+
+The measured capacitance (via multimeter) we obtained from our resistor was \(1.78 \mu F\).
+
+\subsection{The Value Of \(RC\)}
+\label{sec:orgbc9c601}
+
+For our computer determined RC constant, we found it to be \(3.72 * 10^{-2}\) s.
+
+\section{Discussion}
+\label{sec:org8408366}
+\subsection{Building a Resistor}
+\label{sec:org9b4e64e}
+Our target value was \(22.00 k \Omega\), and we came out with \(21.68 k \Omega\) - an error of 1.45\%.
+
+\subsection{Building a Capacitor}
+\label{sec:orgf2e0c7e}
+Our target value was \(1.67 \mu F\), and we came out with \(1.78 \mu F\) - an error of 6.59\%.
+
+\subsection{The Value of \(RC\)}
+\label{sec:org7e41eff}
+If our resistor and capacitor were exactly on the target value, our \(RC\) constant would be \((2.20 * 10^4 \Omega)(1.67 * 10^{-6} F) = 3.67 * 10^{-2}\) s.
+
+The \(RC\) constant from the measured resistance and capacitance would be \((2.17 * 10^4 \Omega)(1.78 * 10^{-6} F) = 3.86 * 10^-2\) s.
+
+But, our human-gradient-descent-plus-excel-magic-thanks-computer told us it was \(3.72 * 10^{-2}\) s - a 3.62\% error from the
+theoretical measured value, and 1.36\% from the overall "target" value.
+\end{document}
\ No newline at end of file
diff --git a/Homework/phys2210/Physics-II-Lab/eq.org b/Homework/phys2210/Physics-II-Lab/eq.org
new file mode 100644
index 0000000..9f715ef
--- /dev/null
+++ b/Homework/phys2210/Physics-II-Lab/eq.org
@@ -0,0 +1,51 @@
+#+STARTUP: entitiespretty fold inlineimages
+#+LATEX_HEADER:  \usepackage{ dsfont } \usepackage{amsmath} \usepackage[a4paper,margin=1in,portrait]{geometry}
+#+LATEX: 
+#+OPTIONS: toc:nil
+
+* a
+** 26
+*** B from x_{dist} On axis of a current loop of radius a
+$B = \frac{\mu_0 I a^2}{2(x_{dist}_{}^2 + a^2)^{3/2}}$
+
+
+*** B on axis from magnetic dipole
+$B = \frac{\mu_0}{2 \pi} \frac{\mu}{x^3}$
+
+
+*** Net Torque on closed loop with area A at orientation \theta
+$\tau = I A B \text{sin}(\theta)$
+
+
+*** Field outside, inside any current distribution with line symmetry
+$B = \frac{\mu_0 I}{2 \pi r}$
+
+$B = \frac{\mu_0 I r_{inside}}{2 \pi R_{outside}^2}$
+
+*** Sheet with uniform current density J
+*** Solenoid with turns n per unit length
+
+** 27
+*** Flux through solenoid with n turns per unit length
+$\phi_B = BA = \mu_0 n I \pi R^2$
+
+
+*** Flux through rectangular loop with $l$ parallel to wire at distance $a$
+
+$\phi_B = \int B dA = \int_{a}^{a+w} \frac{\mu_0 I}{2 \pi r} l dr = \frac{\mu_0 I l}{2 \pi} \text{ln}(\frac{a+w}{a})$
+
+
+*** Induced current through circuit with bars at distance $l$ and moving bar velocity $v$
+$I = \frac{Blv} {r}$
+
+*** Flux through coil with $N$ turns turning at frequency $f$ in field $B$
+$\phi_B = N B \pi r^2 \text{cos}(2 \pi f t)$
+
+$E = - \frac{d \phi_B}{dt}$
+
+*** Inductance of a solenoid
+$L = \frac{\phi_B}{I} = \mu_0 n^2 A l$
+
+*** Electric field of a solenoid of radius $R$ at loop radius $r$ with $B = bt$
+$E = \frac{R^2 b}{2r}$
+
diff --git a/Homework/phys2210/Physics-II-Lab/eq.pdf b/Homework/phys2210/Physics-II-Lab/eq.pdf
new file mode 100644
index 0000000..b9b3f4b
--- /dev/null
+++ b/Homework/phys2210/Physics-II-Lab/eq.pdf
diff --git a/Homework/phys2210/Physics-II-Lab/eq.tex b/Homework/phys2210/Physics-II-Lab/eq.tex
new file mode 100644
index 0000000..2db7548
--- /dev/null
+++ b/Homework/phys2210/Physics-II-Lab/eq.tex
@@ -0,0 +1,87 @@
+% 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}
\ No newline at end of file
diff --git a/Homework/phys2210/Physics-II-Lab/rc-discharge.png b/Homework/phys2210/Physics-II-Lab/rc-discharge.png
new file mode 100644
index 0000000..307c5ed
--- /dev/null
+++ b/Homework/phys2210/Physics-II-Lab/rc-discharge.png
diff --git a/Homework/phys2210/Physics-II-Lab/resistors.png b/Homework/phys2210/Physics-II-Lab/resistors.png
new file mode 100644
index 0000000..c08f4ed
--- /dev/null
+++ b/Homework/phys2210/Physics-II-Lab/resistors.png
diff --git a/Homework/phys2210/Physics-II-Lab/total_circuit.png b/Homework/phys2210/Physics-II-Lab/total_circuit.png
new file mode 100644
index 0000000..8a1514d
--- /dev/null
+++ b/Homework/phys2210/Physics-II-Lab/total_circuit.png