Completed rec9 solutions

[course.git] / latex / problems / Young_and_Freedman_12 / problem28.18.tex

diff --git a/latex/problems/Young_and_Freedman_12/problem28.18.tex b/latex/problems/Young_and_Freedman_12/problem28.18.tex
index b5857719ce8183deb96d06edbd5194ee5ea56d08..0fc786aa5a95f6eddbc0a176904912ca73a0f8b4 100644 (file)
--- a/latex/problems/Young_and_Freedman_12/problem28.18.tex
+++ b/latex/problems/Young_and_Freedman_12/problem28.18.tex
@@ -1,5 +1,40 @@
 \begin{problem*}{28.18}
+Two long, straight wires, one above the other, are seperated by a
+distance $2a$ and are parallel to the $x$-axis.  Let the $+y$-axis be
+in the plane of the wires in the direction from the lower wire to the
+upper wire.  Each wire carries current $I$ in the $+x$-direction.
+What are the magnitude and direction of the net magnetif field of the
+two wires at a point in the plane of the wires \Part{a} midway between
+them; \Part{b} at a distance $a$ above the upper wire; \Part{c} at a
+distance $a$ below the lower wire?
 \end{problem*}
 
 \begin{solution}
+\Part{a}
+Using the right hand rules for magnetic field from a wire, we see that
+the upper wire will create a magnetic field into the page while the
+lower wire will create a magnetic field out of the page.  The
+magnitude of the field from a single wire is given by
+\begin{equation}
+  B = \frac{\mu_0 I}{2\pi r} \;,
+\end{equation}
+with the same current $I$ and distance $r=a$ for both wires.
+Therefore the net magnetic field is \ans{zero}.
+
+\Part{b}
+Both wires create a magnetic field out of the page.  The magnitude of
+the toal field will be
+\begin{equation}
+  B = \frac{\mu_0 I}{2\pi a} + \frac{\mu_0 I}{2\pi (3a)}
+    = \ans{\frac{2 \mu_0 I}{3\pi a}} \;.
+\end{equation}
+
+\Part{c}
+Both wires create a magnetic field into the page.  The magnitude of
+the toal field will be
+\begin{equation}
+  B = \frac{\mu_0 I}{2\pi (3a)} + \frac{\mu_0 I}{2\pi a}
+    = \ans{\frac{2 \mu_0 I}{3\pi a}} \;,
+\end{equation}
+the same as the magnitude for \Part{b}.
 \end{solution}