# QB/d cp2.5

< QB

The enrollment key for each course is 123. They are all is set to practice mode, giving students unlimited attempts at each question. Instructors can also print out copies of the quiz for classroom use. If you have any problems leave a message at user talk:Guy vandegrift.

• Quizbank now resides on MyOpenMath at https://www.myopenmath.com (although I hope Wikiversity can play an important role in helping students and teachers use these questions!)
• At the moment, most of the physics questions have already been transferred. To see them, join myopenmath.com as a student, and "enroll" in one or both of the following courses:
• Quizbank physics 1 (id 60675)
• Quizbank physics 2 (id 61712)
• Quizbank astronomy (id 63705)

See special:permalink/1894334 for a wikitext version of this quiz.

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%%%    EDIT QUIZ INFO  HERE   %%%%%%%%%%%%%%%%%%%%%%%%%%%
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%%%%% PREAMBLE%%%%%%%%%%%%
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% BEGIN DOCUMENT
\begin{document}
\title{d\_cp2.5}
\author{The LaTex code that creates this quiz is released to the Public Domain\\
Attribution for each question is documented in the Appendix}
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\\Latex markup at\\
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\begin{multicols}{3}
\tableofcontents
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\pagebreak\section{Quiz}
\keytrue
\begin{questions}
\question
\includegraphics[width=0.12\textwidth]{ThreeChargesAtCornerOfRectangle.png}Three small charged objects are placed as shown, where $$b=2a$$, and $$a=2\times 10^{-7}\text{m}$$. What is the magnitude of the net force on $$q_2$$ if $$q_1=2e$$, $$q_2=-3e$$, and $$q_3=5e$$?\ifkey\endnote{Example 5.2 from OpenStax University Physics2: https://cnx.org/contents/eg-XcBxE@9.8:UtVGui9n@7/53-Coulombs-Law\_1 placed in Public Domain by Guy Vandegrift: {\url{https://en.wikiversity.org/wiki/special:permalink/1894334}}}\fi
\begin{choices}
\choice 3.710E-14 N
\CorrectChoice 4.081E-14 N
\choice 4.489E-14 N
\choice 4.938E-14 N
\choice 5.432E-14 N
\end{choices}

\question
\includegraphics[width=0.12\textwidth]{ThreeChargesAtCornerOfRectangle.png}Three small charged objects are placed as shown, where $$b=2a$$, and $$a=2\times 10^{-7}\text{m}$$.what angle does the force on $$q_2$$ make above the $$-x$$ axis if $$q_1=2e$$, $$q_2=-3e$$, and $$q_3=5e$$?\ifkey\endnote{Example 5.2 from OpenStax University Physics2: https://cnx.org/contents/eg-XcBxE@9.8:UtVGui9n@7/53-Coulombs-Law\_1 placed in Public Domain by Guy Vandegrift: {\url{https://en.wikiversity.org/wiki/special:permalink/1894334}}}\fi
\begin{choices}
\choice 3.961E+01 degrees
\choice 4.357E+01 degrees
\choice 4.793E+01 degrees
\choice 5.272E+01 degrees
\CorrectChoice 5.799E+01 degrees
\end{choices}

\question
\includegraphics[width=0.142\textwidth]{ChargedLineSegmentTestQuestion.png} $$E_z(x=0,z)=\int_{-a}^b f(x,z)dx$$is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.5 m.  Evaluate $$f(x,y)$$ at x=1 m if a=0.7 m, b=1.2 m.  The total charge on the rod is 2 nC.\ifkey\endnote{Inspired by Example 5.4 from OpenStax University Physics2: by [[user:Guy vandegrift]] CC0 Public Domain license\_1 placed in Public Domain by Guy Vandegrift: {\url{https://en.wikiversity.org/wiki/special:permalink/1894334}}}\fi
\begin{choices}
\CorrectChoice 2.422E+00 V/m\textsuperscript{2}
\choice 2.664E+00 V/m\textsuperscript{2}
\choice 2.931E+00 V/m\textsuperscript{2}
\choice 3.224E+00 V/m\textsuperscript{2}
\choice 3.546E+00 V/m\textsuperscript{2}
\end{choices}

\question
\includegraphics[width=0.142\textwidth]{QuizbankQuestionLoopeFieldOnAxis.png}A ring is uniformly charged with a net charge of 2 nC. The radius of the ring is R=1.1 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=0.5 m (on axis) away from the loop's center?\ifkey\endnote{Inspired by Example 5.7 from OpenStax University Physics2: [[user:Guy vandegrift]] CC0 in Public Domain\_1 placed in Public Domain by Guy Vandegrift: {\url{https://en.wikiversity.org/wiki/special:permalink/1894334}}}\fi
\begin{choices}
\choice 4.210E+09 N/C\textsuperscript{2}
\choice 4.631E+09 N/C\textsuperscript{2}
\CorrectChoice 5.095E+09 N/C\textsuperscript{2}
\choice 5.604E+09 N/C\textsuperscript{2}
\choice 6.164E+09 N/C\textsuperscript{2}
\end{choices}

\question  $$E(z)=\int_{0}^R f(r',z)dr'$$is an integral that calculates the magnitude of the electric field at a distance $$z$$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk.  The disk's radius is $$R=2\text{ m}$$ and the surface charge density is $$\sigma=1\text{ nC/m}^3$$. Evaluate $$f(r',z)$$ at $$r'=1\text{ m}$$.\ifkey\endnote{Inspired by Example 5.8 from OpenStax University Physics2: [[user:Guy vandegrift]] Public Domain CC0\_1 placed in Public Domain by Guy Vandegrift: {\url{https://en.wikiversity.org/wiki/special:permalink/1894334}}}\fi
\begin{choices}
\choice 1.364E+01 V/m\textsuperscript{2}
\choice 1.500E+01 V/m\textsuperscript{2}
\choice 1.650E+01 V/m\textsuperscript{2}
\choice 1.815E+01 V/m\textsuperscript{2}
\CorrectChoice 1.997E+01 V/m\textsuperscript{2}
\end{choices}

\question A large thin isolated square plate has an area of 2 m\textsuperscript{2}. It is uniformly charged with 3 nC of charge.  What is the magnitude of the electric field 2 mm from the center of the plate's surface?\ifkey\endnote{Example 5.9 from OpenStax University Physics2: https://cnx.org/contents/eg-XcBxE@9.8:Bhqzg0Ka@6/55-Calculating-Electric-Fields\_1 placed in Public Domain by Guy Vandegrift: {\url{https://en.wikiversity.org/wiki/special:permalink/1894334}}}\fi
\begin{choices}
\CorrectChoice 8.471E+01 N/C
\choice 9.318E+01 N/C
\choice 1.025E+02 N/C
\choice 1.127E+02 N/C
\choice 1.240E+02 N/C
\end{choices}
\end{questions}\newpage %Ends quiz

\section{Renditions}  %%% Renditions %%%%

\subsection{}%%%% subsection 1

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

\question
\includegraphics[width=0.12\textwidth]{ThreeChargesAtCornerOfRectangle.png}Three small charged objects are placed as shown, where $$b=2a$$, and $$a=2\times 10^{-7}\text{m}$$. What is the magnitude of the net force on $$q_2$$ if $$q_1=1e$$, $$q_2=-8e$$, and $$q_3=3e$$?
\begin{choices} %%%%%%% begin choices
\CorrectChoice 5.768E-14 N
\choice  6.344E-14 N
\choice  6.979E-14 N
\choice  7.677E-14 N
\choice  8.444E-14 N
\end{choices} %%% end choices

\question
\includegraphics[width=0.12\textwidth]{ThreeChargesAtCornerOfRectangle.png}Three small charged objects are placed as shown, where $$b=2a$$, and $$a=4\times 10^{-7}\text{m}$$. What is the magnitude of the net force on $$q_2$$ if $$q_1=3e$$, $$q_2=-7e$$, and $$q_3=6e$$?
\begin{choices} %%%%%%% begin choices
\choice  2.544E-14 N
\choice  2.798E-14 N
\choice  3.078E-14 N
\CorrectChoice 3.385E-14 N
\choice  3.724E-14 N
\end{choices} %%% end choices

\question
\includegraphics[width=0.12\textwidth]{ThreeChargesAtCornerOfRectangle.png}Three small charged objects are placed as shown, where $$b=2a$$, and $$a=6\times 10^{-7}\text{m}$$. What is the magnitude of the net force on $$q_2$$ if $$q_1=3e$$, $$q_2=-7e$$, and $$q_3=6e$$?
\begin{choices} %%%%%%% begin choices
\choice  1.028E-14 N
\choice  1.130E-14 N
\choice  1.244E-14 N
\choice  1.368E-14 N
\CorrectChoice 1.505E-14 N
\end{choices} %%% end choices

\question
\includegraphics[width=0.12\textwidth]{ThreeChargesAtCornerOfRectangle.png}Three small charged objects are placed as shown, where $$b=2a$$, and $$a=6\times 10^{-7}\text{m}$$. What is the magnitude of the net force on $$q_2$$ if $$q_1=2e$$, $$q_2=-8e$$, and $$q_3=4e$$?
\begin{choices} %%%%%%% begin choices
\choice  8.613E-15 N
\choice  9.474E-15 N
\choice  1.042E-14 N
\CorrectChoice 1.146E-14 N
\choice  1.261E-14 N
\end{choices} %%% end choices

\question
\includegraphics[width=0.12\textwidth]{ThreeChargesAtCornerOfRectangle.png}Three small charged objects are placed as shown, where $$b=2a$$, and $$a=2\times 10^{-7}\text{m}$$. What is the magnitude of the net force on $$q_2$$ if $$q_1=3e$$, $$q_2=-9e$$, and $$q_3=6e$$?
\begin{choices} %%%%%%% begin choices
\choice  1.308E-13 N
\choice  1.439E-13 N
\choice  1.583E-13 N
\CorrectChoice 1.741E-13 N
\choice  1.915E-13 N
\end{choices} %%% end choices

\question
\includegraphics[width=0.12\textwidth]{ThreeChargesAtCornerOfRectangle.png}Three small charged objects are placed as shown, where $$b=2a$$, and $$a=2\times 10^{-7}\text{m}$$. What is the magnitude of the net force on $$q_2$$ if $$q_1=1e$$, $$q_2=-8e$$, and $$q_3=3e$$?
\begin{choices} %%%%%%% begin choices
\choice  5.243E-14 N
\CorrectChoice 5.768E-14 N
\choice  6.344E-14 N
\choice  6.979E-14 N
\choice  7.677E-14 N
\end{choices} %%% end choices

\question
\includegraphics[width=0.12\textwidth]{ThreeChargesAtCornerOfRectangle.png}Three small charged objects are placed as shown, where $$b=2a$$, and $$a=6\times 10^{-7}\text{m}$$. What is the magnitude of the net force on $$q_2$$ if $$q_1=1e$$, $$q_2=-8e$$, and $$q_3=2e$$?
\begin{choices} %%%%%%% begin choices
\CorrectChoice 5.732E-15 N
\choice  6.305E-15 N
\choice  6.936E-15 N
\choice  7.629E-15 N
\choice  8.392E-15 N
\end{choices} %%% end choices

\question
\includegraphics[width=0.12\textwidth]{ThreeChargesAtCornerOfRectangle.png}Three small charged objects are placed as shown, where $$b=2a$$, and $$a=6\times 10^{-7}\text{m}$$. What is the magnitude of the net force on $$q_2$$ if $$q_1=1e$$, $$q_2=-7e$$, and $$q_3=2e$$?
\begin{choices} %%%%%%% begin choices
\choice  3.426E-15 N
\choice  3.768E-15 N
\choice  4.145E-15 N
\choice  4.560E-15 N
\CorrectChoice 5.015E-15 N
\end{choices} %%% end choices

\question
\includegraphics[width=0.12\textwidth]{ThreeChargesAtCornerOfRectangle.png}Three small charged objects are placed as shown, where $$b=2a$$, and $$a=6\times 10^{-7}\text{m}$$. What is the magnitude of the net force on $$q_2$$ if $$q_1=2e$$, $$q_2=-8e$$, and $$q_3=5e$$?
\begin{choices} %%%%%%% begin choices
\choice  8.259E-15 N
\choice  9.085E-15 N
\choice  9.993E-15 N
\choice  1.099E-14 N
\CorrectChoice 1.209E-14 N
\end{choices} %%% end choices

\question
\includegraphics[width=0.12\textwidth]{ThreeChargesAtCornerOfRectangle.png}Three small charged objects are placed as shown, where $$b=2a$$, and $$a=4\times 10^{-7}\text{m}$$. What is the magnitude of the net force on $$q_2$$ if $$q_1=2e$$, $$q_2=-7e$$, and $$q_3=3e$$?
\begin{choices} %%%%%%% begin choices
\choice  1.473E-14 N
\choice  1.620E-14 N
\choice  1.782E-14 N
\choice  1.960E-14 N
\CorrectChoice 2.156E-14 N
\end{choices} %%% end choices

\question
\includegraphics[width=0.12\textwidth]{ThreeChargesAtCornerOfRectangle.png}Three small charged objects are placed as shown, where $$b=2a$$, and $$a=4\times 10^{-7}\text{m}$$. What is the magnitude of the net force on $$q_2$$ if $$q_1=2e$$, $$q_2=-8e$$, and $$q_3=5e$$?
\begin{choices} %%%%%%% begin choices
\choice  2.248E-14 N
\choice  2.473E-14 N
\CorrectChoice 2.721E-14 N
\choice  2.993E-14 N
\choice  3.292E-14 N
\end{choices} %%% end choices

\question
\includegraphics[width=0.12\textwidth]{ThreeChargesAtCornerOfRectangle.png}Three small charged objects are placed as shown, where $$b=2a$$, and $$a=6\times 10^{-7}\text{m}$$. What is the magnitude of the net force on $$q_2$$ if $$q_1=3e$$, $$q_2=-7e$$, and $$q_3=5e$$?
\begin{choices} %%%%%%% begin choices
\choice  9.958E-15 N
\choice  1.095E-14 N
\choice  1.205E-14 N
\choice  1.325E-14 N
\CorrectChoice 1.458E-14 N
\end{choices} %%% end choices

\question
\includegraphics[width=0.12\textwidth]{ThreeChargesAtCornerOfRectangle.png}Three small charged objects are placed as shown, where $$b=2a$$, and $$a=2\times 10^{-7}\text{m}$$. What is the magnitude of the net force on $$q_2$$ if $$q_1=1e$$, $$q_2=-7e$$, and $$q_3=3e$$?
\begin{choices} %%%%%%% begin choices
\choice  4.171E-14 N
\choice  4.588E-14 N
\CorrectChoice 5.047E-14 N
\choice  5.551E-14 N
\choice  6.107E-14 N
\end{choices} %%% end choices

\question
\includegraphics[width=0.12\textwidth]{ThreeChargesAtCornerOfRectangle.png}Three small charged objects are placed as shown, where $$b=2a$$, and $$a=4\times 10^{-7}\text{m}$$. What is the magnitude of the net force on $$q_2$$ if $$q_1=1e$$, $$q_2=-8e$$, and $$q_3=2e$$?
\begin{choices} %%%%%%% begin choices
\choice  1.172E-14 N
\CorrectChoice 1.290E-14 N
\choice  1.419E-14 N
\choice  1.561E-14 N
\choice  1.717E-14 N
\end{choices} %%% end choices

\question
\includegraphics[width=0.12\textwidth]{ThreeChargesAtCornerOfRectangle.png}Three small charged objects are placed as shown, where $$b=2a$$, and $$a=2\times 10^{-7}\text{m}$$. What is the magnitude of the net force on $$q_2$$ if $$q_1=1e$$, $$q_2=-8e$$, and $$q_3=2e$$?
\begin{choices} %%%%%%% begin choices
\choice  3.876E-14 N
\choice  4.263E-14 N
\choice  4.690E-14 N
\CorrectChoice 5.159E-14 N
\choice  5.675E-14 N
\end{choices} %%% end choices

\question
\includegraphics[width=0.12\textwidth]{ThreeChargesAtCornerOfRectangle.png}Three small charged objects are placed as shown, where $$b=2a$$, and $$a=2\times 10^{-7}\text{m}$$. What is the magnitude of the net force on $$q_2$$ if $$q_1=1e$$, $$q_2=-7e$$, and $$q_3=2e$$?
\begin{choices} %%%%%%% begin choices
\choice  3.391E-14 N
\choice  3.731E-14 N
\choice  4.104E-14 N
\CorrectChoice 4.514E-14 N
\choice  4.965E-14 N
\end{choices} %%% end choices

\question
\includegraphics[width=0.12\textwidth]{ThreeChargesAtCornerOfRectangle.png}Three small charged objects are placed as shown, where $$b=2a$$, and $$a=4\times 10^{-7}\text{m}$$. What is the magnitude of the net force on $$q_2$$ if $$q_1=2e$$, $$q_2=-8e$$, and $$q_3=3e$$?
\begin{choices} %%%%%%% begin choices
\choice  2.036E-14 N
\choice  2.240E-14 N
\CorrectChoice 2.464E-14 N
\choice  2.710E-14 N
\choice  2.981E-14 N
\end{choices} %%% end choices

\question
\includegraphics[width=0.12\textwidth]{ThreeChargesAtCornerOfRectangle.png}Three small charged objects are placed as shown, where $$b=2a$$, and $$a=4\times 10^{-7}\text{m}$$. What is the magnitude of the net force on $$q_2$$ if $$q_1=1e$$, $$q_2=-7e$$, and $$q_3=4e$$?
\begin{choices} %%%%%%% begin choices
\choice  9.750E-15 N
\choice  1.072E-14 N
\choice  1.180E-14 N
\choice  1.298E-14 N
\CorrectChoice 1.427E-14 N
\end{choices} %%% end choices

\question
\includegraphics[width=0.12\textwidth]{ThreeChargesAtCornerOfRectangle.png}Three small charged objects are placed as shown, where $$b=2a$$, and $$a=2\times 10^{-7}\text{m}$$. What is the magnitude of the net force on $$q_2$$ if $$q_1=1e$$, $$q_2=-9e$$, and $$q_3=4e$$?
\begin{choices} %%%%%%% begin choices
\choice  5.014E-14 N
\choice  5.515E-14 N
\choice  6.067E-14 N
\choice  6.674E-14 N
\CorrectChoice 7.341E-14 N
\end{choices} %%% end choices
%\pagebreak
%\end{choices}%??????????????
\end{questions}%%%%%%%% end questions

\subsection{}%%%% subsection 2

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

\question
\includegraphics[width=0.12\textwidth]{ThreeChargesAtCornerOfRectangle.png}Three small charged objects are placed as shown, where $$b=2a$$, and $$a=4\times 10^{-7}\text{m}$$.what angle does the force on $$q_2$$ make above the $$-x$$ axis if $$q_1=2e$$, $$q_2=-7e$$, and $$q_3=3e$$?
\begin{choices} %%%%%%% begin choices
\choice  5.217E+01 degrees
\choice  5.739E+01 degrees
\choice  6.313E+01 degrees
\CorrectChoice 6.944E+01 degrees
\choice  7.639E+01 degrees
\end{choices} %%% end choices

\question
\includegraphics[width=0.12\textwidth]{ThreeChargesAtCornerOfRectangle.png}Three small charged objects are placed as shown, where $$b=2a$$, and $$a=2\times 10^{-7}\text{m}$$.what angle does the force on $$q_2$$ make above the $$-x$$ axis if $$q_1=1e$$, $$q_2=-7e$$, and $$q_3=4e$$?
\begin{choices} %%%%%%% begin choices
\choice  4.091E+01 degrees
\CorrectChoice 4.500E+01 degrees
\choice  4.950E+01 degrees
\choice  5.445E+01 degrees
\choice  5.990E+01 degrees
\end{choices} %%% end choices

\question
\includegraphics[width=0.12\textwidth]{ThreeChargesAtCornerOfRectangle.png}Three small charged objects are placed as shown, where $$b=2a$$, and $$a=4\times 10^{-7}\text{m}$$.what angle does the force on $$q_2$$ make above the $$-x$$ axis if $$q_1=1e$$, $$q_2=-8e$$, and $$q_3=4e$$?
\begin{choices} %%%%%%% begin choices
\choice  3.719E+01 degrees
\choice  4.091E+01 degrees
\CorrectChoice 4.500E+01 degrees
\choice  4.950E+01 degrees
\choice  5.445E+01 degrees
\end{choices} %%% end choices

\question
\includegraphics[width=0.12\textwidth]{ThreeChargesAtCornerOfRectangle.png}Three small charged objects are placed as shown, where $$b=2a$$, and $$a=4\times 10^{-7}\text{m}$$.what angle does the force on $$q_2$$ make above the $$-x$$ axis if $$q_1=3e$$, $$q_2=-7e$$, and $$q_3=5e$$?
\begin{choices} %%%%%%% begin choices
\choice  5.569E+01 degrees
\choice  6.125E+01 degrees
\CorrectChoice 6.738E+01 degrees
\choice  7.412E+01 degrees
\choice  8.153E+01 degrees
\end{choices} %%% end choices

\question
\includegraphics[width=0.12\textwidth]{ThreeChargesAtCornerOfRectangle.png}Three small charged objects are placed as shown, where $$b=2a$$, and $$a=6\times 10^{-7}\text{m}$$.what angle does the force on $$q_2$$ make above the $$-x$$ axis if $$q_1=2e$$, $$q_2=-9e$$, and $$q_3=5e$$?
\begin{choices} %%%%%%% begin choices
\choice  5.272E+01 degrees
\CorrectChoice 5.799E+01 degrees
\choice  6.379E+01 degrees
\choice  7.017E+01 degrees
\choice  7.719E+01 degrees
\end{choices} %%% end choices

\question
\includegraphics[width=0.12\textwidth]{ThreeChargesAtCornerOfRectangle.png}Three small charged objects are placed as shown, where $$b=2a$$, and $$a=2\times 10^{-7}\text{m}$$.what angle does the force on $$q_2$$ make above the $$-x$$ axis if $$q_1=3e$$, $$q_2=-9e$$, and $$q_3=5e$$?
\begin{choices} %%%%%%% begin choices
\choice  6.125E+01 degrees
\CorrectChoice 6.738E+01 degrees
\choice  7.412E+01 degrees
\choice  8.153E+01 degrees
\choice  8.968E+01 degrees
\end{choices} %%% end choices

\question
\includegraphics[width=0.12\textwidth]{ThreeChargesAtCornerOfRectangle.png}Three small charged objects are placed as shown, where $$b=2a$$, and $$a=4\times 10^{-7}\text{m}$$.what angle does the force on $$q_2$$ make above the $$-x$$ axis if $$q_1=3e$$, $$q_2=-7e$$, and $$q_3=5e$$?
\begin{choices} %%%%%%% begin choices
\choice  5.569E+01 degrees
\choice  6.125E+01 degrees
\CorrectChoice 6.738E+01 degrees
\choice  7.412E+01 degrees
\choice  8.153E+01 degrees
\end{choices} %%% end choices

\question
\includegraphics[width=0.12\textwidth]{ThreeChargesAtCornerOfRectangle.png}Three small charged objects are placed as shown, where $$b=2a$$, and $$a=6\times 10^{-7}\text{m}$$.what angle does the force on $$q_2$$ make above the $$-x$$ axis if $$q_1=3e$$, $$q_2=-7e$$, and $$q_3=6e$$?
\begin{choices} %%%%%%% begin choices
\CorrectChoice 6.343E+01 degrees
\choice  6.978E+01 degrees
\choice  7.676E+01 degrees
\choice  8.443E+01 degrees
\choice  9.288E+01 degrees
\end{choices} %%% end choices

\question
\includegraphics[width=0.12\textwidth]{ThreeChargesAtCornerOfRectangle.png}Three small charged objects are placed as shown, where $$b=2a$$, and $$a=4\times 10^{-7}\text{m}$$.what angle does the force on $$q_2$$ make above the $$-x$$ axis if $$q_1=2e$$, $$q_2=-9e$$, and $$q_3=5e$$?
\begin{choices} %%%%%%% begin choices
\choice  3.961E+01 degrees
\choice  4.357E+01 degrees
\choice  4.793E+01 degrees
\choice  5.272E+01 degrees
\CorrectChoice 5.799E+01 degrees
\end{choices} %%% end choices

\question
\includegraphics[width=0.12\textwidth]{ThreeChargesAtCornerOfRectangle.png}Three small charged objects are placed as shown, where $$b=2a$$, and $$a=6\times 10^{-7}\text{m}$$.what angle does the force on $$q_2$$ make above the $$-x$$ axis if $$q_1=3e$$, $$q_2=-7e$$, and $$q_3=4e$$?
\begin{choices} %%%%%%% begin choices
\choice  5.377E+01 degrees
\choice  5.914E+01 degrees
\choice  6.506E+01 degrees
\CorrectChoice 7.157E+01 degrees
\choice  7.872E+01 degrees
\end{choices} %%% end choices

\question
\includegraphics[width=0.12\textwidth]{ThreeChargesAtCornerOfRectangle.png}Three small charged objects are placed as shown, where $$b=2a$$, and $$a=2\times 10^{-7}\text{m}$$.what angle does the force on $$q_2$$ make above the $$-x$$ axis if $$q_1=2e$$, $$q_2=-7e$$, and $$q_3=5e$$?
\begin{choices} %%%%%%% begin choices
\choice  4.357E+01 degrees
\choice  4.793E+01 degrees
\choice  5.272E+01 degrees
\CorrectChoice 5.799E+01 degrees
\choice  6.379E+01 degrees
\end{choices} %%% end choices

\question
\includegraphics[width=0.12\textwidth]{ThreeChargesAtCornerOfRectangle.png}Three small charged objects are placed as shown, where $$b=2a$$, and $$a=2\times 10^{-7}\text{m}$$.what angle does the force on $$q_2$$ make above the $$-x$$ axis if $$q_1=2e$$, $$q_2=-7e$$, and $$q_3=3e$$?
\begin{choices} %%%%%%% begin choices
\choice  4.743E+01 degrees
\choice  5.217E+01 degrees
\choice  5.739E+01 degrees
\choice  6.313E+01 degrees
\CorrectChoice 6.944E+01 degrees
\end{choices} %%% end choices

\question
\includegraphics[width=0.12\textwidth]{ThreeChargesAtCornerOfRectangle.png}Three small charged objects are placed as shown, where $$b=2a$$, and $$a=2\times 10^{-7}\text{m}$$.what angle does the force on $$q_2$$ make above the $$-x$$ axis if $$q_1=2e$$, $$q_2=-9e$$, and $$q_3=4e$$?
\begin{choices} %%%%%%% begin choices
\choice  5.243E+01 degrees
\choice  5.767E+01 degrees
\CorrectChoice 6.343E+01 degrees
\choice  6.978E+01 degrees
\choice  7.676E+01 degrees
\end{choices} %%% end choices

\question
\includegraphics[width=0.12\textwidth]{ThreeChargesAtCornerOfRectangle.png}Three small charged objects are placed as shown, where $$b=2a$$, and $$a=4\times 10^{-7}\text{m}$$.what angle does the force on $$q_2$$ make above the $$-x$$ axis if $$q_1=3e$$, $$q_2=-9e$$, and $$q_3=6e$$?
\begin{choices} %%%%%%% begin choices
\choice  5.767E+01 degrees
\CorrectChoice 6.343E+01 degrees
\choice  6.978E+01 degrees
\choice  7.676E+01 degrees
\choice  8.443E+01 degrees
\end{choices} %%% end choices

\question
\includegraphics[width=0.12\textwidth]{ThreeChargesAtCornerOfRectangle.png}Three small charged objects are placed as shown, where $$b=2a$$, and $$a=4\times 10^{-7}\text{m}$$.what angle does the force on $$q_2$$ make above the $$-x$$ axis if $$q_1=3e$$, $$q_2=-8e$$, and $$q_3=6e$$?
\begin{choices} %%%%%%% begin choices
\choice  5.243E+01 degrees
\choice  5.767E+01 degrees
\CorrectChoice 6.343E+01 degrees
\choice  6.978E+01 degrees
\choice  7.676E+01 degrees
\end{choices} %%% end choices

\question
\includegraphics[width=0.12\textwidth]{ThreeChargesAtCornerOfRectangle.png}Three small charged objects are placed as shown, where $$b=2a$$, and $$a=6\times 10^{-7}\text{m}$$.what angle does the force on $$q_2$$ make above the $$-x$$ axis if $$q_1=3e$$, $$q_2=-7e$$, and $$q_3=4e$$?
\begin{choices} %%%%%%% begin choices
\choice  5.914E+01 degrees
\choice  6.506E+01 degrees
\CorrectChoice 7.157E+01 degrees
\choice  7.872E+01 degrees
\choice  8.659E+01 degrees
\end{choices} %%% end choices

\question
\includegraphics[width=0.12\textwidth]{ThreeChargesAtCornerOfRectangle.png}Three small charged objects are placed as shown, where $$b=2a$$, and $$a=6\times 10^{-7}\text{m}$$.what angle does the force on $$q_2$$ make above the $$-x$$ axis if $$q_1=2e$$, $$q_2=-9e$$, and $$q_3=4e$$?
\begin{choices} %%%%%%% begin choices
\choice  4.766E+01 degrees
\choice  5.243E+01 degrees
\choice  5.767E+01 degrees
\CorrectChoice 6.343E+01 degrees
\choice  6.978E+01 degrees
\end{choices} %%% end choices

\question
\includegraphics[width=0.12\textwidth]{ThreeChargesAtCornerOfRectangle.png}Three small charged objects are placed as shown, where $$b=2a$$, and $$a=6\times 10^{-7}\text{m}$$.what angle does the force on $$q_2$$ make above the $$-x$$ axis if $$q_1=3e$$, $$q_2=-8e$$, and $$q_3=5e$$?
\begin{choices} %%%%%%% begin choices
\choice  5.062E+01 degrees
\choice  5.569E+01 degrees
\choice  6.125E+01 degrees
\CorrectChoice 6.738E+01 degrees
\choice  7.412E+01 degrees
\end{choices} %%% end choices

\question
\includegraphics[width=0.12\textwidth]{ThreeChargesAtCornerOfRectangle.png}Three small charged objects are placed as shown, where $$b=2a$$, and $$a=2\times 10^{-7}\text{m}$$.what angle does the force on $$q_2$$ make above the $$-x$$ axis if $$q_1=1e$$, $$q_2=-8e$$, and $$q_3=3e$$?
\begin{choices} %%%%%%% begin choices
\choice  3.629E+01 degrees
\choice  3.992E+01 degrees
\choice  4.391E+01 degrees
\choice  4.830E+01 degrees
\CorrectChoice 5.313E+01 degrees
\end{choices} %%% end choices
%\pagebreak
%\end{choices}%??????????????
\end{questions}%%%%%%%% end questions

\subsection{}%%%% subsection 3

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

\question
\includegraphics[width=0.142\textwidth]{ChargedLineSegmentTestQuestion.png} $$E_z(x=0,z)=\int_{-a}^b f(x,z)dx$$is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.8 m.  Evaluate $$f(x,y)$$ at x=0.83 m if a=1.1 m, b=1.9 m.  The total charge on the rod is 2 nC.
\begin{choices} %%%%%%% begin choices
\choice  1.040E+00 V/m\textsuperscript{2}
\choice  1.145E+00 V/m\textsuperscript{2}
\choice  1.259E+00 V/m\textsuperscript{2}
\CorrectChoice 1.385E+00 V/m\textsuperscript{2}
\choice  1.523E+00 V/m\textsuperscript{2}
\end{choices} %%% end choices

\question
\includegraphics[width=0.142\textwidth]{ChargedLineSegmentTestQuestion.png} $$E_z(x=0,z)=\int_{-a}^b f(x,z)dx$$is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.7 m.  Evaluate $$f(x,y)$$ at x=0.76 m if a=1.1 m, b=1.6 m.  The total charge on the rod is 8 nC.
\begin{choices} %%%%%%% begin choices
\choice  5.267E+00 V/m\textsuperscript{2}
\choice  5.794E+00 V/m\textsuperscript{2}
\choice  6.374E+00 V/m\textsuperscript{2}
\CorrectChoice 7.011E+00 V/m\textsuperscript{2}
\choice  7.712E+00 V/m\textsuperscript{2}
\end{choices} %%% end choices

\question
\includegraphics[width=0.142\textwidth]{ChargedLineSegmentTestQuestion.png} $$E_z(x=0,z)=\int_{-a}^b f(x,z)dx$$is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.4 m.  Evaluate $$f(x,y)$$ at x=1.1 m if a=0.69 m, b=2.2 m.  The total charge on the rod is 6 nC.
\begin{choices} %%%%%%% begin choices
\choice  3.161E+00 V/m\textsuperscript{2}
\choice  3.477E+00 V/m\textsuperscript{2}
\choice  3.825E+00 V/m\textsuperscript{2}
\choice  4.208E+00 V/m\textsuperscript{2}
\CorrectChoice 4.628E+00 V/m\textsuperscript{2}
\end{choices} %%% end choices

\question
\includegraphics[width=0.142\textwidth]{ChargedLineSegmentTestQuestion.png} $$E_z(x=0,z)=\int_{-a}^b f(x,z)dx$$is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.5 m.  Evaluate $$f(x,y)$$ at x=1.1 m if a=0.61 m, b=1.7 m.  The total charge on the rod is 8 nC.
\begin{choices} %%%%%%% begin choices
\choice  5.995E+00 V/m\textsuperscript{2}
\choice  6.595E+00 V/m\textsuperscript{2}
\CorrectChoice 7.254E+00 V/m\textsuperscript{2}
\choice  7.980E+00 V/m\textsuperscript{2}
\choice  8.778E+00 V/m\textsuperscript{2}
\end{choices} %%% end choices

\question
\includegraphics[width=0.142\textwidth]{ChargedLineSegmentTestQuestion.png} $$E_z(x=0,z)=\int_{-a}^b f(x,z)dx$$is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.3 m.  Evaluate $$f(x,y)$$ at x=0.83 m if a=0.82 m, b=1.3 m.  The total charge on the rod is 7 nC.
\begin{choices} %%%%%%% begin choices
\choice  8.690E+00 V/m\textsuperscript{2}
\choice  9.559E+00 V/m\textsuperscript{2}
\CorrectChoice 1.051E+01 V/m\textsuperscript{2}
\choice  1.157E+01 V/m\textsuperscript{2}
\choice  1.272E+01 V/m\textsuperscript{2}
\end{choices} %%% end choices

\question
\includegraphics[width=0.142\textwidth]{ChargedLineSegmentTestQuestion.png} $$E_z(x=0,z)=\int_{-a}^b f(x,z)dx$$is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.8 m.  Evaluate $$f(x,y)$$ at x=1.0 m if a=1.0 m, b=1.8 m.  The total charge on the rod is 6 nC.
\begin{choices} %%%%%%% begin choices
\choice  3.610E+00 V/m\textsuperscript{2}
\CorrectChoice 3.971E+00 V/m\textsuperscript{2}
\choice  4.368E+00 V/m\textsuperscript{2}
\choice  4.804E+00 V/m\textsuperscript{2}
\choice  5.285E+00 V/m\textsuperscript{2}
\end{choices} %%% end choices

\question
\includegraphics[width=0.142\textwidth]{ChargedLineSegmentTestQuestion.png} $$E_z(x=0,z)=\int_{-a}^b f(x,z)dx$$is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.5 m.  Evaluate $$f(x,y)$$ at x=1.0 m if a=1.1 m, b=1.4 m.  The total charge on the rod is 5 nC.
\begin{choices} %%%%%%% begin choices
\CorrectChoice 4.602E+00 V/m\textsuperscript{2}
\choice  5.062E+00 V/m\textsuperscript{2}
\choice  5.568E+00 V/m\textsuperscript{2}
\choice  6.125E+00 V/m\textsuperscript{2}
\choice  6.738E+00 V/m\textsuperscript{2}
\end{choices} %%% end choices

\question
\includegraphics[width=0.142\textwidth]{ChargedLineSegmentTestQuestion.png} $$E_z(x=0,z)=\int_{-a}^b f(x,z)dx$$is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.2 m.  Evaluate $$f(x,y)$$ at x=0.73 m if a=0.52 m, b=1.6 m.  The total charge on the rod is 7 nC.
\begin{choices} %%%%%%% begin choices
\choice  9.655E+00 V/m\textsuperscript{2}
\choice  1.062E+01 V/m\textsuperscript{2}
\choice  1.168E+01 V/m\textsuperscript{2}
\CorrectChoice 1.285E+01 V/m\textsuperscript{2}
\choice  1.414E+01 V/m\textsuperscript{2}
\end{choices} %%% end choices

\question
\includegraphics[width=0.142\textwidth]{ChargedLineSegmentTestQuestion.png} $$E_z(x=0,z)=\int_{-a}^b f(x,z)dx$$is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.5 m.  Evaluate $$f(x,y)$$ at x=0.79 m if a=0.75 m, b=2.1 m.  The total charge on the rod is 6 nC.
\begin{choices} %%%%%%% begin choices
\CorrectChoice 5.825E+00 V/m\textsuperscript{2}
\choice  6.407E+00 V/m\textsuperscript{2}
\choice  7.048E+00 V/m\textsuperscript{2}
\choice  7.753E+00 V/m\textsuperscript{2}
\choice  8.528E+00 V/m\textsuperscript{2}
\end{choices} %%% end choices

\question
\includegraphics[width=0.142\textwidth]{ChargedLineSegmentTestQuestion.png} $$E_z(x=0,z)=\int_{-a}^b f(x,z)dx$$is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.3 m.  Evaluate $$f(x,y)$$ at x=0.96 m if a=0.63 m, b=1.4 m.  The total charge on the rod is 3 nC.
\begin{choices} %%%%%%% begin choices
\choice  3.719E+00 V/m\textsuperscript{2}
\CorrectChoice 4.091E+00 V/m\textsuperscript{2}
\choice  4.500E+00 V/m\textsuperscript{2}
\choice  4.950E+00 V/m\textsuperscript{2}
\choice  5.445E+00 V/m\textsuperscript{2}
\end{choices} %%% end choices

\question
\includegraphics[width=0.142\textwidth]{ChargedLineSegmentTestQuestion.png} $$E_z(x=0,z)=\int_{-a}^b f(x,z)dx$$is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.8 m.  Evaluate $$f(x,y)$$ at x=0.65 m if a=0.85 m, b=1.8 m.  The total charge on the rod is 5 nC.
\begin{choices} %%%%%%% begin choices
\choice  3.959E+00 V/m\textsuperscript{2}
\CorrectChoice 4.355E+00 V/m\textsuperscript{2}
\choice  4.790E+00 V/m\textsuperscript{2}
\choice  5.269E+00 V/m\textsuperscript{2}
\choice  5.796E+00 V/m\textsuperscript{2}
\end{choices} %%% end choices

\question
\includegraphics[width=0.142\textwidth]{ChargedLineSegmentTestQuestion.png} $$E_z(x=0,z)=\int_{-a}^b f(x,z)dx$$is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.8 m.  Evaluate $$f(x,y)$$ at x=0.5 m if a=0.67 m, b=2.4 m.  The total charge on the rod is 9 nC.
\begin{choices} %%%%%%% begin choices
\choice  5.465E+00 V/m\textsuperscript{2}
\choice  6.012E+00 V/m\textsuperscript{2}
\choice  6.613E+00 V/m\textsuperscript{2}
\CorrectChoice 7.274E+00 V/m\textsuperscript{2}
\choice  8.002E+00 V/m\textsuperscript{2}
\end{choices} %%% end choices

\question
\includegraphics[width=0.142\textwidth]{ChargedLineSegmentTestQuestion.png} $$E_z(x=0,z)=\int_{-a}^b f(x,z)dx$$is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.5 m.  Evaluate $$f(x,y)$$ at x=1.1 m if a=0.62 m, b=1.3 m.  The total charge on the rod is 7 nC.
\begin{choices} %%%%%%% begin choices
\choice  6.311E+00 V/m\textsuperscript{2}
\choice  6.943E+00 V/m\textsuperscript{2}
\CorrectChoice 7.637E+00 V/m\textsuperscript{2}
\choice  8.401E+00 V/m\textsuperscript{2}
\choice  9.241E+00 V/m\textsuperscript{2}
\end{choices} %%% end choices

\question
\includegraphics[width=0.142\textwidth]{ChargedLineSegmentTestQuestion.png} $$E_z(x=0,z)=\int_{-a}^b f(x,z)dx$$is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.9 m.  Evaluate $$f(x,y)$$ at x=0.83 m if a=0.7 m, b=1.8 m.  The total charge on the rod is 9 nC.
\begin{choices} %%%%%%% begin choices
\CorrectChoice 6.897E+00 V/m\textsuperscript{2}
\choice  7.587E+00 V/m\textsuperscript{2}
\choice  8.345E+00 V/m\textsuperscript{2}
\choice  9.180E+00 V/m\textsuperscript{2}
\choice  1.010E+01 V/m\textsuperscript{2}
\end{choices} %%% end choices

\question
\includegraphics[width=0.142\textwidth]{ChargedLineSegmentTestQuestion.png} $$E_z(x=0,z)=\int_{-a}^b f(x,z)dx$$is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.7 m.  Evaluate $$f(x,y)$$ at x=0.52 m if a=0.88 m, b=1.3 m.  The total charge on the rod is 6 nC.
\begin{choices} %%%%%%% begin choices
\choice  6.804E+00 V/m\textsuperscript{2}
\CorrectChoice 7.485E+00 V/m\textsuperscript{2}
\choice  8.233E+00 V/m\textsuperscript{2}
\choice  9.056E+00 V/m\textsuperscript{2}
\choice  9.962E+00 V/m\textsuperscript{2}
\end{choices} %%% end choices

\question
\includegraphics[width=0.142\textwidth]{ChargedLineSegmentTestQuestion.png} $$E_z(x=0,z)=\int_{-a}^b f(x,z)dx$$is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.2 m.  Evaluate $$f(x,y)$$ at x=0.54 m if a=0.76 m, b=1.7 m.  The total charge on the rod is 8 nC.
\begin{choices} %%%%%%% begin choices
\choice  1.399E+01 V/m\textsuperscript{2}
\CorrectChoice 1.539E+01 V/m\textsuperscript{2}
\choice  1.693E+01 V/m\textsuperscript{2}
\choice  1.862E+01 V/m\textsuperscript{2}
\choice  2.049E+01 V/m\textsuperscript{2}
\end{choices} %%% end choices

\question
\includegraphics[width=0.142\textwidth]{ChargedLineSegmentTestQuestion.png} $$E_z(x=0,z)=\int_{-a}^b f(x,z)dx$$is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.9 m.  Evaluate $$f(x,y)$$ at x=0.54 m if a=1.0 m, b=2.0 m.  The total charge on the rod is 3 nC.
\begin{choices} %%%%%%% begin choices
\choice  1.665E+00 V/m\textsuperscript{2}
\choice  1.831E+00 V/m\textsuperscript{2}
\choice  2.014E+00 V/m\textsuperscript{2}
\CorrectChoice 2.216E+00 V/m\textsuperscript{2}
\choice  2.437E+00 V/m\textsuperscript{2}
\end{choices} %%% end choices

\question
\includegraphics[width=0.142\textwidth]{ChargedLineSegmentTestQuestion.png} $$E_z(x=0,z)=\int_{-a}^b f(x,z)dx$$is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.6 m.  Evaluate $$f(x,y)$$ at x=0.73 m if a=0.64 m, b=1.8 m.  The total charge on the rod is 3 nC.
\begin{choices} %%%%%%% begin choices
\choice  2.955E+00 V/m\textsuperscript{2}
\CorrectChoice 3.250E+00 V/m\textsuperscript{2}
\choice  3.575E+00 V/m\textsuperscript{2}
\choice  3.933E+00 V/m\textsuperscript{2}
\choice  4.326E+00 V/m\textsuperscript{2}
\end{choices} %%% end choices

\question
\includegraphics[width=0.142\textwidth]{ChargedLineSegmentTestQuestion.png} $$E_z(x=0,z)=\int_{-a}^b f(x,z)dx$$is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.9 m.  Evaluate $$f(x,y)$$ at x=0.96 m if a=0.95 m, b=1.8 m.  The total charge on the rod is 7 nC.
\begin{choices} %%%%%%% begin choices
\choice  3.385E+00 V/m\textsuperscript{2}
\choice  3.724E+00 V/m\textsuperscript{2}
\choice  4.096E+00 V/m\textsuperscript{2}
\CorrectChoice 4.506E+00 V/m\textsuperscript{2}
\choice  4.957E+00 V/m\textsuperscript{2}
\end{choices} %%% end choices
%\pagebreak
%\end{choices}%??????????????
\end{questions}%%%%%%%% end questions

\subsection{}%%%% subsection 4

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

\question
\includegraphics[width=0.142\textwidth]{QuizbankQuestionLoopeFieldOnAxis.png}A ring is uniformly charged with a net charge of 3 nC. The radius of the ring is R=1.5 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=1.1 m (on axis) away from the loop's center?
\begin{choices} %%%%%%% begin choices
\CorrectChoice 4.608E+09 N/C\textsuperscript{2}
\choice  5.069E+09 N/C\textsuperscript{2}
\choice  5.576E+09 N/C\textsuperscript{2}
\choice  6.134E+09 N/C\textsuperscript{2}
\choice  6.747E+09 N/C\textsuperscript{2}
\end{choices} %%% end choices

\question
\includegraphics[width=0.142\textwidth]{QuizbankQuestionLoopeFieldOnAxis.png}A ring is uniformly charged with a net charge of 4 nC. The radius of the ring is R=1.6 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=1.1 m (on axis) away from the loop's center?
\begin{choices} %%%%%%% begin choices
\CorrectChoice 5.402E+09 N/C\textsuperscript{2}
\choice  5.943E+09 N/C\textsuperscript{2}
\choice  6.537E+09 N/C\textsuperscript{2}
\choice  7.191E+09 N/C\textsuperscript{2}
\choice  7.910E+09 N/C\textsuperscript{2}
\end{choices} %%% end choices

\question
\includegraphics[width=0.142\textwidth]{QuizbankQuestionLoopeFieldOnAxis.png}A ring is uniformly charged with a net charge of 9 nC. The radius of the ring is R=1.9 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=1.4 m (on axis) away from the loop's center?
\begin{choices} %%%%%%% begin choices
\choice  7.119E+09 N/C\textsuperscript{2}
\choice  7.831E+09 N/C\textsuperscript{2}
\CorrectChoice 8.614E+09 N/C\textsuperscript{2}
\choice  9.476E+09 N/C\textsuperscript{2}
\choice  1.042E+10 N/C\textsuperscript{2}
\end{choices} %%% end choices

\question
\includegraphics[width=0.142\textwidth]{QuizbankQuestionLoopeFieldOnAxis.png}A ring is uniformly charged with a net charge of 6 nC. The radius of the ring is R=1.9 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=0.4 m (on axis) away from the loop's center?
\begin{choices} %%%%%%% begin choices
\choice  2.013E+09 N/C\textsuperscript{2}
\choice  2.214E+09 N/C\textsuperscript{2}
\choice  2.435E+09 N/C\textsuperscript{2}
\choice  2.679E+09 N/C\textsuperscript{2}
\CorrectChoice 2.947E+09 N/C\textsuperscript{2}
\end{choices} %%% end choices

\question
\includegraphics[width=0.142\textwidth]{QuizbankQuestionLoopeFieldOnAxis.png}A ring is uniformly charged with a net charge of 9 nC. The radius of the ring is R=1.6 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=0.73 m (on axis) away from the loop's center?
\begin{choices} %%%%%%% begin choices
\choice  7.415E+09 N/C\textsuperscript{2}
\choice  8.156E+09 N/C\textsuperscript{2}
\choice  8.972E+09 N/C\textsuperscript{2}
\choice  9.869E+09 N/C\textsuperscript{2}
\CorrectChoice 1.086E+10 N/C\textsuperscript{2}
\end{choices} %%% end choices

\question
\includegraphics[width=0.142\textwidth]{QuizbankQuestionLoopeFieldOnAxis.png}A ring is uniformly charged with a net charge of 7 nC. The radius of the ring is R=1.6 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=0.34 m (on axis) away from the loop's center?
\begin{choices} %%%%%%% begin choices
\choice  3.672E+09 N/C\textsuperscript{2}
\choice  4.039E+09 N/C\textsuperscript{2}
\choice  4.443E+09 N/C\textsuperscript{2}
\CorrectChoice 4.887E+09 N/C\textsuperscript{2}
\choice  5.376E+09 N/C\textsuperscript{2}
\end{choices} %%% end choices

\question
\includegraphics[width=0.142\textwidth]{QuizbankQuestionLoopeFieldOnAxis.png}A ring is uniformly charged with a net charge of 2 nC. The radius of the ring is R=1.5 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=0.33 m (on axis) away from the loop's center?
\begin{choices} %%%%%%% begin choices
\choice  1.353E+09 N/C\textsuperscript{2}
\choice  1.488E+09 N/C\textsuperscript{2}
\CorrectChoice 1.637E+09 N/C\textsuperscript{2}
\choice  1.801E+09 N/C\textsuperscript{2}
\choice  1.981E+09 N/C\textsuperscript{2}
\end{choices} %%% end choices

\question
\includegraphics[width=0.142\textwidth]{QuizbankQuestionLoopeFieldOnAxis.png}A ring is uniformly charged with a net charge of 2 nC. The radius of the ring is R=1.8 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=1.3 m (on axis) away from the loop's center?
\begin{choices} %%%%%%% begin choices
\choice  1.764E+09 N/C\textsuperscript{2}
\choice  1.941E+09 N/C\textsuperscript{2}
\CorrectChoice 2.135E+09 N/C\textsuperscript{2}
\choice  2.348E+09 N/C\textsuperscript{2}
\choice  2.583E+09 N/C\textsuperscript{2}
\end{choices} %%% end choices

\question
\includegraphics[width=0.142\textwidth]{QuizbankQuestionLoopeFieldOnAxis.png}A ring is uniformly charged with a net charge of 5 nC. The radius of the ring is R=1.6 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=1.1 m (on axis) away from the loop's center?
\begin{choices} %%%%%%% begin choices
\choice  5.581E+09 N/C\textsuperscript{2}
\choice  6.139E+09 N/C\textsuperscript{2}
\CorrectChoice 6.753E+09 N/C\textsuperscript{2}
\choice  7.428E+09 N/C\textsuperscript{2}
\choice  8.171E+09 N/C\textsuperscript{2}
\end{choices} %%% end choices

\question
\includegraphics[width=0.142\textwidth]{QuizbankQuestionLoopeFieldOnAxis.png}A ring is uniformly charged with a net charge of 3 nC. The radius of the ring is R=1.8 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=1.1 m (on axis) away from the loop's center?
\begin{choices} %%%%%%% begin choices
\CorrectChoice 3.159E+09 N/C\textsuperscript{2}
\choice  3.475E+09 N/C\textsuperscript{2}
\choice  3.823E+09 N/C\textsuperscript{2}
\choice  4.205E+09 N/C\textsuperscript{2}
\choice  4.626E+09 N/C\textsuperscript{2}
\end{choices} %%% end choices

\question
\includegraphics[width=0.142\textwidth]{QuizbankQuestionLoopeFieldOnAxis.png}A ring is uniformly charged with a net charge of 4 nC. The radius of the ring is R=1.6 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=1.0 m (on axis) away from the loop's center?
\begin{choices} %%%%%%% begin choices
\CorrectChoice 5.352E+09 N/C\textsuperscript{2}
\choice  5.887E+09 N/C\textsuperscript{2}
\choice  6.476E+09 N/C\textsuperscript{2}
\choice  7.124E+09 N/C\textsuperscript{2}
\choice  7.836E+09 N/C\textsuperscript{2}
\end{choices} %%% end choices

\question
\includegraphics[width=0.142\textwidth]{QuizbankQuestionLoopeFieldOnAxis.png}A ring is uniformly charged with a net charge of 2 nC. The radius of the ring is R=1.6 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=0.99 m (on axis) away from the loop's center?
\begin{choices} %%%%%%% begin choices
\choice  2.429E+09 N/C\textsuperscript{2}
\CorrectChoice 2.672E+09 N/C\textsuperscript{2}
\choice  2.939E+09 N/C\textsuperscript{2}
\choice  3.233E+09 N/C\textsuperscript{2}
\choice  3.556E+09 N/C\textsuperscript{2}
\end{choices} %%% end choices

\question
\includegraphics[width=0.142\textwidth]{QuizbankQuestionLoopeFieldOnAxis.png}A ring is uniformly charged with a net charge of 7 nC. The radius of the ring is R=1.7 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=1.2 m (on axis) away from the loop's center?
\begin{choices} %%%%%%% begin choices
\choice  6.925E+09 N/C\textsuperscript{2}
\choice  7.617E+09 N/C\textsuperscript{2}
\CorrectChoice 8.379E+09 N/C\textsuperscript{2}
\choice  9.217E+09 N/C\textsuperscript{2}
\choice  1.014E+10 N/C\textsuperscript{2}
\end{choices} %%% end choices

\question
\includegraphics[width=0.142\textwidth]{QuizbankQuestionLoopeFieldOnAxis.png}A ring is uniformly charged with a net charge of 3 nC. The radius of the ring is R=1.7 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=0.34 m (on axis) away from the loop's center?
\begin{choices} %%%%%%% begin choices
\choice  1.202E+09 N/C\textsuperscript{2}
\choice  1.322E+09 N/C\textsuperscript{2}
\choice  1.454E+09 N/C\textsuperscript{2}
\choice  1.599E+09 N/C\textsuperscript{2}
\CorrectChoice 1.759E+09 N/C\textsuperscript{2}
\end{choices} %%% end choices

\question
\includegraphics[width=0.142\textwidth]{QuizbankQuestionLoopeFieldOnAxis.png}A ring is uniformly charged with a net charge of 8 nC. The radius of the ring is R=1.7 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=0.32 m (on axis) away from the loop's center?
\begin{choices} %%%%%%% begin choices
\choice  3.339E+09 N/C\textsuperscript{2}
\choice  3.673E+09 N/C\textsuperscript{2}
\choice  4.041E+09 N/C\textsuperscript{2}
\CorrectChoice 4.445E+09 N/C\textsuperscript{2}
\choice  4.889E+09 N/C\textsuperscript{2}
\end{choices} %%% end choices

\question
\includegraphics[width=0.142\textwidth]{QuizbankQuestionLoopeFieldOnAxis.png}A ring is uniformly charged with a net charge of 7 nC. The radius of the ring is R=1.6 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=0.35 m (on axis) away from the loop's center?
\begin{choices} %%%%%%% begin choices
\choice  4.142E+09 N/C\textsuperscript{2}
\choice  4.556E+09 N/C\textsuperscript{2}
\CorrectChoice 5.012E+09 N/C\textsuperscript{2}
\choice  5.513E+09 N/C\textsuperscript{2}
\choice  6.064E+09 N/C\textsuperscript{2}
\end{choices} %%% end choices

\question
\includegraphics[width=0.142\textwidth]{QuizbankQuestionLoopeFieldOnAxis.png}A ring is uniformly charged with a net charge of 3 nC. The radius of the ring is R=1.8 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=1.1 m (on axis) away from the loop's center?
\begin{choices} %%%%%%% begin choices
\CorrectChoice 3.159E+09 N/C\textsuperscript{2}
\choice  3.475E+09 N/C\textsuperscript{2}
\choice  3.823E+09 N/C\textsuperscript{2}
\choice  4.205E+09 N/C\textsuperscript{2}
\choice  4.626E+09 N/C\textsuperscript{2}
\end{choices} %%% end choices

\question
\includegraphics[width=0.142\textwidth]{QuizbankQuestionLoopeFieldOnAxis.png}A ring is uniformly charged with a net charge of 5 nC. The radius of the ring is R=1.9 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=1.3 m (on axis) away from the loop's center?
\begin{choices} %%%%%%% begin choices
\CorrectChoice 4.788E+09 N/C\textsuperscript{2}
\choice  5.267E+09 N/C\textsuperscript{2}
\choice  5.793E+09 N/C\textsuperscript{2}
\choice  6.373E+09 N/C\textsuperscript{2}
\choice  7.010E+09 N/C\textsuperscript{2}
\end{choices} %%% end choices

\question
\includegraphics[width=0.142\textwidth]{QuizbankQuestionLoopeFieldOnAxis.png}A ring is uniformly charged with a net charge of 7 nC. The radius of the ring is R=1.7 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=1.1 m (on axis) away from the loop's center?
\begin{choices} %%%%%%% begin choices
\CorrectChoice 8.336E+09 N/C\textsuperscript{2}
\choice  9.170E+09 N/C\textsuperscript{2}
\choice  1.009E+10 N/C\textsuperscript{2}
\choice  1.110E+10 N/C\textsuperscript{2}
\choice  1.220E+10 N/C\textsuperscript{2}
\end{choices} %%% end choices
%\pagebreak
%\end{choices}%??????????????
\end{questions}%%%%%%%% end questions

\subsection{}%%%% subsection 5

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

\question  $$E(z)=\int_{0}^R f(r',z)dr'$$is an integral that calculates the magnitude of the electric field at a distance $$z$$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk.  The disk's radius is $$R=5.9\text{ m}$$ and the surface charge density is $$\sigma=4\text{ nC/m}^3$$. Evaluate $$f(r',z)$$ at $$r'=3.5\text{ m}$$.
\begin{choices} %%%%%%% begin choices
\choice  2.021E+00 V/m\textsuperscript{2}
\choice  2.224E+00 V/m\textsuperscript{2}
\choice  2.446E+00 V/m\textsuperscript{2}
\CorrectChoice 2.691E+00 V/m\textsuperscript{2}
\choice  2.960E+00 V/m\textsuperscript{2}
\end{choices} %%% end choices

\question  $$E(z)=\int_{0}^R f(r',z)dr'$$is an integral that calculates the magnitude of the electric field at a distance $$z$$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk.  The disk's radius is $$R=6.9\text{ m}$$ and the surface charge density is $$\sigma=9\text{ nC/m}^3$$. Evaluate $$f(r',z)$$ at $$r'=4.3\text{ m}$$.
\begin{choices} %%%%%%% begin choices
\choice  8.924E-01 V/m\textsuperscript{2}
\choice  9.816E-01 V/m\textsuperscript{2}
\CorrectChoice 1.080E+00 V/m\textsuperscript{2}
\choice  1.188E+00 V/m\textsuperscript{2}
\choice  1.307E+00 V/m\textsuperscript{2}
\end{choices} %%% end choices

\question  $$E(z)=\int_{0}^R f(r',z)dr'$$is an integral that calculates the magnitude of the electric field at a distance $$z$$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk.  The disk's radius is $$R=8.7\text{ m}$$ and the surface charge density is $$\sigma=7\text{ nC/m}^3$$. Evaluate $$f(r',z)$$ at $$r'=5.8\text{ m}$$.
\begin{choices} %%%%%%% begin choices
\choice  3.722E-01 V/m\textsuperscript{2}
\choice  4.094E-01 V/m\textsuperscript{2}
\choice  4.504E-01 V/m\textsuperscript{2}
\CorrectChoice 4.954E-01 V/m\textsuperscript{2}
\choice  5.450E-01 V/m\textsuperscript{2}
\end{choices} %%% end choices

\question  $$E(z)=\int_{0}^R f(r',z)dr'$$is an integral that calculates the magnitude of the electric field at a distance $$z$$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk.  The disk's radius is $$R=4.3\text{ m}$$ and the surface charge density is $$\sigma=2\text{ nC/m}^3$$. Evaluate $$f(r',z)$$ at $$r'=2.4\text{ m}$$.
\begin{choices} %%%%%%% begin choices
\CorrectChoice 5.647E+00 V/m\textsuperscript{2}
\choice  6.212E+00 V/m\textsuperscript{2}
\choice  6.833E+00 V/m\textsuperscript{2}
\choice  7.517E+00 V/m\textsuperscript{2}
\choice  8.268E+00 V/m\textsuperscript{2}
\end{choices} %%% end choices

\question  $$E(z)=\int_{0}^R f(r',z)dr'$$is an integral that calculates the magnitude of the electric field at a distance $$z$$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk.  The disk's radius is $$R=9.1\text{ m}$$ and the surface charge density is $$\sigma=2\text{ nC/m}^3$$. Evaluate $$f(r',z)$$ at $$r'=6.2\text{ m}$$.
\begin{choices} %%%%%%% begin choices
\choice  4.961E-01 V/m\textsuperscript{2}
\choice  5.457E-01 V/m\textsuperscript{2}
\choice  6.002E-01 V/m\textsuperscript{2}
\choice  6.603E-01 V/m\textsuperscript{2}
\CorrectChoice 7.263E-01 V/m\textsuperscript{2}
\end{choices} %%% end choices

\question  $$E(z)=\int_{0}^R f(r',z)dr'$$is an integral that calculates the magnitude of the electric field at a distance $$z$$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk.  The disk's radius is $$R=6.8\text{ m}$$ and the surface charge density is $$\sigma=6\text{ nC/m}^3$$. Evaluate $$f(r',z)$$ at $$r'=3.6\text{ m}$$.
\begin{choices} %%%%%%% begin choices
\choice  1.258E+00 V/m\textsuperscript{2}
\choice  1.384E+00 V/m\textsuperscript{2}
\choice  1.522E+00 V/m\textsuperscript{2}
\CorrectChoice 1.674E+00 V/m\textsuperscript{2}
\choice  1.842E+00 V/m\textsuperscript{2}
\end{choices} %%% end choices

\question  $$E(z)=\int_{0}^R f(r',z)dr'$$is an integral that calculates the magnitude of the electric field at a distance $$z$$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk.  The disk's radius is $$R=1.4\text{ m}$$ and the surface charge density is $$\sigma=6\text{ nC/m}^3$$. Evaluate $$f(r',z)$$ at $$r'=0.56\text{ m}$$.
\begin{choices} %%%%%%% begin choices
\choice  2.567E+01 V/m\textsuperscript{2}
\choice  2.824E+01 V/m\textsuperscript{2}
\choice  3.106E+01 V/m\textsuperscript{2}
\choice  3.417E+01 V/m\textsuperscript{2}
\CorrectChoice 3.759E+01 V/m\textsuperscript{2}
\end{choices} %%% end choices

\question  $$E(z)=\int_{0}^R f(r',z)dr'$$is an integral that calculates the magnitude of the electric field at a distance $$z$$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk.  The disk's radius is $$R=8.1\text{ m}$$ and the surface charge density is $$\sigma=3\text{ nC/m}^3$$. Evaluate $$f(r',z)$$ at $$r'=4.2\text{ m}$$.
\begin{choices} %%%%%%% begin choices
\choice  5.134E-01 V/m\textsuperscript{2}
\CorrectChoice 5.648E-01 V/m\textsuperscript{2}
\choice  6.212E-01 V/m\textsuperscript{2}
\choice  6.834E-01 V/m\textsuperscript{2}
\choice  7.517E-01 V/m\textsuperscript{2}
\end{choices} %%% end choices

\question  $$E(z)=\int_{0}^R f(r',z)dr'$$is an integral that calculates the magnitude of the electric field at a distance $$z$$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk.  The disk's radius is $$R=2.0\text{ m}$$ and the surface charge density is $$\sigma=9\text{ nC/m}^3$$. Evaluate $$f(r',z)$$ at $$r'=1.2\text{ m}$$.
\begin{choices} %%%%%%% begin choices
\choice  8.933E+00 V/m\textsuperscript{2}
\choice  9.826E+00 V/m\textsuperscript{2}
\CorrectChoice 1.081E+01 V/m\textsuperscript{2}
\choice  1.189E+01 V/m\textsuperscript{2}
\choice  1.308E+01 V/m\textsuperscript{2}
\end{choices} %%% end choices

\question  $$E(z)=\int_{0}^R f(r',z)dr'$$is an integral that calculates the magnitude of the electric field at a distance $$z$$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk.  The disk's radius is $$R=8.3\text{ m}$$ and the surface charge density is $$\sigma=5\text{ nC/m}^3$$. Evaluate $$f(r',z)$$ at $$r'=5.3\text{ m}$$.
\begin{choices} %%%%%%% begin choices
\CorrectChoice 1.022E+00 V/m\textsuperscript{2}
\choice  1.125E+00 V/m\textsuperscript{2}
\choice  1.237E+00 V/m\textsuperscript{2}
\choice  1.361E+00 V/m\textsuperscript{2}
\choice  1.497E+00 V/m\textsuperscript{2}
\end{choices} %%% end choices

\question  $$E(z)=\int_{0}^R f(r',z)dr'$$is an integral that calculates the magnitude of the electric field at a distance $$z$$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk.  The disk's radius is $$R=7.2\text{ m}$$ and the surface charge density is $$\sigma=3\text{ nC/m}^3$$. Evaluate $$f(r',z)$$ at $$r'=3.6\text{ m}$$.
\begin{choices} %%%%%%% begin choices
\CorrectChoice 1.606E+00 V/m\textsuperscript{2}
\choice  1.767E+00 V/m\textsuperscript{2}
\choice  1.943E+00 V/m\textsuperscript{2}
\choice  2.138E+00 V/m\textsuperscript{2}
\choice  2.351E+00 V/m\textsuperscript{2}
\end{choices} %%% end choices

\question  $$E(z)=\int_{0}^R f(r',z)dr'$$is an integral that calculates the magnitude of the electric field at a distance $$z$$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk.  The disk's radius is $$R=1.8\text{ m}$$ and the surface charge density is $$\sigma=3\text{ nC/m}^3$$. Evaluate $$f(r',z)$$ at $$r'=1.1\text{ m}$$.
\begin{choices} %%%%%%% begin choices
\choice  7.517E+00 V/m\textsuperscript{2}
\choice  8.269E+00 V/m\textsuperscript{2}
\choice  9.096E+00 V/m\textsuperscript{2}
\choice  1.001E+01 V/m\textsuperscript{2}
\CorrectChoice 1.101E+01 V/m\textsuperscript{2}
\end{choices} %%% end choices

\question  $$E(z)=\int_{0}^R f(r',z)dr'$$is an integral that calculates the magnitude of the electric field at a distance $$z$$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk.  The disk's radius is $$R=7.9\text{ m}$$ and the surface charge density is $$\sigma=2\text{ nC/m}^3$$. Evaluate $$f(r',z)$$ at $$r'=5.1\text{ m}$$.
\begin{choices} %%%%%%% begin choices
\choice  8.253E-01 V/m\textsuperscript{2}
\choice  9.079E-01 V/m\textsuperscript{2}
\CorrectChoice 9.987E-01 V/m\textsuperscript{2}
\choice  1.099E+00 V/m\textsuperscript{2}
\choice  1.208E+00 V/m\textsuperscript{2}
\end{choices} %%% end choices

\question  $$E(z)=\int_{0}^R f(r',z)dr'$$is an integral that calculates the magnitude of the electric field at a distance $$z$$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk.  The disk's radius is $$R=7.5\text{ m}$$ and the surface charge density is $$\sigma=3\text{ nC/m}^3$$. Evaluate $$f(r',z)$$ at $$r'=2.6\text{ m}$$.
\begin{choices} %%%%%%% begin choices
\choice  7.820E-01 V/m\textsuperscript{2}
\CorrectChoice 8.602E-01 V/m\textsuperscript{2}
\choice  9.462E-01 V/m\textsuperscript{2}
\choice  1.041E+00 V/m\textsuperscript{2}
\choice  1.145E+00 V/m\textsuperscript{2}
\end{choices} %%% end choices

\question  $$E(z)=\int_{0}^R f(r',z)dr'$$is an integral that calculates the magnitude of the electric field at a distance $$z$$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk.  The disk's radius is $$R=1.8\text{ m}$$ and the surface charge density is $$\sigma=9\text{ nC/m}^3$$. Evaluate $$f(r',z)$$ at $$r'=0.83\text{ m}$$.
\begin{choices} %%%%%%% begin choices
\CorrectChoice 2.898E+01 V/m\textsuperscript{2}
\choice  3.188E+01 V/m\textsuperscript{2}
\choice  3.507E+01 V/m\textsuperscript{2}
\choice  3.857E+01 V/m\textsuperscript{2}
\choice  4.243E+01 V/m\textsuperscript{2}
\end{choices} %%% end choices

\question  $$E(z)=\int_{0}^R f(r',z)dr'$$is an integral that calculates the magnitude of the electric field at a distance $$z$$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk.  The disk's radius is $$R=3.2\text{ m}$$ and the surface charge density is $$\sigma=2\text{ nC/m}^3$$. Evaluate $$f(r',z)$$ at $$r'=2.2\text{ m}$$.
\begin{choices} %%%%%%% begin choices
\choice  3.228E+00 V/m\textsuperscript{2}
\choice  3.551E+00 V/m\textsuperscript{2}
\choice  3.906E+00 V/m\textsuperscript{2}
\choice  4.297E+00 V/m\textsuperscript{2}
\CorrectChoice 4.727E+00 V/m\textsuperscript{2}
\end{choices} %%% end choices

\question  $$E(z)=\int_{0}^R f(r',z)dr'$$is an integral that calculates the magnitude of the electric field at a distance $$z$$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk.  The disk's radius is $$R=3.0\text{ m}$$ and the surface charge density is $$\sigma=8\text{ nC/m}^3$$. Evaluate $$f(r',z)$$ at $$r'=2.0\text{ m}$$.
\begin{choices} %%%%%%% begin choices
\choice  9.459E+00 V/m\textsuperscript{2}
\CorrectChoice 1.040E+01 V/m\textsuperscript{2}
\choice  1.145E+01 V/m\textsuperscript{2}
\choice  1.259E+01 V/m\textsuperscript{2}
\choice  1.385E+01 V/m\textsuperscript{2}
\end{choices} %%% end choices

\question  $$E(z)=\int_{0}^R f(r',z)dr'$$is an integral that calculates the magnitude of the electric field at a distance $$z$$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk.  The disk's radius is $$R=2.8\text{ m}$$ and the surface charge density is $$\sigma=3\text{ nC/m}^3$$. Evaluate $$f(r',z)$$ at $$r'=1.9\text{ m}$$.
\begin{choices} %%%%%%% begin choices
\choice  4.295E+00 V/m\textsuperscript{2}
\CorrectChoice 4.724E+00 V/m\textsuperscript{2}
\choice  5.196E+00 V/m\textsuperscript{2}
\choice  5.716E+00 V/m\textsuperscript{2}
\choice  6.288E+00 V/m\textsuperscript{2}
\end{choices} %%% end choices

\question  $$E(z)=\int_{0}^R f(r',z)dr'$$is an integral that calculates the magnitude of the electric field at a distance $$z$$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk.  The disk's radius is $$R=3.3\text{ m}$$ and the surface charge density is $$\sigma=4\text{ nC/m}^3$$. Evaluate $$f(r',z)$$ at $$r'=2.0\text{ m}$$.
\begin{choices} %%%%%%% begin choices
\choice  6.877E+00 V/m\textsuperscript{2}
\choice  7.565E+00 V/m\textsuperscript{2}
\CorrectChoice 8.321E+00 V/m\textsuperscript{2}
\choice  9.153E+00 V/m\textsuperscript{2}
\choice  1.007E+01 V/m\textsuperscript{2}
\end{choices} %%% end choices
%\pagebreak
%\end{choices}%??????????????
\end{questions}%%%%%%%% end questions

\subsection{}%%%% subsection 6

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

\question A large thin isolated square plate has an area of 9 m\textsuperscript{2}. It is uniformly charged with 8 nC of charge.  What is the magnitude of the electric field 3 mm from the center of the plate's surface?
\begin{choices} %%%%%%% begin choices
\CorrectChoice 5.020E+01 N/C
\choice  5.522E+01 N/C
\choice  6.074E+01 N/C
\choice  6.681E+01 N/C
\choice  7.349E+01 N/C
\end{choices} %%% end choices

\question A large thin isolated square plate has an area of 3 m\textsuperscript{2}. It is uniformly charged with 9 nC of charge.  What is the magnitude of the electric field 3 mm from the center of the plate's surface?
\begin{choices} %%%%%%% begin choices
\CorrectChoice 1.694E+02 N/C
\choice  1.864E+02 N/C
\choice  2.050E+02 N/C
\choice  2.255E+02 N/C
\choice  2.480E+02 N/C
\end{choices} %%% end choices

\question A large thin isolated square plate has an area of 3 m\textsuperscript{2}. It is uniformly charged with 5 nC of charge.  What is the magnitude of the electric field 3 mm from the center of the plate's surface?
\begin{choices} %%%%%%% begin choices
\CorrectChoice 9.412E+01 N/C
\choice  1.035E+02 N/C
\choice  1.139E+02 N/C
\choice  1.253E+02 N/C
\choice  1.378E+02 N/C
\end{choices} %%% end choices

\question A large thin isolated square plate has an area of 4 m\textsuperscript{2}. It is uniformly charged with 9 nC of charge.  What is the magnitude of the electric field 2 mm from the center of the plate's surface?
\begin{choices} %%%%%%% begin choices
\choice  9.546E+01 N/C
\choice  1.050E+02 N/C
\choice  1.155E+02 N/C
\CorrectChoice 1.271E+02 N/C
\choice  1.398E+02 N/C
\end{choices} %%% end choices

\question A large thin isolated square plate has an area of 9 m\textsuperscript{2}. It is uniformly charged with 6 nC of charge.  What is the magnitude of the electric field 1 mm from the center of the plate's surface?
\begin{choices} %%%%%%% begin choices
\choice  2.571E+01 N/C
\choice  2.828E+01 N/C
\choice  3.111E+01 N/C
\choice  3.422E+01 N/C
\CorrectChoice 3.765E+01 N/C
\end{choices} %%% end choices

\question A large thin isolated square plate has an area of 5 m\textsuperscript{2}. It is uniformly charged with 7 nC of charge.  What is the magnitude of the electric field 1 mm from the center of the plate's surface?
\begin{choices} %%%%%%% begin choices
\choice  6.534E+01 N/C
\choice  7.187E+01 N/C
\CorrectChoice 7.906E+01 N/C
\choice  8.696E+01 N/C
\choice  9.566E+01 N/C
\end{choices} %%% end choices

\question A large thin isolated square plate has an area of 4 m\textsuperscript{2}. It is uniformly charged with 5 nC of charge.  What is the magnitude of the electric field 1 mm from the center of the plate's surface?
\begin{choices} %%%%%%% begin choices
\choice  4.821E+01 N/C
\choice  5.303E+01 N/C
\choice  5.834E+01 N/C
\choice  6.417E+01 N/C
\CorrectChoice 7.059E+01 N/C
\end{choices} %%% end choices

\question A large thin isolated square plate has an area of 8 m\textsuperscript{2}. It is uniformly charged with 5 nC of charge.  What is the magnitude of the electric field 1 mm from the center of the plate's surface?
\begin{choices} %%%%%%% begin choices
\choice  2.652E+01 N/C
\choice  2.917E+01 N/C
\choice  3.209E+01 N/C
\CorrectChoice 3.529E+01 N/C
\choice  3.882E+01 N/C
\end{choices} %%% end choices

\question A large thin isolated square plate has an area of 5 m\textsuperscript{2}. It is uniformly charged with 8 nC of charge.  What is the magnitude of the electric field 3 mm from the center of the plate's surface?
\begin{choices} %%%%%%% begin choices
\choice  6.171E+01 N/C
\choice  6.788E+01 N/C
\choice  7.467E+01 N/C
\choice  8.214E+01 N/C
\CorrectChoice 9.035E+01 N/C
\end{choices} %%% end choices

\question A large thin isolated square plate has an area of 9 m\textsuperscript{2}. It is uniformly charged with 8 nC of charge.  What is the magnitude of the electric field 3 mm from the center of the plate's surface?
\begin{choices} %%%%%%% begin choices
\choice  3.428E+01 N/C
\choice  3.771E+01 N/C
\choice  4.148E+01 N/C
\choice  4.563E+01 N/C
\CorrectChoice 5.020E+01 N/C
\end{choices} %%% end choices

\question A large thin isolated square plate has an area of 6 m\textsuperscript{2}. It is uniformly charged with 9 nC of charge.  What is the magnitude of the electric field 2 mm from the center of the plate's surface?
\begin{choices} %%%%%%% begin choices
\choice  7.000E+01 N/C
\choice  7.701E+01 N/C
\CorrectChoice 8.471E+01 N/C
\choice  9.318E+01 N/C
\choice  1.025E+02 N/C
\end{choices} %%% end choices

\question A large thin isolated square plate has an area of 6 m\textsuperscript{2}. It is uniformly charged with 5 nC of charge.  What is the magnitude of the electric field 2 mm from the center of the plate's surface?
\begin{choices} %%%%%%% begin choices
\choice  3.214E+01 N/C
\choice  3.536E+01 N/C
\choice  3.889E+01 N/C
\choice  4.278E+01 N/C
\CorrectChoice 4.706E+01 N/C
\end{choices} %%% end choices

\question A large thin isolated square plate has an area of 8 m\textsuperscript{2}. It is uniformly charged with 7 nC of charge.  What is the magnitude of the electric field 3 mm from the center of the plate's surface?
\begin{choices} %%%%%%% begin choices
\choice  4.492E+01 N/C
\CorrectChoice 4.941E+01 N/C
\choice  5.435E+01 N/C
\choice  5.979E+01 N/C
\choice  6.577E+01 N/C
\end{choices} %%% end choices

\question A large thin isolated square plate has an area of 9 m\textsuperscript{2}. It is uniformly charged with 5 nC of charge.  What is the magnitude of the electric field 1 mm from the center of the plate's surface?
\begin{choices} %%%%%%% begin choices
\choice  2.357E+01 N/C
\choice  2.593E+01 N/C
\choice  2.852E+01 N/C
\CorrectChoice 3.137E+01 N/C
\choice  3.451E+01 N/C
\end{choices} %%% end choices

\question A large thin isolated square plate has an area of 6 m\textsuperscript{2}. It is uniformly charged with 5 nC of charge.  What is the magnitude of the electric field 1 mm from the center of the plate's surface?
\begin{choices} %%%%%%% begin choices
\choice  3.214E+01 N/C
\choice  3.536E+01 N/C
\choice  3.889E+01 N/C
\choice  4.278E+01 N/C
\CorrectChoice 4.706E+01 N/C
\end{choices} %%% end choices

\question A large thin isolated square plate has an area of 6 m\textsuperscript{2}. It is uniformly charged with 6 nC of charge.  What is the magnitude of the electric field 2 mm from the center of the plate's surface?
\begin{choices} %%%%%%% begin choices
\CorrectChoice 5.647E+01 N/C
\choice  6.212E+01 N/C
\choice  6.833E+01 N/C
\choice  7.516E+01 N/C
\choice  8.268E+01 N/C
\end{choices} %%% end choices

\question A large thin isolated square plate has an area of 8 m\textsuperscript{2}. It is uniformly charged with 6 nC of charge.  What is the magnitude of the electric field 1 mm from the center of the plate's surface?
\begin{choices} %%%%%%% begin choices
\choice  3.500E+01 N/C
\choice  3.850E+01 N/C
\CorrectChoice 4.235E+01 N/C
\choice  4.659E+01 N/C
\choice  5.125E+01 N/C
\end{choices} %%% end choices

\question A large thin isolated square plate has an area of 6 m\textsuperscript{2}. It is uniformly charged with 9 nC of charge.  What is the magnitude of the electric field 1 mm from the center of the plate's surface?
\begin{choices} %%%%%%% begin choices
\choice  7.701E+01 N/C
\CorrectChoice 8.471E+01 N/C
\choice  9.318E+01 N/C
\choice  1.025E+02 N/C
\choice  1.127E+02 N/C
\end{choices} %%% end choices

\question A large thin isolated square plate has an area of 6 m\textsuperscript{2}. It is uniformly charged with 9 nC of charge.  What is the magnitude of the electric field 3 mm from the center of the plate's surface?
\begin{choices} %%%%%%% begin choices
\CorrectChoice 8.471E+01 N/C
\choice  9.318E+01 N/C
\choice  1.025E+02 N/C
\choice  1.127E+02 N/C
\choice  1.240E+02 N/C
\end{choices} %%% end choices
\end{questions}
\pagebreak