From 172638b10aec15ba32f2cfc385c2e2ee06b0d172 Mon Sep 17 00:00:00 2001
From: "W. Trevor King" <wking@drexel.edu>
Date: Fri, 21 Aug 2009 09:11:40 -0400
Subject: [PATCH] Working on rec9 solutions

---
 .../Young_and_Freedman_12/problem28.12.tex    | 60 +++++++++++++++++++
 .../Young_and_Freedman_12/problem28.18.tex    |  5 ++
 .../Young_and_Freedman_12/problem28.23.tex    |  5 ++
 .../Young_and_Freedman_12/problem28.30.tex    |  5 ++
 .../Young_and_Freedman_12/problem28.60.tex    |  5 ++
 .../Young_and_Freedman_12/problem28.62.tex    |  5 ++
 6 files changed, 85 insertions(+)
 create mode 100644 latex/problems/Young_and_Freedman_12/problem28.12.tex
 create mode 100644 latex/problems/Young_and_Freedman_12/problem28.18.tex
 create mode 100644 latex/problems/Young_and_Freedman_12/problem28.23.tex
 create mode 100644 latex/problems/Young_and_Freedman_12/problem28.30.tex
 create mode 100644 latex/problems/Young_and_Freedman_12/problem28.60.tex
 create mode 100644 latex/problems/Young_and_Freedman_12/problem28.62.tex

diff --git a/latex/problems/Young_and_Freedman_12/problem28.12.tex b/latex/problems/Young_and_Freedman_12/problem28.12.tex
new file mode 100644
index 0000000..4b0ce19
--- /dev/null
+++ b/latex/problems/Young_and_Freedman_12/problem28.12.tex
@@ -0,0 +1,60 @@
+\newcommand{\dB}{d\vect{B}}
+\newcommand{\dl}{d\vect{l}}
+\newcommand{\rhat}{\hat{r}}
+
+\begin{problem*}{28.12}
+
+\begin{center}
+\begin{asy}
+import Mechanics;
+import ElectroMag;
+
+real u = 0.1cm;
+real Ysep = 5u;
+real hypot = 8u;
+real Xsep = sqrt(hypot**2 - (Ysep/2)**2);
+real Xslush = 1u;
+
+Wire wtop_seg = Wire(
+Wire wtop = Wire((), (Xslush,Ysep/2));
+
+wtop.draw();
+wtop_seg.draw();
+\end{asy}
+\end{center}
+\end{problem*}
+
+\begin{solution}
+Using our right hand rules for current-created \vect{B} fields, we see
+that both segments create magnetic fields that are into the page at
+$P$, so the sum will also be directed \ans{into the page}.  To find
+the magnitude, we'll use the Biot-Savart law
+\begin{equation}
+  \dB = \frac{\mu_0}{4\pi}\cdot\frac{I\dl\times\rhat}{r^2}
+\end{equation}
+on both segments.  All of the components are given except for
+$\dl\times\rhat$.  Drawing a picture for the top segment
+\begin{center}
+\begin{asy}
+\end{asy}
+\end{center}
+Using our knowledge of cross products and trigonometry
+\begin{equation}
+  |\dl\times\rhat|=|\dl|\cdot|\rhat|\cdot\sin\theta
+    = 1.50\U{mm}\cdot1\cdot\sin\theta
+    = 1.50\U{mm}\cdot\frac{2.50\U{cm}}{8.00\U{cm}}
+    = 1.50\U{mm}\cdot\frac{2.50\U{cm}}{8.00\U{cm}}
+    = 4.6875\E{-4}\U{m} \;.
+\end{equation}
+It's also pretty clear that this cross product will have the same
+magnitude and direction for the bottom segment, although you could
+work that out in detail if you didn't notice right off.
+
+The net magnetic field $B_p$ is then
+\begin{equation}
+  B_p = B_{pt} + B_{pb}
+    = \frac{$\mu_0$}{4\pi}\cdot\frac{4.6875\E{-4}\U{m}}{(8.00\E{-2}\U{m})^2}
+      \cdot(12.0\U{A}+24.0\U{A})
+    = \ans{264\U{nT}} \;.
+\end{equation}
+\end{solution}
diff --git a/latex/problems/Young_and_Freedman_12/problem28.18.tex b/latex/problems/Young_and_Freedman_12/problem28.18.tex
new file mode 100644
index 0000000..b585771
--- /dev/null
+++ b/latex/problems/Young_and_Freedman_12/problem28.18.tex
@@ -0,0 +1,5 @@
+\begin{problem*}{28.18}
+\end{problem*}
+
+\begin{solution}
+\end{solution}
diff --git a/latex/problems/Young_and_Freedman_12/problem28.23.tex b/latex/problems/Young_and_Freedman_12/problem28.23.tex
new file mode 100644
index 0000000..e844ac4
--- /dev/null
+++ b/latex/problems/Young_and_Freedman_12/problem28.23.tex
@@ -0,0 +1,5 @@
+\begin{problem*}{28.23}
+\end{problem*}
+
+\begin{solution}
+\end{solution}
diff --git a/latex/problems/Young_and_Freedman_12/problem28.30.tex b/latex/problems/Young_and_Freedman_12/problem28.30.tex
new file mode 100644
index 0000000..778235f
--- /dev/null
+++ b/latex/problems/Young_and_Freedman_12/problem28.30.tex
@@ -0,0 +1,5 @@
+\begin{problem*}{28.30}
+\end{problem*}
+
+\begin{solution}
+\end{solution}
diff --git a/latex/problems/Young_and_Freedman_12/problem28.60.tex b/latex/problems/Young_and_Freedman_12/problem28.60.tex
new file mode 100644
index 0000000..570f2a7
--- /dev/null
+++ b/latex/problems/Young_and_Freedman_12/problem28.60.tex
@@ -0,0 +1,5 @@
+\begin{problem*}{28.60}
+\end{problem*}
+
+\begin{solution}
+\end{solution}
diff --git a/latex/problems/Young_and_Freedman_12/problem28.62.tex b/latex/problems/Young_and_Freedman_12/problem28.62.tex
new file mode 100644
index 0000000..cda5006
--- /dev/null
+++ b/latex/problems/Young_and_Freedman_12/problem28.62.tex
@@ -0,0 +1,5 @@
+\begin{problem*}{28.62}
+\end{problem*}
+
+\begin{solution}
+\end{solution}
-- 
2.26.2