QB/d cp2.6

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Equations & sol. to #6     -

See special:permalink/1894335 for a wikitext version of this quiz.

LaTexMarkup begin[edit | edit source]

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\begin{document}
\title{d\_cp2.6}
\author{The LaTex code that creates this quiz is released to the Public Domain\\
Attribution for each question is documented in the Appendix}
\maketitle
\begin{center}                                                                                
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\\Latex markup at\\
\footnotesize{ \url{https://en.wikiversity.org/wiki/special:permalink/1894335}}
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\begin{multicols}{3}
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\pagebreak\section{Quiz}
\keytrue
\printanswers
\begin{questions}
\question 
    \includegraphics[width=0.12\textwidth]{Boxin2Dxyzaligned.png}Each surface of the rectangular box shown is aligned with the xyz coordinate system.  Two surfaces occupy identical rectangles in the planes x=0 and x=x\textsubscript{1}=3\,m. The other four surfaces are rectangles in y=y\textsubscript{0}=1\,m, y=y\textsubscript{1}=5\,m, z=z\textsubscript{0}=1\,m, and z=z\textsubscript{1}=3\,m. The surfaces in the yz plane each have area 8m\textsuperscript{2}. Those in the xy plane have area 12m\textsuperscript{2} ,and those in the zx plane have area 6m\textsuperscript{2}. An electric field of magnitude 10\,N/C has components in the y and z directions and is directed at 30\(^\circ\) above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?\ifkey\endnote{Example 6.3 from OpenStax University Physics2: https://cnx.org/contents/eg-XcBxE@9.8:7Rx6Svvy@4/61-Electric-Flux\_1 placed in Public Domain by Guy Vandegrift: {\url{https://en.wikiversity.org/wiki/special:permalink/1894335}}}\fi
 \begin{choices}
  \choice 3.549E+01\,N\(\cdot\) m\textsuperscript{2}/C
  \choice 3.904E+01\,N\(\cdot\) m\textsuperscript{2}/C
  \choice 4.294E+01\,N\(\cdot\) m\textsuperscript{2}/C
  \choice 4.724E+01\,N\(\cdot\) m\textsuperscript{2}/C
  \CorrectChoice 5.196E+01\,N\(\cdot\) m\textsuperscript{2}/C
\end{choices}

\question 
    \includegraphics[width=0.12\textwidth]{Boxin2Dxyzaligned.png}Each surface of the rectangular box shown is aligned with the xyz coordinate system.  Two surfaces occupy identical rectangles in the planes x=0 and x=x\textsubscript{1}=3\,m. The other four surfaces are rectangles in y=y\textsubscript{0}=1\,m, y=y\textsubscript{1}=5\,m, z=z\textsubscript{0}=1\,m, and z=z\textsubscript{1}=3\,m. The surfaces in the yz plane each have area 8m\textsuperscript{2}. Those in the xy plane have area 12m\textsuperscript{2} ,and those in the zx plane have area 6m\textsuperscript{2}. An electric field of magnitude 10\,N/C has components in the y and z directions and is directed at 60\(^\circ\) from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?\ifkey\endnote{Example 6.3a from OpenStax University Physics2: https://cnx.org/contents/eg-XcBxE@9.8:7Rx6Svvy@4/61-Electric-Flux\_1 placed in Public Domain by Guy Vandegrift: {\url{https://en.wikiversity.org/wiki/special:permalink/1894335}}}\fi
 \begin{choices}
  \choice 4.724E+01\,N\(\cdot\) m\textsuperscript{2}/C
  \CorrectChoice 5.196E+01\,N\(\cdot\) m\textsuperscript{2}/C
  \choice 5.716E+01\,N\(\cdot\) m\textsuperscript{2}/C
  \choice 6.287E+01\,N\(\cdot\) m\textsuperscript{2}/C
  \choice 6.916E+01\,N\(\cdot\) m\textsuperscript{2}/C
\end{choices}

\question 
    \includegraphics[width=0.12\textwidth]{Boxin2Dxyzaligned.png}Each surface of the rectangular box shown is aligned with the xyz coordinate system.  Two surfaces occupy identical rectangles in the planes x=0 and x=x\textsubscript{1}=3\,m. The other four surfaces are rectangles in y=y\textsubscript{0}=1\,m, y=y\textsubscript{1}=5\,m, z=z\textsubscript{0}=1\,m, and z=z\textsubscript{1}=3\,m. The surfaces in the yz plane each have area 8m\textsuperscript{2}. Those in the xy plane have area 12m\textsuperscript{2} ,and those in the zx plane have area 6m\textsuperscript{2}. An electric field has the xyz components (0,\,8.7,\,5.0)\,N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?\ifkey\endnote{Example 6.3b from OpenStax University Physics2: https://cnx.org/contents/eg-XcBxE@9.8:7Rx6Svvy@4/61-Electric-Flux\_1 placed in Public Domain by Guy Vandegrift: {\url{https://en.wikiversity.org/wiki/special:permalink/1894335}}}\fi
 \begin{choices}
  \choice 4.745E+01\,N\(\cdot\) m\textsuperscript{2}/C
  \CorrectChoice 5.220E+01\,N\(\cdot\) m\textsuperscript{2}/C
  \choice 5.742E+01\,N\(\cdot\) m\textsuperscript{2}/C
  \choice 6.316E+01\,N\(\cdot\) m\textsuperscript{2}/C
  \choice 6.948E+01\,N\(\cdot\) m\textsuperscript{2}/C
\end{choices}

\question What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0,\,y=0), (x=3,\,y=0), (x=0,\,y=2), and (x=3,\,y=2), where x and y are measured in meters. The electric field is, \(\vec E=1y^{1}\hat i +2x^{3}\hat j +3y^{2}\hat k\). \ifkey\endnote{Example 6.4 from OpenStax University Physics2: https://cnx.org/contents/eg-XcBxE@9.8:7Rx6Svvy@4/61-Electric-Flux\_1 placed in Public Domain by Guy Vandegrift: {\url{https://en.wikiversity.org/wiki/special:permalink/1894335}}}\fi
 \begin{choices}
  \choice 1.983E+01\,V\(\cdot\) m
  \choice 2.182E+01\,V\(\cdot\) m
  \CorrectChoice 2.400E+01\,V\(\cdot\) m
  \choice 2.640E+01\,V\(\cdot\) m
  \choice 2.904E+01\,V\(\cdot\) m
\end{choices}

\question Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 5\,nano-Coulombs. What is the magnitude of the electric field at a distance of 3.5\,m from the center of the shells?\ifkey\endnote{Inspired by Example 6.6 from OpenStax University Physics2, but modified by [[user:Guy vandegrift]] to be Public Domain (CC0)\_1 placed in Public Domain by Guy Vandegrift: {\url{https://en.wikiversity.org/wiki/special:permalink/1894335}}}\fi
 \begin{choices}
  \CorrectChoice 1.102E+01\,N/C
  \choice 1.212E+01\,N/C
  \choice 1.333E+01\,N/C
  \choice 1.467E+01\,N/C
  \choice 1.613E+01\,N/C
\end{choices}

\question A non-conducting sphere of radius R=2\,m has a non-uniform charge density that varies with the distnce from its center as given by \textrho(r)=ar\textsuperscript{2} (r\(x\)R) where a=1\,nC\(\cdot\) m\textsuperscript{-1}. What is the magnitude of the electric field at a distance of 1\,m from the center? \ifkey\endnote{Example 6.7 from OpenStax University Physics2: https://cnx.org/contents/eg-XcBxE@9.8:7NEpGtkt@4/63-Applying-Gausss-Law\_1 placed in Public Domain by Guy Vandegrift: {\url{https://en.wikiversity.org/wiki/special:permalink/1894335}}}\fi
 \begin{choices}
  \choice 1.867E+01\,N/C
  \choice 2.053E+01\,N/C
  \CorrectChoice 2.259E+01\,N/C
  \choice 2.485E+01\,N/C
  \choice 2.733E+01\,N/C
\end{choices}

\end{questions}
\newpage
\section{Renditions}  %%% Renditions %%%%

\subsection{}%%%% subsection 1

\begin{questions} %%%%%%% begin questions

\question 
    \includegraphics[width=0.12\textwidth]{Boxin2Dxyzaligned.png}Each surface of the rectangular box shown is aligned with the xyz coordinate system.  Two surfaces occupy identical rectangles in the planes x=0 and x=x\textsubscript{1}=2.8\,m. The other four surfaces are rectangles in y=y\textsubscript{0}=1.2\,m, y=y\textsubscript{1}=4.4\,m, z=z\textsubscript{0}=1.2\,m, and z=z\textsubscript{1}=4.6\,m. The surfaces in the yz plane each have area 11.0m\textsuperscript{2}. Those in the xy plane have area 9.0m\textsuperscript{2} ,and those in the zx plane have area 9.5m\textsuperscript{2}. An electric field of magnitude 11\,N/C has components in the y and z directions and is directed at 35\(^\circ\) above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
\begin{choices} %%%%%%% begin choices
    \choice  6.445E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  7.089E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  7.798E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \CorrectChoice 8.578E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  9.436E+01\,N\(\cdot\) m\textsuperscript{2}/C
\end{choices} %%% end choices

\question 
    \includegraphics[width=0.12\textwidth]{Boxin2Dxyzaligned.png}Each surface of the rectangular box shown is aligned with the xyz coordinate system.  Two surfaces occupy identical rectangles in the planes x=0 and x=x\textsubscript{1}=1.4\,m. The other four surfaces are rectangles in y=y\textsubscript{0}=1.6\,m, y=y\textsubscript{1}=4.2\,m, z=z\textsubscript{0}=1.1\,m, and z=z\textsubscript{1}=5.9\,m. The surfaces in the yz plane each have area 12.0m\textsuperscript{2}. Those in the xy plane have area 3.6m\textsuperscript{2} ,and those in the zx plane have area 6.7m\textsuperscript{2}. An electric field of magnitude 16\,N/C has components in the y and z directions and is directed at 53\(^\circ\) above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
\begin{choices} %%%%%%% begin choices
    \choice  4.420E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  4.862E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  5.348E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  5.882E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \CorrectChoice 6.471E+01\,N\(\cdot\) m\textsuperscript{2}/C
\end{choices} %%% end choices

\question 
    \includegraphics[width=0.12\textwidth]{Boxin2Dxyzaligned.png}Each surface of the rectangular box shown is aligned with the xyz coordinate system.  Two surfaces occupy identical rectangles in the planes x=0 and x=x\textsubscript{1}=1.1\,m. The other four surfaces are rectangles in y=y\textsubscript{0}=1.5\,m, y=y\textsubscript{1}=5.0\,m, z=z\textsubscript{0}=1.8\,m, and z=z\textsubscript{1}=5.7\,m. The surfaces in the yz plane each have area 14.0m\textsuperscript{2}. Those in the xy plane have area 3.9m\textsuperscript{2} ,and those in the zx plane have area 4.3m\textsuperscript{2}. An electric field of magnitude 18\,N/C has components in the y and z directions and is directed at 31\(^\circ\) above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
\begin{choices} %%%%%%% begin choices
    \choice  4.521E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  4.973E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  5.470E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  6.017E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \CorrectChoice 6.619E+01\,N\(\cdot\) m\textsuperscript{2}/C
\end{choices} %%% end choices

\question 
    \includegraphics[width=0.12\textwidth]{Boxin2Dxyzaligned.png}Each surface of the rectangular box shown is aligned with the xyz coordinate system.  Two surfaces occupy identical rectangles in the planes x=0 and x=x\textsubscript{1}=1.9\,m. The other four surfaces are rectangles in y=y\textsubscript{0}=1.6\,m, y=y\textsubscript{1}=5.1\,m, z=z\textsubscript{0}=1.3\,m, and z=z\textsubscript{1}=4.7\,m. The surfaces in the yz plane each have area 12.0m\textsuperscript{2}. Those in the xy plane have area 6.6m\textsuperscript{2} ,and those in the zx plane have area 6.5m\textsuperscript{2}. An electric field of magnitude 12\,N/C has components in the y and z directions and is directed at 46\(^\circ\) above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
\begin{choices} %%%%%%% begin choices
    \CorrectChoice 5.385E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  5.923E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  6.516E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  7.167E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  7.884E+01\,N\(\cdot\) m\textsuperscript{2}/C
\end{choices} %%% end choices

\question 
    \includegraphics[width=0.12\textwidth]{Boxin2Dxyzaligned.png}Each surface of the rectangular box shown is aligned with the xyz coordinate system.  Two surfaces occupy identical rectangles in the planes x=0 and x=x\textsubscript{1}=1.3\,m. The other four surfaces are rectangles in y=y\textsubscript{0}=1.6\,m, y=y\textsubscript{1}=5.2\,m, z=z\textsubscript{0}=1.6\,m, and z=z\textsubscript{1}=4.7\,m. The surfaces in the yz plane each have area 11.0m\textsuperscript{2}. Those in the xy plane have area 4.7m\textsuperscript{2} ,and those in the zx plane have area 4.0m\textsuperscript{2}. An electric field of magnitude 11\,N/C has components in the y and z directions and is directed at 43\(^\circ\) above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
\begin{choices} %%%%%%% begin choices
    \choice  2.214E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  2.436E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  2.679E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  2.947E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \CorrectChoice 3.242E+01\,N\(\cdot\) m\textsuperscript{2}/C
\end{choices} %%% end choices

\question 
    \includegraphics[width=0.12\textwidth]{Boxin2Dxyzaligned.png}Each surface of the rectangular box shown is aligned with the xyz coordinate system.  Two surfaces occupy identical rectangles in the planes x=0 and x=x\textsubscript{1}=2.1\,m. The other four surfaces are rectangles in y=y\textsubscript{0}=1.7\,m, y=y\textsubscript{1}=5.6\,m, z=z\textsubscript{0}=1.8\,m, and z=z\textsubscript{1}=4.2\,m. The surfaces in the yz plane each have area 9.4m\textsuperscript{2}. Those in the xy plane have area 8.2m\textsuperscript{2} ,and those in the zx plane have area 5.0m\textsuperscript{2}. An electric field of magnitude 6\,N/C has components in the y and z directions and is directed at 29\(^\circ\) above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
\begin{choices} %%%%%%% begin choices
    \choice  2.186E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  2.404E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \CorrectChoice 2.645E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  2.909E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  3.200E+01\,N\(\cdot\) m\textsuperscript{2}/C
\end{choices} %%% end choices

\question 
    \includegraphics[width=0.12\textwidth]{Boxin2Dxyzaligned.png}Each surface of the rectangular box shown is aligned with the xyz coordinate system.  Two surfaces occupy identical rectangles in the planes x=0 and x=x\textsubscript{1}=2.6\,m. The other four surfaces are rectangles in y=y\textsubscript{0}=1.2\,m, y=y\textsubscript{1}=5.6\,m, z=z\textsubscript{0}=1.2\,m, and z=z\textsubscript{1}=4.4\,m. The surfaces in the yz plane each have area 14.0m\textsuperscript{2}. Those in the xy plane have area 11.0m\textsuperscript{2} ,and those in the zx plane have area 8.3m\textsuperscript{2}. An electric field of magnitude 9\,N/C has components in the y and z directions and is directed at 39\(^\circ\) above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
\begin{choices} %%%%%%% begin choices
    \choice  4.809E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  5.290E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \CorrectChoice 5.819E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  6.401E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  7.041E+01\,N\(\cdot\) m\textsuperscript{2}/C
\end{choices} %%% end choices

\question 
    \includegraphics[width=0.12\textwidth]{Boxin2Dxyzaligned.png}Each surface of the rectangular box shown is aligned with the xyz coordinate system.  Two surfaces occupy identical rectangles in the planes x=0 and x=x\textsubscript{1}=2.1\,m. The other four surfaces are rectangles in y=y\textsubscript{0}=1.1\,m, y=y\textsubscript{1}=5.3\,m, z=z\textsubscript{0}=1.1\,m, and z=z\textsubscript{1}=4.3\,m. The surfaces in the yz plane each have area 13.0m\textsuperscript{2}. Those in the xy plane have area 8.8m\textsuperscript{2} ,and those in the zx plane have area 6.7m\textsuperscript{2}. An electric field of magnitude 10\,N/C has components in the y and z directions and is directed at 39\(^\circ\) above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
\begin{choices} %%%%%%% begin choices
    \choice  3.924E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  4.316E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  4.748E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \CorrectChoice 5.222E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  5.745E+01\,N\(\cdot\) m\textsuperscript{2}/C
\end{choices} %%% end choices

\question 
    \includegraphics[width=0.12\textwidth]{Boxin2Dxyzaligned.png}Each surface of the rectangular box shown is aligned with the xyz coordinate system.  Two surfaces occupy identical rectangles in the planes x=0 and x=x\textsubscript{1}=2.4\,m. The other four surfaces are rectangles in y=y\textsubscript{0}=1.2\,m, y=y\textsubscript{1}=4.2\,m, z=z\textsubscript{0}=1.2\,m, and z=z\textsubscript{1}=4.1\,m. The surfaces in the yz plane each have area 8.7m\textsuperscript{2}. Those in the xy plane have area 7.2m\textsuperscript{2} ,and those in the zx plane have area 7.0m\textsuperscript{2}. An electric field of magnitude 12\,N/C has components in the y and z directions and is directed at 58\(^\circ\) above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
\begin{choices} %%%%%%% begin choices
    \choice  4.024E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \CorrectChoice 4.426E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  4.868E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  5.355E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  5.891E+01\,N\(\cdot\) m\textsuperscript{2}/C
\end{choices} %%% end choices

\question 
    \includegraphics[width=0.12\textwidth]{Boxin2Dxyzaligned.png}Each surface of the rectangular box shown is aligned with the xyz coordinate system.  Two surfaces occupy identical rectangles in the planes x=0 and x=x\textsubscript{1}=2.4\,m. The other four surfaces are rectangles in y=y\textsubscript{0}=1.7\,m, y=y\textsubscript{1}=5.8\,m, z=z\textsubscript{0}=1.3\,m, and z=z\textsubscript{1}=4.4\,m. The surfaces in the yz plane each have area 13.0m\textsuperscript{2}. Those in the xy plane have area 9.8m\textsuperscript{2} ,and those in the zx plane have area 7.4m\textsuperscript{2}. An electric field of magnitude 18\,N/C has components in the y and z directions and is directed at 46\(^\circ\) above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
\begin{choices} %%%%%%% begin choices
    \choice  8.457E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \CorrectChoice 9.303E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  1.023E+02\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  1.126E+02\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  1.238E+02\,N\(\cdot\) m\textsuperscript{2}/C
\end{choices} %%% end choices

\question 
    \includegraphics[width=0.12\textwidth]{Boxin2Dxyzaligned.png}Each surface of the rectangular box shown is aligned with the xyz coordinate system.  Two surfaces occupy identical rectangles in the planes x=0 and x=x\textsubscript{1}=1.7\,m. The other four surfaces are rectangles in y=y\textsubscript{0}=1.5\,m, y=y\textsubscript{1}=5.7\,m, z=z\textsubscript{0}=1.4\,m, and z=z\textsubscript{1}=4.8\,m. The surfaces in the yz plane each have area 14.0m\textsuperscript{2}. Those in the xy plane have area 7.1m\textsuperscript{2} ,and those in the zx plane have area 5.8m\textsuperscript{2}. An electric field of magnitude 19\,N/C has components in the y and z directions and is directed at 33\(^\circ\) above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
\begin{choices} %%%%%%% begin choices
    \choice  6.920E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  7.612E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  8.373E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \CorrectChoice 9.210E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  1.013E+02\,N\(\cdot\) m\textsuperscript{2}/C
\end{choices} %%% end choices

\question 
    \includegraphics[width=0.12\textwidth]{Boxin2Dxyzaligned.png}Each surface of the rectangular box shown is aligned with the xyz coordinate system.  Two surfaces occupy identical rectangles in the planes x=0 and x=x\textsubscript{1}=1.7\,m. The other four surfaces are rectangles in y=y\textsubscript{0}=1.9\,m, y=y\textsubscript{1}=4.3\,m, z=z\textsubscript{0}=1.7\,m, and z=z\textsubscript{1}=5.7\,m. The surfaces in the yz plane each have area 9.6m\textsuperscript{2}. Those in the xy plane have area 4.1m\textsuperscript{2} ,and those in the zx plane have area 6.8m\textsuperscript{2}. An electric field of magnitude 13\,N/C has components in the y and z directions and is directed at 27\(^\circ\) above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
\begin{choices} %%%%%%% begin choices
    \CorrectChoice 7.876E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  8.664E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  9.531E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  1.048E+02\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  1.153E+02\,N\(\cdot\) m\textsuperscript{2}/C
\end{choices} %%% end choices

\question 
    \includegraphics[width=0.12\textwidth]{Boxin2Dxyzaligned.png}Each surface of the rectangular box shown is aligned with the xyz coordinate system.  Two surfaces occupy identical rectangles in the planes x=0 and x=x\textsubscript{1}=1.5\,m. The other four surfaces are rectangles in y=y\textsubscript{0}=1.4\,m, y=y\textsubscript{1}=4.9\,m, z=z\textsubscript{0}=1.1\,m, and z=z\textsubscript{1}=4.4\,m. The surfaces in the yz plane each have area 12.0m\textsuperscript{2}. Those in the xy plane have area 5.3m\textsuperscript{2} ,and those in the zx plane have area 5.0m\textsuperscript{2}. An electric field of magnitude 18\,N/C has components in the y and z directions and is directed at 29\(^\circ\) above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
\begin{choices} %%%%%%% begin choices
    \CorrectChoice 7.793E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  8.572E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  9.429E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  1.037E+02\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  1.141E+02\,N\(\cdot\) m\textsuperscript{2}/C
\end{choices} %%% end choices

\question 
    \includegraphics[width=0.12\textwidth]{Boxin2Dxyzaligned.png}Each surface of the rectangular box shown is aligned with the xyz coordinate system.  Two surfaces occupy identical rectangles in the planes x=0 and x=x\textsubscript{1}=2.8\,m. The other four surfaces are rectangles in y=y\textsubscript{0}=1.5\,m, y=y\textsubscript{1}=5.8\,m, z=z\textsubscript{0}=1.1\,m, and z=z\textsubscript{1}=5.2\,m. The surfaces in the yz plane each have area 18.0m\textsuperscript{2}. Those in the xy plane have area 12.0m\textsuperscript{2} ,and those in the zx plane have area 11.0m\textsuperscript{2}. An electric field of magnitude 13\,N/C has components in the y and z directions and is directed at 60\(^\circ\) above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
\begin{choices} %%%%%%% begin choices
    \choice  5.606E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  6.167E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  6.784E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \CorrectChoice 7.462E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  8.208E+01\,N\(\cdot\) m\textsuperscript{2}/C
\end{choices} %%% end choices

\question 
    \includegraphics[width=0.12\textwidth]{Boxin2Dxyzaligned.png}Each surface of the rectangular box shown is aligned with the xyz coordinate system.  Two surfaces occupy identical rectangles in the planes x=0 and x=x\textsubscript{1}=1.4\,m. The other four surfaces are rectangles in y=y\textsubscript{0}=1.2\,m, y=y\textsubscript{1}=5.8\,m, z=z\textsubscript{0}=1.2\,m, and z=z\textsubscript{1}=5.0\,m. The surfaces in the yz plane each have area 17.0m\textsuperscript{2}. Those in the xy plane have area 6.4m\textsuperscript{2} ,and those in the zx plane have area 5.3m\textsuperscript{2}. An electric field of magnitude 5\,N/C has components in the y and z directions and is directed at 25\(^\circ\) above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
\begin{choices} %%%%%%% begin choices
    \choice  1.992E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  2.192E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \CorrectChoice 2.411E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  2.652E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  2.917E+01\,N\(\cdot\) m\textsuperscript{2}/C
\end{choices} %%% end choices

\question 
    \includegraphics[width=0.12\textwidth]{Boxin2Dxyzaligned.png}Each surface of the rectangular box shown is aligned with the xyz coordinate system.  Two surfaces occupy identical rectangles in the planes x=0 and x=x\textsubscript{1}=2.3\,m. The other four surfaces are rectangles in y=y\textsubscript{0}=1.2\,m, y=y\textsubscript{1}=5.5\,m, z=z\textsubscript{0}=1.7\,m, and z=z\textsubscript{1}=5.1\,m. The surfaces in the yz plane each have area 15.0m\textsuperscript{2}. Those in the xy plane have area 9.9m\textsuperscript{2} ,and those in the zx plane have area 7.8m\textsuperscript{2}. An electric field of magnitude 6\,N/C has components in the y and z directions and is directed at 58\(^\circ\) above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
\begin{choices} %%%%%%% begin choices
    \choice  1.698E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  1.868E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  2.055E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  2.260E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \CorrectChoice 2.486E+01\,N\(\cdot\) m\textsuperscript{2}/C
\end{choices} %%% end choices

\question 
    \includegraphics[width=0.12\textwidth]{Boxin2Dxyzaligned.png}Each surface of the rectangular box shown is aligned with the xyz coordinate system.  Two surfaces occupy identical rectangles in the planes x=0 and x=x\textsubscript{1}=1.3\,m. The other four surfaces are rectangles in y=y\textsubscript{0}=1.5\,m, y=y\textsubscript{1}=5.8\,m, z=z\textsubscript{0}=1.7\,m, and z=z\textsubscript{1}=5.8\,m. The surfaces in the yz plane each have area 18.0m\textsuperscript{2}. Those in the xy plane have area 5.6m\textsuperscript{2} ,and those in the zx plane have area 5.3m\textsuperscript{2}. An electric field of magnitude 11\,N/C has components in the y and z directions and is directed at 40\(^\circ\) above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
\begin{choices} %%%%%%% begin choices
    \choice  3.712E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  4.083E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \CorrectChoice 4.491E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  4.940E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  5.434E+01\,N\(\cdot\) m\textsuperscript{2}/C
\end{choices} %%% end choices

\question 
    \includegraphics[width=0.12\textwidth]{Boxin2Dxyzaligned.png}Each surface of the rectangular box shown is aligned with the xyz coordinate system.  Two surfaces occupy identical rectangles in the planes x=0 and x=x\textsubscript{1}=2.0\,m. The other four surfaces are rectangles in y=y\textsubscript{0}=1.3\,m, y=y\textsubscript{1}=4.4\,m, z=z\textsubscript{0}=1.3\,m, and z=z\textsubscript{1}=4.2\,m. The surfaces in the yz plane each have area 9.0m\textsuperscript{2}. Those in the xy plane have area 6.2m\textsuperscript{2} ,and those in the zx plane have area 5.8m\textsuperscript{2}. An electric field of magnitude 11\,N/C has components in the y and z directions and is directed at 32\(^\circ\) above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
\begin{choices} %%%%%%% begin choices
    \choice  3.695E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  4.065E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  4.472E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  4.919E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \CorrectChoice 5.411E+01\,N\(\cdot\) m\textsuperscript{2}/C
\end{choices} %%% end choices

\question 
    \includegraphics[width=0.12\textwidth]{Boxin2Dxyzaligned.png}Each surface of the rectangular box shown is aligned with the xyz coordinate system.  Two surfaces occupy identical rectangles in the planes x=0 and x=x\textsubscript{1}=1.8\,m. The other four surfaces are rectangles in y=y\textsubscript{0}=1.1\,m, y=y\textsubscript{1}=4.9\,m, z=z\textsubscript{0}=1.3\,m, and z=z\textsubscript{1}=5.6\,m. The surfaces in the yz plane each have area 16.0m\textsuperscript{2}. Those in the xy plane have area 6.8m\textsuperscript{2} ,and those in the zx plane have area 7.7m\textsuperscript{2}. An electric field of magnitude 18\,N/C has components in the y and z directions and is directed at 57\(^\circ\) above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
\begin{choices} %%%%%%% begin choices
    \choice  6.898E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \CorrectChoice 7.588E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  8.347E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  9.181E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  1.010E+02\,N\(\cdot\) m\textsuperscript{2}/C
\end{choices} %%% end choices
%\pagebreak
%\end{choices}%??????????????
\end{questions}%%%%%%%% end questions

\subsection{}%%%% subsection 2

\begin{questions} %%%%%%% begin questions

\question 
    \includegraphics[width=0.12\textwidth]{Boxin2Dxyzaligned.png}Each surface of the rectangular box shown is aligned with the xyz coordinate system.  Two surfaces occupy identical rectangles in the planes x=0 and x=x\textsubscript{1}=1.2\,m. The other four surfaces are rectangles in y=y\textsubscript{0}=1.8\,m, y=y\textsubscript{1}=4.8\,m, z=z\textsubscript{0}=1.8\,m, and z=z\textsubscript{1}=4.3\,m. The surfaces in the yz plane each have area 7.5m\textsuperscript{2}. Those in the xy plane have area 3.6m\textsuperscript{2} ,and those in the zx plane have area 3.0m\textsuperscript{2}. An electric field of magnitude 11\,N/C has components in the y and z directions and is directed at 49\(^\circ\) from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
\begin{choices} %%%%%%% begin choices
    \choice  2.058E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  2.264E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \CorrectChoice 2.491E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  2.740E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  3.014E+01\,N\(\cdot\) m\textsuperscript{2}/C
\end{choices} %%% end choices

\question 
    \includegraphics[width=0.12\textwidth]{Boxin2Dxyzaligned.png}Each surface of the rectangular box shown is aligned with the xyz coordinate system.  Two surfaces occupy identical rectangles in the planes x=0 and x=x\textsubscript{1}=2.9\,m. The other four surfaces are rectangles in y=y\textsubscript{0}=1.7\,m, y=y\textsubscript{1}=5.9\,m, z=z\textsubscript{0}=1.3\,m, and z=z\textsubscript{1}=5.3\,m. The surfaces in the yz plane each have area 17.0m\textsuperscript{2}. Those in the xy plane have area 12.0m\textsuperscript{2} ,and those in the zx plane have area 12.0m\textsuperscript{2}. An electric field of magnitude 5\,N/C has components in the y and z directions and is directed at 26\(^\circ\) from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
\begin{choices} %%%%%%% begin choices
    \choice  1.737E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  1.910E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  2.101E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  2.311E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \CorrectChoice 2.543E+01\,N\(\cdot\) m\textsuperscript{2}/C
\end{choices} %%% end choices

\question 
    \includegraphics[width=0.12\textwidth]{Boxin2Dxyzaligned.png}Each surface of the rectangular box shown is aligned with the xyz coordinate system.  Two surfaces occupy identical rectangles in the planes x=0 and x=x\textsubscript{1}=2.6\,m. The other four surfaces are rectangles in y=y\textsubscript{0}=1.7\,m, y=y\textsubscript{1}=5.4\,m, z=z\textsubscript{0}=1.4\,m, and z=z\textsubscript{1}=5.6\,m. The surfaces in the yz plane each have area 16.0m\textsuperscript{2}. Those in the xy plane have area 9.6m\textsuperscript{2} ,and those in the zx plane have area 11.0m\textsuperscript{2}. An electric field of magnitude 15\,N/C has components in the y and z directions and is directed at 33\(^\circ\) from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
\begin{choices} %%%%%%% begin choices
    \CorrectChoice 8.921E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  9.813E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  1.079E+02\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  1.187E+02\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  1.306E+02\,N\(\cdot\) m\textsuperscript{2}/C
\end{choices} %%% end choices

\question 
    \includegraphics[width=0.12\textwidth]{Boxin2Dxyzaligned.png}Each surface of the rectangular box shown is aligned with the xyz coordinate system.  Two surfaces occupy identical rectangles in the planes x=0 and x=x\textsubscript{1}=2.3\,m. The other four surfaces are rectangles in y=y\textsubscript{0}=1.5\,m, y=y\textsubscript{1}=4.6\,m, z=z\textsubscript{0}=1.6\,m, and z=z\textsubscript{1}=5.8\,m. The surfaces in the yz plane each have area 13.0m\textsuperscript{2}. Those in the xy plane have area 7.1m\textsuperscript{2} ,and those in the zx plane have area 9.7m\textsuperscript{2}. An electric field of magnitude 17\,N/C has components in the y and z directions and is directed at 43\(^\circ\) from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
\begin{choices} %%%%%%% begin choices
    \choice  8.415E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  9.256E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  1.018E+02\,N\(\cdot\) m\textsuperscript{2}/C
    \CorrectChoice 1.120E+02\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  1.232E+02\,N\(\cdot\) m\textsuperscript{2}/C
\end{choices} %%% end choices

\question 
    \includegraphics[width=0.12\textwidth]{Boxin2Dxyzaligned.png}Each surface of the rectangular box shown is aligned with the xyz coordinate system.  Two surfaces occupy identical rectangles in the planes x=0 and x=x\textsubscript{1}=2.0\,m. The other four surfaces are rectangles in y=y\textsubscript{0}=1.8\,m, y=y\textsubscript{1}=5.8\,m, z=z\textsubscript{0}=1.9\,m, and z=z\textsubscript{1}=5.9\,m. The surfaces in the yz plane each have area 16.0m\textsuperscript{2}. Those in the xy plane have area 8.0m\textsuperscript{2} ,and those in the zx plane have area 8.0m\textsuperscript{2}. An electric field of magnitude 8\,N/C has components in the y and z directions and is directed at 39\(^\circ\) from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
\begin{choices} %%%%%%% begin choices
    \choice  3.662E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \CorrectChoice 4.028E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  4.430E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  4.873E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  5.361E+01\,N\(\cdot\) m\textsuperscript{2}/C
\end{choices} %%% end choices

\question 
    \includegraphics[width=0.12\textwidth]{Boxin2Dxyzaligned.png}Each surface of the rectangular box shown is aligned with the xyz coordinate system.  Two surfaces occupy identical rectangles in the planes x=0 and x=x\textsubscript{1}=2.7\,m. The other four surfaces are rectangles in y=y\textsubscript{0}=1.6\,m, y=y\textsubscript{1}=4.4\,m, z=z\textsubscript{0}=1.2\,m, and z=z\textsubscript{1}=5.9\,m. The surfaces in the yz plane each have area 13.0m\textsuperscript{2}. Those in the xy plane have area 7.6m\textsuperscript{2} ,and those in the zx plane have area 13.0m\textsuperscript{2}. An electric field of magnitude 8\,N/C has components in the y and z directions and is directed at 46\(^\circ\) from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
\begin{choices} %%%%%%% begin choices
    \choice  4.988E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  5.487E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  6.035E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  6.639E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \CorrectChoice 7.303E+01\,N\(\cdot\) m\textsuperscript{2}/C
\end{choices} %%% end choices

\question 
    \includegraphics[width=0.12\textwidth]{Boxin2Dxyzaligned.png}Each surface of the rectangular box shown is aligned with the xyz coordinate system.  Two surfaces occupy identical rectangles in the planes x=0 and x=x\textsubscript{1}=2.8\,m. The other four surfaces are rectangles in y=y\textsubscript{0}=1.4\,m, y=y\textsubscript{1}=4.7\,m, z=z\textsubscript{0}=1.8\,m, and z=z\textsubscript{1}=4.7\,m. The surfaces in the yz plane each have area 9.6m\textsuperscript{2}. Those in the xy plane have area 9.2m\textsuperscript{2} ,and those in the zx plane have area 8.1m\textsuperscript{2}. An electric field of magnitude 6\,N/C has components in the y and z directions and is directed at 32\(^\circ\) from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
\begin{choices} %%%%%%% begin choices
    \choice  2.134E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  2.347E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \CorrectChoice 2.582E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  2.840E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  3.124E+01\,N\(\cdot\) m\textsuperscript{2}/C
\end{choices} %%% end choices

\question 
    \includegraphics[width=0.12\textwidth]{Boxin2Dxyzaligned.png}Each surface of the rectangular box shown is aligned with the xyz coordinate system.  Two surfaces occupy identical rectangles in the planes x=0 and x=x\textsubscript{1}=2.2\,m. The other four surfaces are rectangles in y=y\textsubscript{0}=1.7\,m, y=y\textsubscript{1}=4.3\,m, z=z\textsubscript{0}=1.5\,m, and z=z\textsubscript{1}=4.7\,m. The surfaces in the yz plane each have area 8.3m\textsuperscript{2}. Those in the xy plane have area 5.7m\textsuperscript{2} ,and those in the zx plane have area 7.0m\textsuperscript{2}. An electric field of magnitude 18\,N/C has components in the y and z directions and is directed at 28\(^\circ\) from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
\begin{choices} %%%%%%% begin choices
    \choice  5.408E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \CorrectChoice 5.949E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  6.544E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  7.198E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  7.918E+01\,N\(\cdot\) m\textsuperscript{2}/C
\end{choices} %%% end choices

\question 
    \includegraphics[width=0.12\textwidth]{Boxin2Dxyzaligned.png}Each surface of the rectangular box shown is aligned with the xyz coordinate system.  Two surfaces occupy identical rectangles in the planes x=0 and x=x\textsubscript{1}=1.6\,m. The other four surfaces are rectangles in y=y\textsubscript{0}=1.5\,m, y=y\textsubscript{1}=4.4\,m, z=z\textsubscript{0}=1.5\,m, and z=z\textsubscript{1}=5.5\,m. The surfaces in the yz plane each have area 12.0m\textsuperscript{2}. Those in the xy plane have area 4.6m\textsuperscript{2} ,and those in the zx plane have area 6.4m\textsuperscript{2}. An electric field of magnitude 8\,N/C has components in the y and z directions and is directed at 39\(^\circ\) from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
\begin{choices} %%%%%%% begin choices
    \CorrectChoice 3.222E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  3.544E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  3.899E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  4.289E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  4.718E+01\,N\(\cdot\) m\textsuperscript{2}/C
\end{choices} %%% end choices

\question 
    \includegraphics[width=0.12\textwidth]{Boxin2Dxyzaligned.png}Each surface of the rectangular box shown is aligned with the xyz coordinate system.  Two surfaces occupy identical rectangles in the planes x=0 and x=x\textsubscript{1}=2.2\,m. The other four surfaces are rectangles in y=y\textsubscript{0}=1.8\,m, y=y\textsubscript{1}=5.3\,m, z=z\textsubscript{0}=1.2\,m, and z=z\textsubscript{1}=5.5\,m. The surfaces in the yz plane each have area 15.0m\textsuperscript{2}. Those in the xy plane have area 7.7m\textsuperscript{2} ,and those in the zx plane have area 9.5m\textsuperscript{2}. An electric field of magnitude 11\,N/C has components in the y and z directions and is directed at 50\(^\circ\) from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
\begin{choices} %%%%%%% begin choices
    \choice  5.989E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  6.588E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  7.247E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \CorrectChoice 7.971E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  8.769E+01\,N\(\cdot\) m\textsuperscript{2}/C
\end{choices} %%% end choices

\question 
    \includegraphics[width=0.12\textwidth]{Boxin2Dxyzaligned.png}Each surface of the rectangular box shown is aligned with the xyz coordinate system.  Two surfaces occupy identical rectangles in the planes x=0 and x=x\textsubscript{1}=1.5\,m. The other four surfaces are rectangles in y=y\textsubscript{0}=1.4\,m, y=y\textsubscript{1}=4.3\,m, z=z\textsubscript{0}=1.2\,m, and z=z\textsubscript{1}=4.6\,m. The surfaces in the yz plane each have area 9.9m\textsuperscript{2}. Those in the xy plane have area 4.3m\textsuperscript{2} ,and those in the zx plane have area 5.1m\textsuperscript{2}. An electric field of magnitude 19\,N/C has components in the y and z directions and is directed at 31\(^\circ\) from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
\begin{choices} %%%%%%% begin choices
    \choice  3.750E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  4.125E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  4.537E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \CorrectChoice 4.991E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  5.490E+01\,N\(\cdot\) m\textsuperscript{2}/C
\end{choices} %%% end choices

\question 
    \includegraphics[width=0.12\textwidth]{Boxin2Dxyzaligned.png}Each surface of the rectangular box shown is aligned with the xyz coordinate system.  Two surfaces occupy identical rectangles in the planes x=0 and x=x\textsubscript{1}=2.5\,m. The other four surfaces are rectangles in y=y\textsubscript{0}=1.4\,m, y=y\textsubscript{1}=4.8\,m, z=z\textsubscript{0}=1.7\,m, and z=z\textsubscript{1}=4.6\,m. The surfaces in the yz plane each have area 9.9m\textsuperscript{2}. Those in the xy plane have area 8.5m\textsuperscript{2} ,and those in the zx plane have area 7.2m\textsuperscript{2}. An electric field of magnitude 14\,N/C has components in the y and z directions and is directed at 55\(^\circ\) from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
\begin{choices} %%%%%%% begin choices
    \CorrectChoice 8.314E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  9.146E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  1.006E+02\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  1.107E+02\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  1.217E+02\,N\(\cdot\) m\textsuperscript{2}/C
\end{choices} %%% end choices

\question 
    \includegraphics[width=0.12\textwidth]{Boxin2Dxyzaligned.png}Each surface of the rectangular box shown is aligned with the xyz coordinate system.  Two surfaces occupy identical rectangles in the planes x=0 and x=x\textsubscript{1}=1.3\,m. The other four surfaces are rectangles in y=y\textsubscript{0}=1.1\,m, y=y\textsubscript{1}=5.7\,m, z=z\textsubscript{0}=1.8\,m, and z=z\textsubscript{1}=4.5\,m. The surfaces in the yz plane each have area 12.0m\textsuperscript{2}. Those in the xy plane have area 6.0m\textsuperscript{2} ,and those in the zx plane have area 3.5m\textsuperscript{2}. An electric field of magnitude 5\,N/C has components in the y and z directions and is directed at 38\(^\circ\) from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
\begin{choices} %%%%%%% begin choices
    \choice  9.823E+00\,N\(\cdot\) m\textsuperscript{2}/C
    \CorrectChoice 1.080E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  1.189E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  1.307E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  1.438E+01\,N\(\cdot\) m\textsuperscript{2}/C
\end{choices} %%% end choices

\question 
    \includegraphics[width=0.12\textwidth]{Boxin2Dxyzaligned.png}Each surface of the rectangular box shown is aligned with the xyz coordinate system.  Two surfaces occupy identical rectangles in the planes x=0 and x=x\textsubscript{1}=2.5\,m. The other four surfaces are rectangles in y=y\textsubscript{0}=1.4\,m, y=y\textsubscript{1}=4.9\,m, z=z\textsubscript{0}=1.1\,m, and z=z\textsubscript{1}=5.3\,m. The surfaces in the yz plane each have area 15.0m\textsuperscript{2}. Those in the xy plane have area 8.8m\textsuperscript{2} ,and those in the zx plane have area 10.0m\textsuperscript{2}. An electric field of magnitude 9\,N/C has components in the y and z directions and is directed at 50\(^\circ\) from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
\begin{choices} %%%%%%% begin choices
    \choice  5.439E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  5.983E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  6.581E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \CorrectChoice 7.239E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  7.963E+01\,N\(\cdot\) m\textsuperscript{2}/C
\end{choices} %%% end choices

\question 
    \includegraphics[width=0.12\textwidth]{Boxin2Dxyzaligned.png}Each surface of the rectangular box shown is aligned with the xyz coordinate system.  Two surfaces occupy identical rectangles in the planes x=0 and x=x\textsubscript{1}=1.6\,m. The other four surfaces are rectangles in y=y\textsubscript{0}=1.3\,m, y=y\textsubscript{1}=4.4\,m, z=z\textsubscript{0}=1.4\,m, and z=z\textsubscript{1}=5.5\,m. The surfaces in the yz plane each have area 13.0m\textsuperscript{2}. Those in the xy plane have area 5.0m\textsuperscript{2} ,and those in the zx plane have area 6.6m\textsuperscript{2}. An electric field of magnitude 11\,N/C has components in the y and z directions and is directed at 34\(^\circ\) from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
\begin{choices} %%%%%%% begin choices
    \choice  2.756E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  3.032E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  3.335E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  3.668E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \CorrectChoice 4.035E+01\,N\(\cdot\) m\textsuperscript{2}/C
\end{choices} %%% end choices

\question 
    \includegraphics[width=0.12\textwidth]{Boxin2Dxyzaligned.png}Each surface of the rectangular box shown is aligned with the xyz coordinate system.  Two surfaces occupy identical rectangles in the planes x=0 and x=x\textsubscript{1}=2.4\,m. The other four surfaces are rectangles in y=y\textsubscript{0}=1.9\,m, y=y\textsubscript{1}=5.3\,m, z=z\textsubscript{0}=1.4\,m, and z=z\textsubscript{1}=5.5\,m. The surfaces in the yz plane each have area 14.0m\textsuperscript{2}. Those in the xy plane have area 8.2m\textsuperscript{2} ,and those in the zx plane have area 9.8m\textsuperscript{2}. An electric field of magnitude 11\,N/C has components in the y and z directions and is directed at 58\(^\circ\) from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
\begin{choices} %%%%%%% begin choices
    \choice  6.270E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  6.897E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  7.586E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  8.345E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \CorrectChoice 9.179E+01\,N\(\cdot\) m\textsuperscript{2}/C
\end{choices} %%% end choices

\question 
    \includegraphics[width=0.12\textwidth]{Boxin2Dxyzaligned.png}Each surface of the rectangular box shown is aligned with the xyz coordinate system.  Two surfaces occupy identical rectangles in the planes x=0 and x=x\textsubscript{1}=2.2\,m. The other four surfaces are rectangles in y=y\textsubscript{0}=1.7\,m, y=y\textsubscript{1}=4.6\,m, z=z\textsubscript{0}=1.4\,m, and z=z\textsubscript{1}=4.5\,m. The surfaces in the yz plane each have area 9.0m\textsuperscript{2}. Those in the xy plane have area 6.4m\textsuperscript{2} ,and those in the zx plane have area 6.8m\textsuperscript{2}. An electric field of magnitude 15\,N/C has components in the y and z directions and is directed at 31\(^\circ\) from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
\begin{choices} %%%%%%% begin choices
    \choice  3.959E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  4.354E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  4.790E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \CorrectChoice 5.269E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  5.796E+01\,N\(\cdot\) m\textsuperscript{2}/C
\end{choices} %%% end choices

\question 
    \includegraphics[width=0.12\textwidth]{Boxin2Dxyzaligned.png}Each surface of the rectangular box shown is aligned with the xyz coordinate system.  Two surfaces occupy identical rectangles in the planes x=0 and x=x\textsubscript{1}=1.8\,m. The other four surfaces are rectangles in y=y\textsubscript{0}=1.2\,m, y=y\textsubscript{1}=5.9\,m, z=z\textsubscript{0}=1.3\,m, and z=z\textsubscript{1}=5.2\,m. The surfaces in the yz plane each have area 18.0m\textsuperscript{2}. Those in the xy plane have area 8.5m\textsuperscript{2} ,and those in the zx plane have area 7.0m\textsuperscript{2}. An electric field of magnitude 12\,N/C has components in the y and z directions and is directed at 49\(^\circ\) from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
\begin{choices} %%%%%%% begin choices
    \choice  4.777E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  5.254E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  5.780E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \CorrectChoice 6.358E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  6.993E+01\,N\(\cdot\) m\textsuperscript{2}/C
\end{choices} %%% end choices

\question 
    \includegraphics[width=0.12\textwidth]{Boxin2Dxyzaligned.png}Each surface of the rectangular box shown is aligned with the xyz coordinate system.  Two surfaces occupy identical rectangles in the planes x=0 and x=x\textsubscript{1}=2.4\,m. The other four surfaces are rectangles in y=y\textsubscript{0}=1.3\,m, y=y\textsubscript{1}=5.7\,m, z=z\textsubscript{0}=1.9\,m, and z=z\textsubscript{1}=5.4\,m. The surfaces in the yz plane each have area 15.0m\textsuperscript{2}. Those in the xy plane have area 11.0m\textsuperscript{2} ,and those in the zx plane have area 8.4m\textsuperscript{2}. An electric field of magnitude 8\,N/C has components in the y and z directions and is directed at 26\(^\circ\) from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
\begin{choices} %%%%%%% begin choices
    \choice  2.012E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  2.213E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  2.435E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  2.678E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \CorrectChoice 2.946E+01\,N\(\cdot\) m\textsuperscript{2}/C
\end{choices} %%% end choices
%\pagebreak
%\end{choices}%??????????????
\end{questions}%%%%%%%% end questions

\subsection{}%%%% subsection 3

\begin{questions} %%%%%%% begin questions

\question 
    \includegraphics[width=0.12\textwidth]{Boxin2Dxyzaligned.png}Each surface of the rectangular box shown is aligned with the xyz coordinate system.  Two surfaces occupy identical rectangles in the planes x=0 and x=x\textsubscript{1}=1.3\,m. The other four surfaces are rectangles in y=y\textsubscript{0}=1.5\,m, y=y\textsubscript{1}=5.0\,m, z=z\textsubscript{0}=1.6\,m, and z=z\textsubscript{1}=4.8\,m. The surfaces in the yz plane each have area 11.0m\textsuperscript{2}. Those in the xy plane have area 4.5m\textsuperscript{2} ,and those in the zx plane have area 4.2m\textsuperscript{2}. An electric field has the xyz components (0,\,6.4,\,6.8)\,N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
\begin{choices} %%%%%%% begin choices
    \CorrectChoice 2.662E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  2.929E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  3.222E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  3.544E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  3.898E+01\,N\(\cdot\) m\textsuperscript{2}/C
\end{choices} %%% end choices

\question 
    \includegraphics[width=0.12\textwidth]{Boxin2Dxyzaligned.png}Each surface of the rectangular box shown is aligned with the xyz coordinate system.  Two surfaces occupy identical rectangles in the planes x=0 and x=x\textsubscript{1}=2.7\,m. The other four surfaces are rectangles in y=y\textsubscript{0}=1.7\,m, y=y\textsubscript{1}=4.3\,m, z=z\textsubscript{0}=1.8\,m, and z=z\textsubscript{1}=4.9\,m. The surfaces in the yz plane each have area 8.1m\textsuperscript{2}. Those in the xy plane have area 7.0m\textsuperscript{2} ,and those in the zx plane have area 8.4m\textsuperscript{2}. An electric field has the xyz components (0,\,9.2,\,7.1)\,N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
\begin{choices} %%%%%%% begin choices
    \choice  6.364E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  7.000E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \CorrectChoice 7.700E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  8.470E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  9.317E+01\,N\(\cdot\) m\textsuperscript{2}/C
\end{choices} %%% end choices

\question 
    \includegraphics[width=0.12\textwidth]{Boxin2Dxyzaligned.png}Each surface of the rectangular box shown is aligned with the xyz coordinate system.  Two surfaces occupy identical rectangles in the planes x=0 and x=x\textsubscript{1}=2.6\,m. The other four surfaces are rectangles in y=y\textsubscript{0}=1.2\,m, y=y\textsubscript{1}=5.9\,m, z=z\textsubscript{0}=1.9\,m, and z=z\textsubscript{1}=5.0\,m. The surfaces in the yz plane each have area 15.0m\textsuperscript{2}. Those in the xy plane have area 12.0m\textsuperscript{2} ,and those in the zx plane have area 8.1m\textsuperscript{2}. An electric field has the xyz components (0,\,8.1,\,6.8)\,N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
\begin{choices} %%%%%%% begin choices
    \CorrectChoice 6.529E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  7.181E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  7.900E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  8.690E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  9.559E+01\,N\(\cdot\) m\textsuperscript{2}/C
\end{choices} %%% end choices

\question 
    \includegraphics[width=0.12\textwidth]{Boxin2Dxyzaligned.png}Each surface of the rectangular box shown is aligned with the xyz coordinate system.  Two surfaces occupy identical rectangles in the planes x=0 and x=x\textsubscript{1}=1.3\,m. The other four surfaces are rectangles in y=y\textsubscript{0}=1.6\,m, y=y\textsubscript{1}=5.3\,m, z=z\textsubscript{0}=1.3\,m, and z=z\textsubscript{1}=5.6\,m. The surfaces in the yz plane each have area 16.0m\textsuperscript{2}. Those in the xy plane have area 4.8m\textsuperscript{2} ,and those in the zx plane have area 5.6m\textsuperscript{2}. An electric field has the xyz components (0,\,5.5,\,9.1)\,N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
\begin{choices} %%%%%%% begin choices
    \CorrectChoice 3.074E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  3.382E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  3.720E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  4.092E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  4.501E+01\,N\(\cdot\) m\textsuperscript{2}/C
\end{choices} %%% end choices

\question 
    \includegraphics[width=0.12\textwidth]{Boxin2Dxyzaligned.png}Each surface of the rectangular box shown is aligned with the xyz coordinate system.  Two surfaces occupy identical rectangles in the planes x=0 and x=x\textsubscript{1}=2.3\,m. The other four surfaces are rectangles in y=y\textsubscript{0}=1.5\,m, y=y\textsubscript{1}=5.2\,m, z=z\textsubscript{0}=1.8\,m, and z=z\textsubscript{1}=4.4\,m. The surfaces in the yz plane each have area 9.6m\textsuperscript{2}. Those in the xy plane have area 8.5m\textsuperscript{2} ,and those in the zx plane have area 6.0m\textsuperscript{2}. An electric field has the xyz components (0,\,8.7,\,8.4)\,N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
\begin{choices} %%%%%%% begin choices
    \choice  4.730E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \CorrectChoice 5.203E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  5.723E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  6.295E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  6.925E+01\,N\(\cdot\) m\textsuperscript{2}/C
\end{choices} %%% end choices

\question 
    \includegraphics[width=0.12\textwidth]{Boxin2Dxyzaligned.png}Each surface of the rectangular box shown is aligned with the xyz coordinate system.  Two surfaces occupy identical rectangles in the planes x=0 and x=x\textsubscript{1}=2.8\,m. The other four surfaces are rectangles in y=y\textsubscript{0}=1.3\,m, y=y\textsubscript{1}=4.2\,m, z=z\textsubscript{0}=1.9\,m, and z=z\textsubscript{1}=5.5\,m. The surfaces in the yz plane each have area 10.0m\textsuperscript{2}. Those in the xy plane have area 8.1m\textsuperscript{2} ,and those in the zx plane have area 10.0m\textsuperscript{2}. An electric field has the xyz components (0,\,8.5,\,6.4)\,N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
\begin{choices} %%%%%%% begin choices
    \choice  7.081E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  7.789E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \CorrectChoice 8.568E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  9.425E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  1.037E+02\,N\(\cdot\) m\textsuperscript{2}/C
\end{choices} %%% end choices

\question 
    \includegraphics[width=0.12\textwidth]{Boxin2Dxyzaligned.png}Each surface of the rectangular box shown is aligned with the xyz coordinate system.  Two surfaces occupy identical rectangles in the planes x=0 and x=x\textsubscript{1}=1.8\,m. The other four surfaces are rectangles in y=y\textsubscript{0}=1.4\,m, y=y\textsubscript{1}=5.0\,m, z=z\textsubscript{0}=1.6\,m, and z=z\textsubscript{1}=5.9\,m. The surfaces in the yz plane each have area 15.0m\textsuperscript{2}. Those in the xy plane have area 6.5m\textsuperscript{2} ,and those in the zx plane have area 7.7m\textsuperscript{2}. An electric field has the xyz components (0,\,8.0,\,9.4)\,N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
\begin{choices} %%%%%%% begin choices
    \CorrectChoice 6.192E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  6.811E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  7.492E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  8.242E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  9.066E+01\,N\(\cdot\) m\textsuperscript{2}/C
\end{choices} %%% end choices

\question 
    \includegraphics[width=0.12\textwidth]{Boxin2Dxyzaligned.png}Each surface of the rectangular box shown is aligned with the xyz coordinate system.  Two surfaces occupy identical rectangles in the planes x=0 and x=x\textsubscript{1}=1.2\,m. The other four surfaces are rectangles in y=y\textsubscript{0}=1.7\,m, y=y\textsubscript{1}=5.0\,m, z=z\textsubscript{0}=1.9\,m, and z=z\textsubscript{1}=4.3\,m. The surfaces in the yz plane each have area 7.9m\textsuperscript{2}. Those in the xy plane have area 4.0m\textsuperscript{2} ,and those in the zx plane have area 2.9m\textsuperscript{2}. An electric field has the xyz components (0,\,5.3,\,9.1)\,N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
\begin{choices} %%%%%%% begin choices
    \choice  1.388E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \CorrectChoice 1.526E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  1.679E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  1.847E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  2.032E+01\,N\(\cdot\) m\textsuperscript{2}/C
\end{choices} %%% end choices

\question 
    \includegraphics[width=0.12\textwidth]{Boxin2Dxyzaligned.png}Each surface of the rectangular box shown is aligned with the xyz coordinate system.  Two surfaces occupy identical rectangles in the planes x=0 and x=x\textsubscript{1}=1.4\,m. The other four surfaces are rectangles in y=y\textsubscript{0}=1.3\,m, y=y\textsubscript{1}=5.6\,m, z=z\textsubscript{0}=1.7\,m, and z=z\textsubscript{1}=4.5\,m. The surfaces in the yz plane each have area 12.0m\textsuperscript{2}. Those in the xy plane have area 6.0m\textsuperscript{2} ,and those in the zx plane have area 3.9m\textsuperscript{2}. An electric field has the xyz components (0,\,6.5,\,9.8)\,N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
\begin{choices} %%%%%%% begin choices
    \choice  1.740E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  1.914E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  2.106E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  2.316E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \CorrectChoice 2.548E+01\,N\(\cdot\) m\textsuperscript{2}/C
\end{choices} %%% end choices

\question 
    \includegraphics[width=0.12\textwidth]{Boxin2Dxyzaligned.png}Each surface of the rectangular box shown is aligned with the xyz coordinate system.  Two surfaces occupy identical rectangles in the planes x=0 and x=x\textsubscript{1}=2.0\,m. The other four surfaces are rectangles in y=y\textsubscript{0}=1.4\,m, y=y\textsubscript{1}=4.7\,m, z=z\textsubscript{0}=1.2\,m, and z=z\textsubscript{1}=4.1\,m. The surfaces in the yz plane each have area 9.6m\textsuperscript{2}. Those in the xy plane have area 6.6m\textsuperscript{2} ,and those in the zx plane have area 5.8m\textsuperscript{2}. An electric field has the xyz components (0,\,8.4,\,5.8)\,N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
\begin{choices} %%%%%%% begin choices
    \choice  3.328E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  3.660E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  4.026E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  4.429E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \CorrectChoice 4.872E+01\,N\(\cdot\) m\textsuperscript{2}/C
\end{choices} %%% end choices

\question 
    \includegraphics[width=0.12\textwidth]{Boxin2Dxyzaligned.png}Each surface of the rectangular box shown is aligned with the xyz coordinate system.  Two surfaces occupy identical rectangles in the planes x=0 and x=x\textsubscript{1}=2.0\,m. The other four surfaces are rectangles in y=y\textsubscript{0}=1.8\,m, y=y\textsubscript{1}=4.2\,m, z=z\textsubscript{0}=1.3\,m, and z=z\textsubscript{1}=5.8\,m. The surfaces in the yz plane each have area 11.0m\textsuperscript{2}. Those in the xy plane have area 4.8m\textsuperscript{2} ,and those in the zx plane have area 9.0m\textsuperscript{2}. An electric field has the xyz components (0,\,6.1,\,5.6)\,N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
\begin{choices} %%%%%%% begin choices
    \choice  4.125E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  4.537E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  4.991E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \CorrectChoice 5.490E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  6.039E+01\,N\(\cdot\) m\textsuperscript{2}/C
\end{choices} %%% end choices

\question 
    \includegraphics[width=0.12\textwidth]{Boxin2Dxyzaligned.png}Each surface of the rectangular box shown is aligned with the xyz coordinate system.  Two surfaces occupy identical rectangles in the planes x=0 and x=x\textsubscript{1}=2.4\,m. The other four surfaces are rectangles in y=y\textsubscript{0}=1.1\,m, y=y\textsubscript{1}=4.8\,m, z=z\textsubscript{0}=1.8\,m, and z=z\textsubscript{1}=4.8\,m. The surfaces in the yz plane each have area 11.0m\textsuperscript{2}. Those in the xy plane have area 8.9m\textsuperscript{2} ,and those in the zx plane have area 7.2m\textsuperscript{2}. An electric field has the xyz components (0,\,5.9,\,8.9)\,N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
\begin{choices} %%%%%%% begin choices
    \choice  2.901E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  3.192E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  3.511E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  3.862E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \CorrectChoice 4.248E+01\,N\(\cdot\) m\textsuperscript{2}/C
\end{choices} %%% end choices

\question 
    \includegraphics[width=0.12\textwidth]{Boxin2Dxyzaligned.png}Each surface of the rectangular box shown is aligned with the xyz coordinate system.  Two surfaces occupy identical rectangles in the planes x=0 and x=x\textsubscript{1}=1.6\,m. The other four surfaces are rectangles in y=y\textsubscript{0}=1.6\,m, y=y\textsubscript{1}=5.6\,m, z=z\textsubscript{0}=1.8\,m, and z=z\textsubscript{1}=4.4\,m. The surfaces in the yz plane each have area 10.0m\textsuperscript{2}. Those in the xy plane have area 6.4m\textsuperscript{2} ,and those in the zx plane have area 4.2m\textsuperscript{2}. An electric field has the xyz components (0,\,5.5,\,7.3)\,N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
\begin{choices} %%%%%%% begin choices
    \choice  1.891E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  2.080E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \CorrectChoice 2.288E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  2.517E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  2.768E+01\,N\(\cdot\) m\textsuperscript{2}/C
\end{choices} %%% end choices

\question 
    \includegraphics[width=0.12\textwidth]{Boxin2Dxyzaligned.png}Each surface of the rectangular box shown is aligned with the xyz coordinate system.  Two surfaces occupy identical rectangles in the planes x=0 and x=x\textsubscript{1}=1.1\,m. The other four surfaces are rectangles in y=y\textsubscript{0}=1.7\,m, y=y\textsubscript{1}=4.2\,m, z=z\textsubscript{0}=1.1\,m, and z=z\textsubscript{1}=4.5\,m. The surfaces in the yz plane each have area 8.5m\textsuperscript{2}. Those in the xy plane have area 2.8m\textsuperscript{2} ,and those in the zx plane have area 3.7m\textsuperscript{2}. An electric field has the xyz components (0,\,7.4,\,8.9)\,N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
\begin{choices} %%%%%%% begin choices
    \choice  2.079E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  2.287E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  2.516E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \CorrectChoice 2.768E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  3.044E+01\,N\(\cdot\) m\textsuperscript{2}/C
\end{choices} %%% end choices

\question 
    \includegraphics[width=0.12\textwidth]{Boxin2Dxyzaligned.png}Each surface of the rectangular box shown is aligned with the xyz coordinate system.  Two surfaces occupy identical rectangles in the planes x=0 and x=x\textsubscript{1}=2.5\,m. The other four surfaces are rectangles in y=y\textsubscript{0}=1.3\,m, y=y\textsubscript{1}=5.3\,m, z=z\textsubscript{0}=1.3\,m, and z=z\textsubscript{1}=4.3\,m. The surfaces in the yz plane each have area 12.0m\textsuperscript{2}. Those in the xy plane have area 10.0m\textsuperscript{2} ,and those in the zx plane have area 7.5m\textsuperscript{2}. An electric field has the xyz components (0,\,9.7,\,9.3)\,N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
\begin{choices} %%%%%%% begin choices
    \choice  6.614E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \CorrectChoice 7.275E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  8.003E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  8.803E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  9.683E+01\,N\(\cdot\) m\textsuperscript{2}/C
\end{choices} %%% end choices

\question 
    \includegraphics[width=0.12\textwidth]{Boxin2Dxyzaligned.png}Each surface of the rectangular box shown is aligned with the xyz coordinate system.  Two surfaces occupy identical rectangles in the planes x=0 and x=x\textsubscript{1}=2.8\,m. The other four surfaces are rectangles in y=y\textsubscript{0}=1.1\,m, y=y\textsubscript{1}=5.6\,m, z=z\textsubscript{0}=1.8\,m, and z=z\textsubscript{1}=5.5\,m. The surfaces in the yz plane each have area 17.0m\textsuperscript{2}. Those in the xy plane have area 13.0m\textsuperscript{2} ,and those in the zx plane have area 10.0m\textsuperscript{2}. An electric field has the xyz components (0,\,7.0,\,5.7)\,N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
\begin{choices} %%%%%%% begin choices
    \choice  4.953E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  5.449E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  5.993E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  6.593E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \CorrectChoice 7.252E+01\,N\(\cdot\) m\textsuperscript{2}/C
\end{choices} %%% end choices

\question 
    \includegraphics[width=0.12\textwidth]{Boxin2Dxyzaligned.png}Each surface of the rectangular box shown is aligned with the xyz coordinate system.  Two surfaces occupy identical rectangles in the planes x=0 and x=x\textsubscript{1}=2.7\,m. The other four surfaces are rectangles in y=y\textsubscript{0}=1.5\,m, y=y\textsubscript{1}=5.6\,m, z=z\textsubscript{0}=1.3\,m, and z=z\textsubscript{1}=4.2\,m. The surfaces in the yz plane each have area 12.0m\textsuperscript{2}. Those in the xy plane have area 11.0m\textsuperscript{2} ,and those in the zx plane have area 7.8m\textsuperscript{2}. An electric field has the xyz components (0,\,8.5,\,7.3)\,N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
\begin{choices} %%%%%%% begin choices
    \choice  5.000E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  5.500E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  6.050E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \CorrectChoice 6.656E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  7.321E+01\,N\(\cdot\) m\textsuperscript{2}/C
\end{choices} %%% end choices

\question 
    \includegraphics[width=0.12\textwidth]{Boxin2Dxyzaligned.png}Each surface of the rectangular box shown is aligned with the xyz coordinate system.  Two surfaces occupy identical rectangles in the planes x=0 and x=x\textsubscript{1}=1.5\,m. The other four surfaces are rectangles in y=y\textsubscript{0}=1.6\,m, y=y\textsubscript{1}=4.3\,m, z=z\textsubscript{0}=1.3\,m, and z=z\textsubscript{1}=5.1\,m. The surfaces in the yz plane each have area 10.0m\textsuperscript{2}. Those in the xy plane have area 4.0m\textsuperscript{2} ,and those in the zx plane have area 5.7m\textsuperscript{2}. An electric field has the xyz components (0,\,5.7,\,7.5)\,N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
\begin{choices} %%%%%%% begin choices
    \CorrectChoice 3.249E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  3.574E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  3.931E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  4.324E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  4.757E+01\,N\(\cdot\) m\textsuperscript{2}/C
\end{choices} %%% end choices

\question 
    \includegraphics[width=0.12\textwidth]{Boxin2Dxyzaligned.png}Each surface of the rectangular box shown is aligned with the xyz coordinate system.  Two surfaces occupy identical rectangles in the planes x=0 and x=x\textsubscript{1}=2.8\,m. The other four surfaces are rectangles in y=y\textsubscript{0}=1.7\,m, y=y\textsubscript{1}=4.5\,m, z=z\textsubscript{0}=1.5\,m, and z=z\textsubscript{1}=5.0\,m. The surfaces in the yz plane each have area 9.8m\textsuperscript{2}. Those in the xy plane have area 7.8m\textsuperscript{2} ,and those in the zx plane have area 9.8m\textsuperscript{2}. An electric field has the xyz components (0,\,6.1,\,9.3)\,N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
\begin{choices} %%%%%%% begin choices
    \CorrectChoice 5.978E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  6.576E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  7.233E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  7.957E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  8.752E+01\,N\(\cdot\) m\textsuperscript{2}/C
\end{choices} %%% end choices
%\pagebreak
%\end{choices}%??????????????
\end{questions}%%%%%%%% end questions

\subsection{}%%%% subsection 4

\begin{questions} %%%%%%% begin questions

\question What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0,\,y=0), (x=4,\,y=0), (x=0,\,y=6), and (x=4,\,y=6), where x and y are measured in meters. The electric field is, \(\vec E=3y^{1.9}\hat i +3x^{1.5}\hat j +3y^{1.6}\hat k\).
\begin{choices} %%%%%%% begin choices
    \choice  3.658E+02\,V\(\cdot\) m
    \choice  4.024E+02\,V\(\cdot\) m
    \choice  4.426E+02\,V\(\cdot\) m
    \CorrectChoice 4.869E+02\,V\(\cdot\) m
    \choice  5.355E+02\,V\(\cdot\) m
\end{choices} %%% end choices

\question What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0,\,y=0), (x=4,\,y=0), (x=0,\,y=4), and (x=4,\,y=4), where x and y are measured in meters. The electric field is, \(\vec E=4y^{2.2}\hat i +1x^{3.0}\hat j +2y^{1.7}\hat k\).
\begin{choices} %%%%%%% begin choices
    \choice  8.545E+01\,V\(\cdot\) m
    \choice  9.400E+01\,V\(\cdot\) m
    \choice  1.034E+02\,V\(\cdot\) m
    \choice  1.137E+02\,V\(\cdot\) m
    \CorrectChoice 1.251E+02\,V\(\cdot\) m
\end{choices} %%% end choices

\question What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0,\,y=0), (x=7,\,y=0), (x=0,\,y=7), and (x=7,\,y=7), where x and y are measured in meters. The electric field is, \(\vec E=4y^{2.3}\hat i +3x^{2.4}\hat j +2y^{1.8}\hat k\).
\begin{choices} %%%%%%% begin choices
    \choice  8.731E+02\,V\(\cdot\) m
    \choice  9.604E+02\,V\(\cdot\) m
    \choice  1.056E+03\,V\(\cdot\) m
    \CorrectChoice 1.162E+03\,V\(\cdot\) m
    \choice  1.278E+03\,V\(\cdot\) m
\end{choices} %%% end choices

\question What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0,\,y=0), (x=5,\,y=0), (x=0,\,y=7), and (x=5,\,y=7), where x and y are measured in meters. The electric field is, \(\vec E=3y^{2.7}\hat i +1x^{2.5}\hat j +3y^{3.3}\hat k\).
\begin{choices} %%%%%%% begin choices
    \choice  1.128E+04\,V\(\cdot\) m
    \choice  1.241E+04\,V\(\cdot\) m
    \choice  1.365E+04\,V\(\cdot\) m
    \CorrectChoice 1.502E+04\,V\(\cdot\) m
    \choice  1.652E+04\,V\(\cdot\) m
\end{choices} %%% end choices

\question What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0,\,y=0), (x=5,\,y=0), (x=0,\,y=7), and (x=5,\,y=7), where x and y are measured in meters. The electric field is, \(\vec E=3y^{2.9}\hat i +3x^{1.6}\hat j +4y^{2.5}\hat k\).
\begin{choices} %%%%%%% begin choices
    \choice  4.286E+03\,V\(\cdot\) m
    \choice  4.714E+03\,V\(\cdot\) m
    \CorrectChoice 5.186E+03\,V\(\cdot\) m
    \choice  5.704E+03\,V\(\cdot\) m
    \choice  6.275E+03\,V\(\cdot\) m
\end{choices} %%% end choices

\question What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0,\,y=0), (x=8,\,y=0), (x=0,\,y=8), and (x=8,\,y=8), where x and y are measured in meters. The electric field is, \(\vec E=1y^{2.8}\hat i +5x^{2.7}\hat j +5y^{1.6}\hat k\).
\begin{choices} %%%%%%% begin choices
    \CorrectChoice 3.429E+03\,V\(\cdot\) m
    \choice  3.771E+03\,V\(\cdot\) m
    \choice  4.149E+03\,V\(\cdot\) m
    \choice  4.564E+03\,V\(\cdot\) m
    \choice  5.020E+03\,V\(\cdot\) m
\end{choices} %%% end choices

\question What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0,\,y=0), (x=7,\,y=0), (x=0,\,y=5), and (x=7,\,y=5), where x and y are measured in meters. The electric field is, \(\vec E=1y^{2.4}\hat i +4x^{1.7}\hat j +4y^{2.1}\hat k\).
\begin{choices} %%%%%%% begin choices
    \choice  1.206E+03\,V\(\cdot\) m
    \CorrectChoice 1.326E+03\,V\(\cdot\) m
    \choice  1.459E+03\,V\(\cdot\) m
    \choice  1.605E+03\,V\(\cdot\) m
    \choice  1.765E+03\,V\(\cdot\) m
\end{choices} %%% end choices

\question What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0,\,y=0), (x=7,\,y=0), (x=0,\,y=6), and (x=7,\,y=6), where x and y are measured in meters. The electric field is, \(\vec E=2y^{2.5}\hat i +3x^{1.8}\hat j +2y^{2.8}\hat k\).
\begin{choices} %%%%%%% begin choices
    \CorrectChoice 3.337E+03\,V\(\cdot\) m
    \choice  3.670E+03\,V\(\cdot\) m
    \choice  4.037E+03\,V\(\cdot\) m
    \choice  4.441E+03\,V\(\cdot\) m
    \choice  4.885E+03\,V\(\cdot\) m
\end{choices} %%% end choices

\question What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0,\,y=0), (x=9,\,y=0), (x=0,\,y=9), and (x=9,\,y=9), where x and y are measured in meters. The electric field is, \(\vec E=3y^{2.8}\hat i +1x^{2.3}\hat j +2y^{2.9}\hat k\).
\begin{choices} %%%%%%% begin choices
    \choice  2.210E+04\,V\(\cdot\) m
    \CorrectChoice 2.431E+04\,V\(\cdot\) m
    \choice  2.674E+04\,V\(\cdot\) m
    \choice  2.941E+04\,V\(\cdot\) m
    \choice  3.235E+04\,V\(\cdot\) m
\end{choices} %%% end choices

\question What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0,\,y=0), (x=7,\,y=0), (x=0,\,y=4), and (x=7,\,y=4), where x and y are measured in meters. The electric field is, \(\vec E=2y^{2.2}\hat i +3x^{2.1}\hat j +5y^{3.3}\hat k\).
\begin{choices} %%%%%%% begin choices
    \choice  2.610E+03\,V\(\cdot\) m
    \choice  2.871E+03\,V\(\cdot\) m
    \CorrectChoice 3.158E+03\,V\(\cdot\) m
    \choice  3.474E+03\,V\(\cdot\) m
    \choice  3.822E+03\,V\(\cdot\) m
\end{choices} %%% end choices

\question What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0,\,y=0), (x=5,\,y=0), (x=0,\,y=7), and (x=5,\,y=7), where x and y are measured in meters. The electric field is, \(\vec E=2y^{2.8}\hat i +3x^{2.8}\hat j +2y^{2.4}\hat k\).
\begin{choices} %%%%%%% begin choices
    \choice  1.997E+03\,V\(\cdot\) m
    \CorrectChoice 2.197E+03\,V\(\cdot\) m
    \choice  2.417E+03\,V\(\cdot\) m
    \choice  2.659E+03\,V\(\cdot\) m
    \choice  2.924E+03\,V\(\cdot\) m
\end{choices} %%% end choices

\question What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0,\,y=0), (x=8,\,y=0), (x=0,\,y=6), and (x=8,\,y=6), where x and y are measured in meters. The electric field is, \(\vec E=4y^{1.4}\hat i +2x^{2.3}\hat j +4y^{2.3}\hat k\).
\begin{choices} %%%%%%% begin choices
    \choice  2.694E+03\,V\(\cdot\) m
    \choice  2.963E+03\,V\(\cdot\) m
    \choice  3.259E+03\,V\(\cdot\) m
    \CorrectChoice 3.585E+03\,V\(\cdot\) m
    \choice  3.944E+03\,V\(\cdot\) m
\end{choices} %%% end choices

\question What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0,\,y=0), (x=6,\,y=0), (x=0,\,y=5), and (x=6,\,y=5), where x and y are measured in meters. The electric field is, \(\vec E=3y^{1.7}\hat i +3x^{1.6}\hat j +4y^{2.7}\hat k\).
\begin{choices} %%%%%%% begin choices
    \choice  2.067E+03\,V\(\cdot\) m
    \choice  2.274E+03\,V\(\cdot\) m
    \CorrectChoice 2.501E+03\,V\(\cdot\) m
    \choice  2.752E+03\,V\(\cdot\) m
    \choice  3.027E+03\,V\(\cdot\) m
\end{choices} %%% end choices

\question What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0,\,y=0), (x=6,\,y=0), (x=0,\,y=6), and (x=6,\,y=6), where x and y are measured in meters. The electric field is, \(\vec E=2y^{1.8}\hat i +3x^{1.9}\hat j +5y^{3.2}\hat k\).
\begin{choices} %%%%%%% begin choices
    \choice  9.952E+03\,V\(\cdot\) m
    \choice  1.095E+04\,V\(\cdot\) m
    \choice  1.204E+04\,V\(\cdot\) m
    \CorrectChoice 1.325E+04\,V\(\cdot\) m
    \choice  1.457E+04\,V\(\cdot\) m
\end{choices} %%% end choices

\question What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0,\,y=0), (x=6,\,y=0), (x=0,\,y=6), and (x=6,\,y=6), where x and y are measured in meters. The electric field is, \(\vec E=4y^{2.0}\hat i +3x^{2.0}\hat j +3y^{3.0}\hat k\).
\begin{choices} %%%%%%% begin choices
    \choice  4.820E+03\,V\(\cdot\) m
    \choice  5.302E+03\,V\(\cdot\) m
    \CorrectChoice 5.832E+03\,V\(\cdot\) m
    \choice  6.415E+03\,V\(\cdot\) m
    \choice  7.057E+03\,V\(\cdot\) m
\end{choices} %%% end choices

\question What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0,\,y=0), (x=6,\,y=0), (x=0,\,y=3), and (x=6,\,y=3), where x and y are measured in meters. The electric field is, \(\vec E=1y^{1.6}\hat i +3x^{2.6}\hat j +2y^{3.2}\hat k\).
\begin{choices} %%%%%%% begin choices
    \choice  1.969E+02\,V\(\cdot\) m
    \choice  2.166E+02\,V\(\cdot\) m
    \choice  2.383E+02\,V\(\cdot\) m
    \choice  2.621E+02\,V\(\cdot\) m
    \CorrectChoice 2.883E+02\,V\(\cdot\) m
\end{choices} %%% end choices

\question What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0,\,y=0), (x=4,\,y=0), (x=0,\,y=3), and (x=4,\,y=3), where x and y are measured in meters. The electric field is, \(\vec E=2y^{2.7}\hat i +2x^{2.9}\hat j +2y^{2.0}\hat k\).
\begin{choices} %%%%%%% begin choices
    \CorrectChoice 7.200E+01\,V\(\cdot\) m
    \choice  7.920E+01\,V\(\cdot\) m
    \choice  8.712E+01\,V\(\cdot\) m
    \choice  9.583E+01\,V\(\cdot\) m
    \choice  1.054E+02\,V\(\cdot\) m
\end{choices} %%% end choices

\question What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0,\,y=0), (x=4,\,y=0), (x=0,\,y=9), and (x=4,\,y=9), where x and y are measured in meters. The electric field is, \(\vec E=1y^{2.2}\hat i +1x^{3.3}\hat j +5y^{2.4}\hat k\).
\begin{choices} %%%%%%% begin choices
    \choice  7.054E+03\,V\(\cdot\) m
    \choice  7.759E+03\,V\(\cdot\) m
    \choice  8.535E+03\,V\(\cdot\) m
    \choice  9.388E+03\,V\(\cdot\) m
    \CorrectChoice 1.033E+04\,V\(\cdot\) m
\end{choices} %%% end choices

\question What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0,\,y=0), (x=8,\,y=0), (x=0,\,y=8), and (x=8,\,y=8), where x and y are measured in meters. The electric field is, \(\vec E=2y^{2.0}\hat i +2x^{2.1}\hat j +3y^{2.5}\hat k\).
\begin{choices} %%%%%%% begin choices
    \choice  9.027E+03\,V\(\cdot\) m
    \CorrectChoice 9.930E+03\,V\(\cdot\) m
    \choice  1.092E+04\,V\(\cdot\) m
    \choice  1.202E+04\,V\(\cdot\) m
    \choice  1.322E+04\,V\(\cdot\) m
\end{choices} %%% end choices
%\pagebreak
%\end{choices}%??????????????
\end{questions}%%%%%%%% end questions

\subsection{}%%%% subsection 5

\begin{questions} %%%%%%% begin questions

\question Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 2.8\,nano-Coulombs. What is the magnitude of the electric field at a distance of 3.5\,m from the center of the shells?
\begin{choices} %%%%%%% begin choices
    \CorrectChoice 6.171E+00\,N/C
    \choice  6.789E+00\,N/C
    \choice  7.467E+00\,N/C
    \choice  8.214E+00\,N/C
    \choice  9.036E+00\,N/C
\end{choices} %%% end choices

\question Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 5.6\,nano-Coulombs. What is the magnitude of the electric field at a distance of 3.6\,m from the center of the shells?
\begin{choices} %%%%%%% begin choices
    \choice  9.642E+00\,N/C
    \choice  1.061E+01\,N/C
    \CorrectChoice 1.167E+01\,N/C
    \choice  1.283E+01\,N/C
    \choice  1.412E+01\,N/C
\end{choices} %%% end choices

\question Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 7.6\,nano-Coulombs. What is the magnitude of the electric field at a distance of 5.8\,m from the center of the shells?
\begin{choices} %%%%%%% begin choices
    \CorrectChoice 1.017E+01\,N/C
    \choice  1.118E+01\,N/C
    \choice  1.230E+01\,N/C
    \choice  1.353E+01\,N/C
    \choice  1.488E+01\,N/C
\end{choices} %%% end choices

\question Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 3.4\,nano-Coulombs. What is the magnitude of the electric field at a distance of 2.8\,m from the center of the shells?
\begin{choices} %%%%%%% begin choices
    \choice  5.865E+00\,N/C
    \choice  6.451E+00\,N/C
    \choice  7.096E+00\,N/C
    \CorrectChoice 7.806E+00\,N/C
    \choice  8.587E+00\,N/C
\end{choices} %%% end choices

\question Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 9.7\,nano-Coulombs. What is the magnitude of the electric field at a distance of 4.4\,m from the center of the shells?
\begin{choices} %%%%%%% begin choices
    \choice  1.491E+01\,N/C
    \choice  1.640E+01\,N/C
    \CorrectChoice 1.804E+01\,N/C
    \choice  1.984E+01\,N/C
    \choice  2.182E+01\,N/C
\end{choices} %%% end choices

\question Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 6.5\,nano-Coulombs. What is the magnitude of the electric field at a distance of 1.3\,m from the center of the shells?
\begin{choices} %%%%%%% begin choices
    \choice  2.601E+01\,N/C
    \choice  2.861E+01\,N/C
    \choice  3.147E+01\,N/C
    \CorrectChoice 3.462E+01\,N/C
    \choice  3.808E+01\,N/C
\end{choices} %%% end choices

\question Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 2.8\,nano-Coulombs. What is the magnitude of the electric field at a distance of 4.8\,m from the center of the shells?
\begin{choices} %%%%%%% begin choices
    \choice  2.988E+00\,N/C
    \choice  3.287E+00\,N/C
    \choice  3.616E+00\,N/C
    \choice  3.977E+00\,N/C
    \CorrectChoice 4.375E+00\,N/C
\end{choices} %%% end choices

\question Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 7.8\,nano-Coulombs. What is the magnitude of the electric field at a distance of 1.3\,m from the center of the shells?
\begin{choices} %%%%%%% begin choices
    \choice  2.837E+01\,N/C
    \choice  3.121E+01\,N/C
    \choice  3.433E+01\,N/C
    \choice  3.776E+01\,N/C
    \CorrectChoice 4.154E+01\,N/C
\end{choices} %%% end choices

\question Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 5.6\,nano-Coulombs. What is the magnitude of the electric field at a distance of 5.6\,m from the center of the shells?
\begin{choices} %%%%%%% begin choices
    \choice  6.641E+00\,N/C
    \choice  7.305E+00\,N/C
    \CorrectChoice 8.036E+00\,N/C
    \choice  8.839E+00\,N/C
    \choice  9.723E+00\,N/C
\end{choices} %%% end choices

\question Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 7.4\,nano-Coulombs. What is the magnitude of the electric field at a distance of 5.4\,m from the center of the shells?
\begin{choices} %%%%%%% begin choices
    \choice  8.580E+00\,N/C
    \choice  9.438E+00\,N/C
    \choice  1.038E+01\,N/C
    \CorrectChoice 1.142E+01\,N/C
    \choice  1.256E+01\,N/C
\end{choices} %%% end choices

\question Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 3.4\,nano-Coulombs. What is the magnitude of the electric field at a distance of 5.5\,m from the center of the shells?
\begin{choices} %%%%%%% begin choices
    \CorrectChoice 5.058E+00\,N/C
    \choice  5.564E+00\,N/C
    \choice  6.120E+00\,N/C
    \choice  6.732E+00\,N/C
    \choice  7.405E+00\,N/C
\end{choices} %%% end choices

\question Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 1.2\,nano-Coulombs. What is the magnitude of the electric field at a distance of 5.8\,m from the center of the shells?
\begin{choices} %%%%%%% begin choices
    \choice  1.096E+00\,N/C
    \choice  1.206E+00\,N/C
    \choice  1.327E+00\,N/C
    \choice  1.459E+00\,N/C
    \CorrectChoice 1.605E+00\,N/C
\end{choices} %%% end choices

\question Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 2.0\,nano-Coulombs. What is the magnitude of the electric field at a distance of 3.7\,m from the center of the shells?
\begin{choices} %%%%%%% begin choices
    \choice  2.964E+00\,N/C
    \choice  3.260E+00\,N/C
    \choice  3.586E+00\,N/C
    \CorrectChoice 3.944E+00\,N/C
    \choice  4.339E+00\,N/C
\end{choices} %%% end choices

\question Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 6.4\,nano-Coulombs. What is the magnitude of the electric field at a distance of 1.1\,m from the center of the shells?
\begin{choices} %%%%%%% begin choices
    \choice  3.251E+01\,N/C
    \choice  3.577E+01\,N/C
    \choice  3.934E+01\,N/C
    \choice  4.328E+01\,N/C
    \CorrectChoice 4.760E+01\,N/C
\end{choices} %%% end choices

\question Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 7.2\,nano-Coulombs. What is the magnitude of the electric field at a distance of 4.6\,m from the center of the shells?
\begin{choices} %%%%%%% begin choices
    \choice  1.114E+01\,N/C
    \CorrectChoice 1.225E+01\,N/C
    \choice  1.347E+01\,N/C
    \choice  1.482E+01\,N/C
    \choice  1.630E+01\,N/C
\end{choices} %%% end choices

\question Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 4.7\,nano-Coulombs. What is the magnitude of the electric field at a distance of 4.2\,m from the center of the shells?
\begin{choices} %%%%%%% begin choices
    \CorrectChoice 9.592E+00\,N/C
    \choice  1.055E+01\,N/C
    \choice  1.161E+01\,N/C
    \choice  1.277E+01\,N/C
    \choice  1.404E+01\,N/C
\end{choices} %%% end choices

\question Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 1.9\,nano-Coulombs. What is the magnitude of the electric field at a distance of 2.1\,m from the center of the shells?
\begin{choices} %%%%%%% begin choices
    \choice  5.297E+00\,N/C
    \choice  5.827E+00\,N/C
    \choice  6.409E+00\,N/C
    \choice  7.050E+00\,N/C
    \CorrectChoice 7.755E+00\,N/C
\end{choices} %%% end choices

\question Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 9.0\,nano-Coulombs. What is the magnitude of the electric field at a distance of 5.5\,m from the center of the shells?
\begin{choices} %%%%%%% begin choices
    \choice  9.144E+00\,N/C
    \choice  1.006E+01\,N/C
    \choice  1.106E+01\,N/C
    \choice  1.217E+01\,N/C
    \CorrectChoice 1.339E+01\,N/C
\end{choices} %%% end choices

\question Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 7.3\,nano-Coulombs. What is the magnitude of the electric field at a distance of 1.5\,m from the center of the shells?
\begin{choices} %%%%%%% begin choices
    \choice  1.994E+01\,N/C
    \choice  2.194E+01\,N/C
    \choice  2.413E+01\,N/C
    \choice  2.655E+01\,N/C
    \CorrectChoice 2.920E+01\,N/C
\end{choices} %%% end choices
%\pagebreak
%\end{choices}%??????????????
\end{questions}%%%%%%%% end questions

\subsection{}%%%% subsection 6

\begin{questions} %%%%%%% begin questions

\question A non-conducting sphere of radius R=1.7\,m has a non-uniform charge density that varies with the distnce from its center as given by \textrho(r)=ar\textsuperscript{1.6} (r\(x\)R) where a=3\,nC\(\cdot\) m\textsuperscript{-1.4}. What is the magnitude of the electric field at a distance of 1.4\,m from the center? 
\begin{choices} %%%%%%% begin choices
    \choice  1.327E+02\,N/C
    \choice  1.460E+02\,N/C
    \choice  1.606E+02\,N/C
    \CorrectChoice 1.767E+02\,N/C
    \choice  1.943E+02\,N/C
\end{choices} %%% end choices

\question A non-conducting sphere of radius R=2.2\,m has a non-uniform charge density that varies with the distnce from its center as given by \textrho(r)=ar\textsuperscript{1.4} (r\(x\)R) where a=3\,nC\(\cdot\) m\textsuperscript{-1.6}. What is the magnitude of the electric field at a distance of 0.86\,m from the center? 
\begin{choices} %%%%%%% begin choices
    \choice  4.874E+01\,N/C
    \CorrectChoice 5.362E+01\,N/C
    \choice  5.898E+01\,N/C
    \choice  6.488E+01\,N/C
    \choice  7.137E+01\,N/C
\end{choices} %%% end choices

\question A non-conducting sphere of radius R=3.5\,m has a non-uniform charge density that varies with the distnce from its center as given by \textrho(r)=ar\textsuperscript{1.5} (r\(x\)R) where a=2\,nC\(\cdot\) m\textsuperscript{-1.5}. What is the magnitude of the electric field at a distance of 2.2\,m from the center? 
\begin{choices} %%%%%%% begin choices
    \CorrectChoice 3.604E+02\,N/C
    \choice  3.964E+02\,N/C
    \choice  4.360E+02\,N/C
    \choice  4.796E+02\,N/C
    \choice  5.276E+02\,N/C
\end{choices} %%% end choices

\question A non-conducting sphere of radius R=3.5\,m has a non-uniform charge density that varies with the distnce from its center as given by \textrho(r)=ar\textsuperscript{1.2} (r\(x\)R) where a=2\,nC\(\cdot\) m\textsuperscript{-1.8}. What is the magnitude of the electric field at a distance of 2.3\,m from the center? 
\begin{choices} %%%%%%% begin choices
    \choice  2.777E+02\,N/C
    \choice  3.055E+02\,N/C
    \CorrectChoice 3.361E+02\,N/C
    \choice  3.697E+02\,N/C
    \choice  4.066E+02\,N/C
\end{choices} %%% end choices

\question A non-conducting sphere of radius R=2.9\,m has a non-uniform charge density that varies with the distnce from its center as given by \textrho(r)=ar\textsuperscript{1.5} (r\(x\)R) where a=2\,nC\(\cdot\) m\textsuperscript{-1.5}. What is the magnitude of the electric field at a distance of 1.5\,m from the center? 
\begin{choices} %%%%%%% begin choices
    \CorrectChoice 1.383E+02\,N/C
    \choice  1.522E+02\,N/C
    \choice  1.674E+02\,N/C
    \choice  1.841E+02\,N/C
    \choice  2.025E+02\,N/C
\end{choices} %%% end choices

\question A non-conducting sphere of radius R=3.8\,m has a non-uniform charge density that varies with the distnce from its center as given by \textrho(r)=ar\textsuperscript{1.5} (r\(x\)R) where a=2\,nC\(\cdot\) m\textsuperscript{-1.5}. What is the magnitude of the electric field at a distance of 3.0\,m from the center? 
\begin{choices} %%%%%%% begin choices
    \CorrectChoice 7.825E+02\,N/C
    \choice  8.607E+02\,N/C
    \choice  9.468E+02\,N/C
    \choice  1.041E+03\,N/C
    \choice  1.146E+03\,N/C
\end{choices} %%% end choices

\question A non-conducting sphere of radius R=3.3\,m has a non-uniform charge density that varies with the distnce from its center as given by \textrho(r)=ar\textsuperscript{1.4} (r\(x\)R) where a=2\,nC\(\cdot\) m\textsuperscript{-1.6}. What is the magnitude of the electric field at a distance of 1.5\,m from the center? 
\begin{choices} %%%%%%% begin choices
    \choice  1.123E+02\,N/C
    \choice  1.235E+02\,N/C
    \CorrectChoice 1.358E+02\,N/C
    \choice  1.494E+02\,N/C
    \choice  1.644E+02\,N/C
\end{choices} %%% end choices

\question A non-conducting sphere of radius R=3.1\,m has a non-uniform charge density that varies with the distnce from its center as given by \textrho(r)=ar\textsuperscript{1.2} (r\(x\)R) where a=2\,nC\(\cdot\) m\textsuperscript{-1.8}. What is the magnitude of the electric field at a distance of 2.7\,m from the center? 
\begin{choices} %%%%%%% begin choices
    \CorrectChoice 4.782E+02\,N/C
    \choice  5.260E+02\,N/C
    \choice  5.787E+02\,N/C
    \choice  6.365E+02\,N/C
    \choice  7.002E+02\,N/C
\end{choices} %%% end choices

\question A non-conducting sphere of radius R=1.7\,m has a non-uniform charge density that varies with the distnce from its center as given by \textrho(r)=ar\textsuperscript{1.2} (r\(x\)R) where a=3\,nC\(\cdot\) m\textsuperscript{-1.8}. What is the magnitude of the electric field at a distance of 0.71\,m from the center? 
\begin{choices} %%%%%%% begin choices
    \CorrectChoice 3.797E+01\,N/C
    \choice  4.177E+01\,N/C
    \choice  4.595E+01\,N/C
    \choice  5.054E+01\,N/C
    \choice  5.560E+01\,N/C
\end{choices} %%% end choices

\question A non-conducting sphere of radius R=1.4\,m has a non-uniform charge density that varies with the distnce from its center as given by \textrho(r)=ar\textsuperscript{1.6} (r\(x\)R) where a=3\,nC\(\cdot\) m\textsuperscript{-1.4}. What is the magnitude of the electric field at a distance of 1.3\,m from the center? 
\begin{choices} %%%%%%% begin choices
    \CorrectChoice 1.457E+02\,N/C
    \choice  1.603E+02\,N/C
    \choice  1.763E+02\,N/C
    \choice  1.939E+02\,N/C
    \choice  2.133E+02\,N/C
\end{choices} %%% end choices

\question A non-conducting sphere of radius R=3.9\,m has a non-uniform charge density that varies with the distnce from its center as given by \textrho(r)=ar\textsuperscript{1.4} (r\(x\)R) where a=2\,nC\(\cdot\) m\textsuperscript{-1.6}. What is the magnitude of the electric field at a distance of 2.6\,m from the center? 
\begin{choices} %%%%%%% begin choices
    \choice  3.821E+02\,N/C
    \choice  4.203E+02\,N/C
    \choice  4.624E+02\,N/C
    \CorrectChoice 5.086E+02\,N/C
    \choice  5.594E+02\,N/C
\end{choices} %%% end choices

\question A non-conducting sphere of radius R=1.5\,m has a non-uniform charge density that varies with the distnce from its center as given by \textrho(r)=ar\textsuperscript{1.5} (r\(x\)R) where a=2\,nC\(\cdot\) m\textsuperscript{-1.5}. What is the magnitude of the electric field at a distance of 0.73\,m from the center? 
\begin{choices} %%%%%%% begin choices
    \CorrectChoice 2.285E+01\,N/C
    \choice  2.514E+01\,N/C
    \choice  2.765E+01\,N/C
    \choice  3.042E+01\,N/C
    \choice  3.346E+01\,N/C
\end{choices} %%% end choices

\question A non-conducting sphere of radius R=3.7\,m has a non-uniform charge density that varies with the distnce from its center as given by \textrho(r)=ar\textsuperscript{1.4} (r\(x\)R) where a=2\,nC\(\cdot\) m\textsuperscript{-1.6}. What is the magnitude of the electric field at a distance of 3.1\,m from the center? 
\begin{choices} %%%%%%% begin choices
    \choice  6.411E+02\,N/C
    \choice  7.052E+02\,N/C
    \CorrectChoice 7.757E+02\,N/C
    \choice  8.533E+02\,N/C
    \choice  9.386E+02\,N/C
\end{choices} %%% end choices

\question A non-conducting sphere of radius R=3.8\,m has a non-uniform charge density that varies with the distnce from its center as given by \textrho(r)=ar\textsuperscript{1.7} (r\(x\)R) where a=3\,nC\(\cdot\) m\textsuperscript{-1.3}. What is the magnitude of the electric field at a distance of 3.1\,m from the center? 
\begin{choices} %%%%%%% begin choices
    \choice  1.390E+03\,N/C
    \CorrectChoice 1.530E+03\,N/C
    \choice  1.682E+03\,N/C
    \choice  1.851E+03\,N/C
    \choice  2.036E+03\,N/C
\end{choices} %%% end choices

\question A non-conducting sphere of radius R=1.7\,m has a non-uniform charge density that varies with the distnce from its center as given by \textrho(r)=ar\textsuperscript{1.5} (r\(x\)R) where a=3\,nC\(\cdot\) m\textsuperscript{-1.5}. What is the magnitude of the electric field at a distance of 0.64\,m from the center? 
\begin{choices} %%%%%%% begin choices
    \choice  2.039E+01\,N/C
    \choice  2.243E+01\,N/C
    \CorrectChoice 2.467E+01\,N/C
    \choice  2.714E+01\,N/C
    \choice  2.985E+01\,N/C
\end{choices} %%% end choices

\question A non-conducting sphere of radius R=1.2\,m has a non-uniform charge density that varies with the distnce from its center as given by \textrho(r)=ar\textsuperscript{1.6} (r\(x\)R) where a=2\,nC\(\cdot\) m\textsuperscript{-1.4}. What is the magnitude of the electric field at a distance of 0.76\,m from the center? 
\begin{choices} %%%%%%% begin choices
    \CorrectChoice 2.406E+01\,N/C
    \choice  2.646E+01\,N/C
    \choice  2.911E+01\,N/C
    \choice  3.202E+01\,N/C
    \choice  3.522E+01\,N/C
\end{choices} %%% end choices

\question A non-conducting sphere of radius R=2.5\,m has a non-uniform charge density that varies with the distnce from its center as given by \textrho(r)=ar\textsuperscript{1.8} (r\(x\)R) where a=2\,nC\(\cdot\) m\textsuperscript{-1.2}. What is the magnitude of the electric field at a distance of 1.7\,m from the center? 
\begin{choices} %%%%%%% begin choices
    \CorrectChoice 2.079E+02\,N/C
    \choice  2.287E+02\,N/C
    \choice  2.516E+02\,N/C
    \choice  2.767E+02\,N/C
    \choice  3.044E+02\,N/C
\end{choices} %%% end choices

\question A non-conducting sphere of radius R=2.9\,m has a non-uniform charge density that varies with the distnce from its center as given by \textrho(r)=ar\textsuperscript{1.5} (r\(x\)R) where a=3\,nC\(\cdot\) m\textsuperscript{-1.5}. What is the magnitude of the electric field at a distance of 1.7\,m from the center? 
\begin{choices} %%%%%%% begin choices
    \choice  2.579E+02\,N/C
    \CorrectChoice 2.837E+02\,N/C
    \choice  3.121E+02\,N/C
    \choice  3.433E+02\,N/C
    \choice  3.776E+02\,N/C
\end{choices} %%% end choices

\question A non-conducting sphere of radius R=3.0\,m has a non-uniform charge density that varies with the distnce from its center as given by \textrho(r)=ar\textsuperscript{1.2} (r\(x\)R) where a=2\,nC\(\cdot\) m\textsuperscript{-1.8}. What is the magnitude of the electric field at a distance of 2.1\,m from the center? 
\begin{choices} %%%%%%% begin choices
    \choice  2.274E+02\,N/C
    \choice  2.501E+02\,N/C
    \CorrectChoice 2.751E+02\,N/C
    \choice  3.026E+02\,N/C
    \choice  3.329E+02\,N/C
\end{choices} %%% end choices
\end{questions}
\pagebreak

\section{Attribution}
\theendnotes
\end{document}

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