Add solutions for Serway and Jewett v8's chapter 31.

[course.git] / latex / problems / Serway_and_Jewett_8 / problem31.46.tex

diff --git a/latex/problems/Serway_and_Jewett_8/problem31.46.tex b/latex/problems/Serway_and_Jewett_8/problem31.46.tex
index e03c4abc4d01c52da7eedce266f770d225a83d7f..6a633513122c33a87f3f294442a7e2231a0bfd69 100644 (file)
--- a/latex/problems/Serway_and_Jewett_8/problem31.46.tex
+++ b/latex/problems/Serway_and_Jewett_8/problem31.46.tex
@@ -24,5 +24,22 @@ label("$I$", (r+dr, 0), align=E);
 \end{problem*}
 
 \begin{solution}
-\end{solution}
+\Part{a}
+A clockwise current induces an inward magnetic field inside the loop,
+so the external flux must be increasingly out of the page.  Therefore,
+the magnetic field is \ans{increasing}.
 
+\Part{b}
+The induced \EMF\ must be
+\begin{align}
+  0 &= \EMF - IR \\
+  \EMF &= IR \;,
+\end{align}
+This is related to the changing field via magnetic flux.
+\begin{align}
+  |\EMF| &= |-\deriv{t}{\Phi_B}| = \deriv{t}{AB} = A\deriv{t}{B}
+    = \pi r^2 \deriv{t}{B} \\
+  \deriv{t}{B} &= \frac{\EMF}{\pi r^2} = \frac{IR}{\pi r^2}
+    = \ans{62.2\U{T/s}} \;.
+\end{align}
+\end{solution}