# QB/d cp2.13

< QB

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Questions 7-9 seem wrong

• Question 5 if this quiz differs significantly from the textbook's example.
• The wikitext version of this quiz at special:permalink/1893631 is flawed. Only the pdf version of this quiz should be used for review. This file is at:
File:Quizbankqb_d cp2.13.pdf

### LaTexMarkup begin

Required images: [[file:Wikiversity-logo-en.svg|45px]][[File:RC switch.svg|45px]]
%This code creates both the question and answer key using \newcommand\mytest
%This "final version" replaces B by E in the line integral for problem 7
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\newcommand{\quizname}{QB/d_cp2.13}

\newcommand{\quiztype}{numerical}%[[Category:QB/numerical]]
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\newif\ifkey %estabkishes Boolean ifkey to turn on and off endnotes

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\begin{document}
\title{d\_cp2.13}
\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}
\includegraphics[width=0.15\textwidth]{666px-Wikiversity-logo-en.png}
\\Latex markup at\\

\Large{
\textbf{NOTICE: \\ Question 7 is solved incorrectly: }\\
The posted solution  used the circle's circumfrence $$2\pi R$$ when the area
$$\pi R^2$$ should have been used.  To get the correct answer, multiply the boldfaced answer by $$\frac 1 2 R$$.\linebreak
}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\end{center}
\begin{frame}{}
\begin{multicols}{3}
\tableofcontents
\end{multicols}
\end{frame}
\pagebreak\section{Quiz}
\keytrue
\begin{questions}
\question A square coil has sides that are L= 0.25\,m long and is tightly wound with N=200\,turns of wire. The resistance of the coil is R=5\,\textOmega\ . The coil is placed in a spacially uniform magnetic field that is directed perpendicular to the face of the coil and whose magnitude is increasing at a rate dB/dt=0.04\,T/s. If R represents the only impedance of the coil, what is the magnitude of the current circulting through it? \ifkey\endnote{Example 13.1 from OpenStax University Physics2: https://cnx.org/contents/eg-XcBxE@9.7:BTZF6vX4@2/131-Faradays-Law\_1 placed in Public Domain by Guy Vandegrift: {\url{https://en.wikiversity.org/wiki/special:permalink/xxx}}}\fi
\begin{choices}
\CorrectChoice 1.000E-01\,A
\choice 1.100E-01\,A
\choice 1.210E-01\,A
\choice 1.331E-01\,A
\choice 1.464E-01\,A
\end{choices}

\question A time dependent magnetic field is directed  perpendicular to the plane of a circular coil with a radius of 0.5\,m. The magnetic field is spatially uniform but decays in time according to $$(1.5)e^{-\alpha t}$$ at time t = 0.05 seconds, and $$\alpha=$$5\,s\textsuperscript{$$-$$1}. What is the current in the coil if the impedance of the coil is 10\,\textOmega\ ?\ifkey\endnote{Example 13.2 from OpenStax University Physics2: https://cnx.org/contents/eg-XcBxE@9.7:ZNcjduzK@4/132-Lenzs-Law\_1 placed in Public Domain by Guy Vandegrift: {\url{https://en.wikiversity.org/wiki/special:permalink/xxx}}}\fi
\begin{choices}
\choice 3.791E-01\,A
\choice 4.170E-01\,A
\CorrectChoice 4.588E-01\,A
\choice 5.046E-01\,A
\choice 5.551E-01\,A
\end{choices}

\question The current through the windings of a solenoid with n= 2.000E+03 turns per meter is changing at a rate dI/dt=3\,A/s.  The solenoid is 50\,cm long and has a cross-sectional diameter of 3\,cm.  A small coil consisting of N=20turns wraped in a circle of diameter 1\,cm is placed in the middle of the solenoid such that the plane of the coil is perpendicular to the central axis of the solenoid. Assume that the infinite-solenoid approximation is valid inside the small coil.  What is the emf induced in the coil?\ifkey\endnote{Example 13.3 from OpenStax University Physics2: https://cnx.org/contents/eg-XcBxE@9.7:ZNcjduzK@4/132-Lenzs-Law\_1 placed in Public Domain by Guy Vandegrift: {\url{https://en.wikiversity.org/wiki/special:permalink/xxx}}}\fi
\begin{choices}
\choice 9.788E-06\,V
\choice 1.077E-05\,V
\CorrectChoice 1.184E-05\,V
\choice 1.303E-05\,V
\choice 1.433E-05\,V
\end{choices}

\question Calculate the motional emf induced along a 20\,km conductor moving at an orbital speed of 7.8\,km/s perpendicular to Earth's 5.000E-05\,Tesla magnetic field.\ifkey\endnote{Example 13.3 from OpenStax University Physics2: https://cnx.org/contents/eg-XcBxE@9.7:ZNcjduzK@4/132-Lenzs-Law\_1 placed in Public Domain by Guy Vandegrift: {\url{https://en.wikiversity.org/wiki/special:permalink/xxx}}}\fi
\begin{choices}
\choice 7.091E+03\,V
\CorrectChoice 7.800E+03\,V
\choice 8.580E+03\,V
\choice 9.438E+03\,V
\choice 1.038E+04\,V
\end{choices}

\question \includegraphics[width=0.12\textwidth]{Wikiversity-wedge.png}A cylinder of height 1.1\,cm and radius 3.1\,cm is cut into a wedge as shown. Now imagine that the volume grows as \straighttheta\  increases while the radius R and height h remains constant.  What is the volume's rate of change if point P is 2.1\,cm from point O and moves at a speed of 5.1\,cm/s? Assume that the wedge grows in such a way as the front face moves by rotating around the axis (that contains point O.)]
\ifkey\endnote{Example 13.5 from OpenStax University Physics2: https://cnx.org/contents/eg-XcBxE@9.7:UbKygyP4@2/133-Motional-Emf\_1 placed in Public Domain by Guy Vandegrift: {\url{https://en.wikiversity.org/wiki/special:permalink/xxx}}}\fi
\begin{choices}
\choice 8.767E+00\,cm\textsuperscript{3}/s
\choice 9.644E+00\,cm\textsuperscript{3}/s
\choice 1.061E+01\,cm\textsuperscript{3}/s
\choice 1.167E+01\,cm\textsuperscript{3}/s
\CorrectChoice 1.284E+01\,cm\textsuperscript{3}/s
\end{choices}

\question A recangular coil with an area of 0.5\,m\textsuperscript{2} and 10\,turns is placed in a uniform magnetic field of 1.5\,T.  The coil is rotated about an axis that is perpendicular to this field. At time t=0 the normal to the coil is oriented parallel to the magnetic field and the coil is rotating with a constant angular frequency of 2.000E+03\,s\textsuperscript{$$-$$1}.  What is the ''magnitude'' (absolute value) of the induced emf at t\,=\,50\,s?\ifkey\endnote{Example 13.6 from OpenStax University Physics2: https://cnx.org/contents/eg-XcBxE@9.7:UbKygyP4@2/133-Motional-Emf\_1 placed in Public Domain by Guy Vandegrift: {\url{https://en.wikiversity.org/wiki/special:permalink/xxx}}}\fi
\begin{choices}
\choice 4.029E+02\,V
\choice 4.432E+02\,V
\choice 4.875E+02\,V
\CorrectChoice 5.362E+02\,V
\choice 5.899E+02\,V
\end{choices}

\question A spatially uniform magnetic points in the z-direction and oscilates with time as $$\vec B(t) = B_0\sin\omega t$$ where $$B_0=$$1.5\,T and $$\omega=$$2.000E+03\,s\textsuperscript{$$-$$1}. Suppose the electric field is always zero at point $$\mathcal O$$, and consider a circle of radius 0.5\,m that is centered at that point and oriented in a plane perpendicular to the magnetic field. Evaluate the maximum value of the line integral  $$\oint \vec E\cdot d\vec s$$ around the circle.\ifkey\endnote{Example 13.7 from OpenStax University Physics2: https://cnx.org/contents/eg-XcBxE@9.7:F-UkvfQz@3/134-Induced-Electric-Fields\_1 placed in Public Domain by Guy Vandegrift: {\url{https://en.wikiversity.org/wiki/special:permalink/xxx}}}\fi
\begin{choices}
\CorrectChoice 9.425E+03\,V
\choice 1.037E+04\,V
\choice 1.140E+04\,V
\choice 1.254E+04\,V
\choice 1.380E+04\,V
\end{choices}

\question A long solenoid has a radius of 0.7\,m and 50\,turns per meter; its current decreases with time according to $$I_0e^{-\alpha t}$$, where $$I_0=$$3\,A and $$\alpha=$$25\,s\textsuperscript{$$-$$1}.What is the induced electric fied at a distance 2.0\,m from the axis at time t=0.04\,s ?\ifkey\endnote{Example 13.8 from OpenStax University Physics2: https://cnx.org/contents/eg-XcBxE@9.7:F-UkvfQz@3/134-Induced-Electric-Fields\_1 placed in Public Domain by Guy Vandegrift: {\url{https://en.wikiversity.org/wiki/special:permalink/xxx}}}\fi
\begin{choices}
\CorrectChoice 2.124E-04\,V/m
\choice 2.336E-04\,V/m
\choice 2.570E-04\,V/m
\choice 2.827E-04\,V/m
\choice 3.109E-04\,V/m
\end{choices}

\question A long solenoid has a radius of 0.7\,m and 50\,turns per meter; its current decreases with time according to $$I_0e^{-\alpha t}$$, where $$I_0=$$3\,A and $$\alpha=$$25\,s\textsuperscript{$$-$$1}.What is the induced electric fied at a distance 0.15\,m from the axis at time t=0.04\,s ?\ifkey\endnote{Example 13.8 from OpenStax University Physics2: https://cnx.org/contents/eg-XcBxE@9.7:F-UkvfQz@3/134-Induced-Electric-Fields\_1 placed in Public Domain by Guy Vandegrift: {\url{https://en.wikiversity.org/wiki/special:permalink/xxx}}}\fi
\begin{choices}
\CorrectChoice 1.300E-04\,V/m
\choice 1.430E-04\,V/m
\choice 1.573E-04\,V/m
\choice 1.731E-04\,V/m
\choice 1.904E-04\,V/m
\end{choices}

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

\subsection{}%%%% subsection 1

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

\question A square coil has sides that are L= 0.673\,m long and is tightly wound with N=211\,turns of wire. The resistance of the coil is R=5.31\,\textOmega\ . The coil is placed in a spacially uniform magnetic field that is directed perpendicular to the face of the coil and whose magnitude is increasing at a rate dB/dt=0.0454\,T/s. If R represents the only impedance of the coil, what is the magnitude of the current circulting through it?
\begin{choices} %%%%%%% begin choices
\choice  6.753E-01\,A
\choice  7.428E-01\,A
\CorrectChoice 8.171E-01\,A
\choice  8.988E-01\,A
\choice  9.887E-01\,A
\end{choices} %%% end choices

\question A square coil has sides that are L= 0.861\,m long and is tightly wound with N=538\,turns of wire. The resistance of the coil is R=9.04\,\textOmega\ . The coil is placed in a spacially uniform magnetic field that is directed perpendicular to the face of the coil and whose magnitude is increasing at a rate dB/dt=0.0433\,T/s. If R represents the only impedance of the coil, what is the magnitude of the current circulting through it?
\begin{choices} %%%%%%% begin choices
\choice  1.737E+00\,A
\CorrectChoice 1.910E+00\,A
\choice  2.101E+00\,A
\choice  2.311E+00\,A
\choice  2.543E+00\,A
\end{choices} %%% end choices

\question A square coil has sides that are L= 0.259\,m long and is tightly wound with N=628\,turns of wire. The resistance of the coil is R=6.51\,\textOmega\ . The coil is placed in a spacially uniform magnetic field that is directed perpendicular to the face of the coil and whose magnitude is increasing at a rate dB/dt=0.0372\,T/s. If R represents the only impedance of the coil, what is the magnitude of the current circulting through it?
\begin{choices} %%%%%%% begin choices
\choice  1.809E-01\,A
\choice  1.989E-01\,A
\choice  2.188E-01\,A
\CorrectChoice 2.407E-01\,A
\choice  2.648E-01\,A
\end{choices} %%% end choices

\question A square coil has sides that are L= 0.894\,m long and is tightly wound with N=255\,turns of wire. The resistance of the coil is R=8.83\,\textOmega\ . The coil is placed in a spacially uniform magnetic field that is directed perpendicular to the face of the coil and whose magnitude is increasing at a rate dB/dt=0.0682\,T/s. If R represents the only impedance of the coil, what is the magnitude of the current circulting through it?
\begin{choices} %%%%%%% begin choices
\choice  1.301E+00\,A
\choice  1.431E+00\,A
\CorrectChoice 1.574E+00\,A
\choice  1.732E+00\,A
\choice  1.905E+00\,A
\end{choices} %%% end choices

\question A square coil has sides that are L= 0.436\,m long and is tightly wound with N=284\,turns of wire. The resistance of the coil is R=6.89\,\textOmega\ . The coil is placed in a spacially uniform magnetic field that is directed perpendicular to the face of the coil and whose magnitude is increasing at a rate dB/dt=0.0733\,T/s. If R represents the only impedance of the coil, what is the magnitude of the current circulting through it?
\begin{choices} %%%%%%% begin choices
\CorrectChoice 5.743E-01\,A
\choice  6.318E-01\,A
\choice  6.950E-01\,A
\choice  7.645E-01\,A
\choice  8.409E-01\,A
\end{choices} %%% end choices

\question A square coil has sides that are L= 0.561\,m long and is tightly wound with N=930\,turns of wire. The resistance of the coil is R=5.08\,\textOmega\ . The coil is placed in a spacially uniform magnetic field that is directed perpendicular to the face of the coil and whose magnitude is increasing at a rate dB/dt=0.0548\,T/s. If R represents the only impedance of the coil, what is the magnitude of the current circulting through it?
\begin{choices} %%%%%%% begin choices
\choice  2.609E+00\,A
\choice  2.870E+00\,A
\CorrectChoice 3.157E+00\,A
\choice  3.473E+00\,A
\choice  3.820E+00\,A
\end{choices} %%% end choices

\question A square coil has sides that are L= 0.547\,m long and is tightly wound with N=198\,turns of wire. The resistance of the coil is R=4.62\,\textOmega\ . The coil is placed in a spacially uniform magnetic field that is directed perpendicular to the face of the coil and whose magnitude is increasing at a rate dB/dt=0.0768\,T/s. If R represents the only impedance of the coil, what is the magnitude of the current circulting through it?
\begin{choices} %%%%%%% begin choices
\choice  8.953E-01\,A
\CorrectChoice 9.848E-01\,A
\choice  1.083E+00\,A
\choice  1.192E+00\,A
\choice  1.311E+00\,A
\end{choices} %%% end choices

\question A square coil has sides that are L= 0.245\,m long and is tightly wound with N=925\,turns of wire. The resistance of the coil is R=8.0\,\textOmega\ . The coil is placed in a spacially uniform magnetic field that is directed perpendicular to the face of the coil and whose magnitude is increasing at a rate dB/dt=0.0618\,T/s. If R represents the only impedance of the coil, what is the magnitude of the current circulting through it?
\begin{choices} %%%%%%% begin choices
\choice  3.545E-01\,A
\choice  3.899E-01\,A
\CorrectChoice 4.289E-01\,A
\choice  4.718E-01\,A
\choice  5.190E-01\,A
\end{choices} %%% end choices

\question A square coil has sides that are L= 0.568\,m long and is tightly wound with N=482\,turns of wire. The resistance of the coil is R=8.78\,\textOmega\ . The coil is placed in a spacially uniform magnetic field that is directed perpendicular to the face of the coil and whose magnitude is increasing at a rate dB/dt=0.0544\,T/s. If R represents the only impedance of the coil, what is the magnitude of the current circulting through it?
\begin{choices} %%%%%%% begin choices
\choice  6.581E-01\,A
\choice  7.239E-01\,A
\choice  7.963E-01\,A
\choice  8.759E-01\,A
\CorrectChoice 9.635E-01\,A
\end{choices} %%% end choices

\question A square coil has sides that are L= 0.638\,m long and is tightly wound with N=927\,turns of wire. The resistance of the coil is R=8.34\,\textOmega\ . The coil is placed in a spacially uniform magnetic field that is directed perpendicular to the face of the coil and whose magnitude is increasing at a rate dB/dt=0.0718\,T/s. If R represents the only impedance of the coil, what is the magnitude of the current circulting through it?
\begin{choices} %%%%%%% begin choices
\choice  2.685E+00\,A
\choice  2.953E+00\,A
\CorrectChoice 3.248E+00\,A
\choice  3.573E+00\,A
\choice  3.931E+00\,A
\end{choices} %%% end choices

\question A square coil has sides that are L= 0.219\,m long and is tightly wound with N=508\,turns of wire. The resistance of the coil is R=8.42\,\textOmega\ . The coil is placed in a spacially uniform magnetic field that is directed perpendicular to the face of the coil and whose magnitude is increasing at a rate dB/dt=0.0619\,T/s. If R represents the only impedance of the coil, what is the magnitude of the current circulting through it?
\begin{choices} %%%%%%% begin choices
\CorrectChoice 1.791E-01\,A
\choice  1.970E-01\,A
\choice  2.167E-01\,A
\choice  2.384E-01\,A
\choice  2.622E-01\,A
\end{choices} %%% end choices

\question A square coil has sides that are L= 0.308\,m long and is tightly wound with N=969\,turns of wire. The resistance of the coil is R=8.64\,\textOmega\ . The coil is placed in a spacially uniform magnetic field that is directed perpendicular to the face of the coil and whose magnitude is increasing at a rate dB/dt=0.0498\,T/s. If R represents the only impedance of the coil, what is the magnitude of the current circulting through it?
\begin{choices} %%%%%%% begin choices
\choice  4.817E-01\,A
\CorrectChoice 5.298E-01\,A
\choice  5.828E-01\,A
\choice  6.411E-01\,A
\choice  7.052E-01\,A
\end{choices} %%% end choices

\question A square coil has sides that are L= 0.738\,m long and is tightly wound with N=717\,turns of wire. The resistance of the coil is R=5.25\,\textOmega\ . The coil is placed in a spacially uniform magnetic field that is directed perpendicular to the face of the coil and whose magnitude is increasing at a rate dB/dt=0.0655\,T/s. If R represents the only impedance of the coil, what is the magnitude of the current circulting through it?
\begin{choices} %%%%%%% begin choices
\choice  3.660E+00\,A
\choice  4.027E+00\,A
\choice  4.429E+00\,A
\CorrectChoice 4.872E+00\,A
\choice  5.359E+00\,A
\end{choices} %%% end choices

\question A square coil has sides that are L= 0.888\,m long and is tightly wound with N=604\,turns of wire. The resistance of the coil is R=4.31\,\textOmega\ . The coil is placed in a spacially uniform magnetic field that is directed perpendicular to the face of the coil and whose magnitude is increasing at a rate dB/dt=0.0441\,T/s. If R represents the only impedance of the coil, what is the magnitude of the current circulting through it?
\begin{choices} %%%%%%% begin choices
\choice  3.661E+00\,A
\choice  4.028E+00\,A
\choice  4.430E+00\,A
\CorrectChoice 4.873E+00\,A
\choice  5.361E+00\,A
\end{choices} %%% end choices

\question A square coil has sides that are L= 0.325\,m long and is tightly wound with N=697\,turns of wire. The resistance of the coil is R=4.87\,\textOmega\ . The coil is placed in a spacially uniform magnetic field that is directed perpendicular to the face of the coil and whose magnitude is increasing at a rate dB/dt=0.0842\,T/s. If R represents the only impedance of the coil, what is the magnitude of the current circulting through it?
\begin{choices} %%%%%%% begin choices
\choice  1.157E+00\,A
\CorrectChoice 1.273E+00\,A
\choice  1.400E+00\,A
\choice  1.540E+00\,A
\choice  1.694E+00\,A
\end{choices} %%% end choices

\question A square coil has sides that are L= 0.727\,m long and is tightly wound with N=376\,turns of wire. The resistance of the coil is R=5.59\,\textOmega\ . The coil is placed in a spacially uniform magnetic field that is directed perpendicular to the face of the coil and whose magnitude is increasing at a rate dB/dt=0.0485\,T/s. If R represents the only impedance of the coil, what is the magnitude of the current circulting through it?
\begin{choices} %%%%%%% begin choices
\choice  1.567E+00\,A
\CorrectChoice 1.724E+00\,A
\choice  1.897E+00\,A
\choice  2.086E+00\,A
\choice  2.295E+00\,A
\end{choices} %%% end choices

\question A square coil has sides that are L= 0.465\,m long and is tightly wound with N=954\,turns of wire. The resistance of the coil is R=6.06\,\textOmega\ . The coil is placed in a spacially uniform magnetic field that is directed perpendicular to the face of the coil and whose magnitude is increasing at a rate dB/dt=0.0367\,T/s. If R represents the only impedance of the coil, what is the magnitude of the current circulting through it?
\begin{choices} %%%%%%% begin choices
\choice  1.136E+00\,A
\CorrectChoice 1.249E+00\,A
\choice  1.374E+00\,A
\choice  1.512E+00\,A
\choice  1.663E+00\,A
\end{choices} %%% end choices

\question A square coil has sides that are L= 0.819\,m long and is tightly wound with N=887\,turns of wire. The resistance of the coil is R=5.69\,\textOmega\ . The coil is placed in a spacially uniform magnetic field that is directed perpendicular to the face of the coil and whose magnitude is increasing at a rate dB/dt=0.0618\,T/s. If R represents the only impedance of the coil, what is the magnitude of the current circulting through it?
\begin{choices} %%%%%%% begin choices
\choice  4.414E+00\,A
\choice  4.855E+00\,A
\choice  5.341E+00\,A
\choice  5.875E+00\,A
\CorrectChoice 6.462E+00\,A
\end{choices} %%% end choices

\question A square coil has sides that are L= 0.458\,m long and is tightly wound with N=742\,turns of wire. The resistance of the coil is R=6.81\,\textOmega\ . The coil is placed in a spacially uniform magnetic field that is directed perpendicular to the face of the coil and whose magnitude is increasing at a rate dB/dt=0.0559\,T/s. If R represents the only impedance of the coil, what is the magnitude of the current circulting through it?
\begin{choices} %%%%%%% begin choices
\choice  1.056E+00\,A
\choice  1.161E+00\,A
\CorrectChoice 1.278E+00\,A
\choice  1.405E+00\,A
\choice  1.546E+00\,A
\end{choices} %%% end choices
%\pagebreak
%\end{choices}%??????????????
\end{questions}%%%%%%%% end questions

\subsection{}%%%% subsection 2

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

\question A time dependent magnetic field is directed  perpendicular to the plane of a circular coil with a radius of 0.72\,m. The magnetic field is spatially uniform but decays in time according to $$(1.3)e^{-\alpha t}$$ at time t = 0.039 seconds, and $$\alpha=$$9.5\,s\textsuperscript{$$-$$1}. What is the current in the coil if the impedance of the coil is 18.0\,\textOmega\ ?
\begin{choices} %%%%%%% begin choices
\choice  7.013E-01\,A
\CorrectChoice 7.714E-01\,A
\choice  8.486E-01\,A
\choice  9.334E-01\,A
\choice  1.027E+00\,A
\end{choices} %%% end choices

\question A time dependent magnetic field is directed  perpendicular to the plane of a circular coil with a radius of 0.76\,m. The magnetic field is spatially uniform but decays in time according to $$(4.2)e^{-\alpha t}$$ at time t = 0.058 seconds, and $$\alpha=$$8.8\,s\textsuperscript{$$-$$1}. What is the current in the coil if the impedance of the coil is 86.0\,\textOmega\ ?
\begin{choices} %%%%%%% begin choices
\CorrectChoice 4.681E-01\,A
\choice  5.149E-01\,A
\choice  5.664E-01\,A
\choice  6.231E-01\,A
\choice  6.854E-01\,A
\end{choices} %%% end choices

\question A time dependent magnetic field is directed  perpendicular to the plane of a circular coil with a radius of 0.28\,m. The magnetic field is spatially uniform but decays in time according to $$(2.7)e^{-\alpha t}$$ at time t = 0.035 seconds, and $$\alpha=$$6.6\,s\textsuperscript{$$-$$1}. What is the current in the coil if the impedance of the coil is 76.0\,\textOmega\ ?
\begin{choices} %%%%%%% begin choices
\choice  3.131E-02\,A
\choice  3.444E-02\,A
\choice  3.788E-02\,A
\choice  4.167E-02\,A
\CorrectChoice 4.584E-02\,A
\end{choices} %%% end choices

\question A time dependent magnetic field is directed  perpendicular to the plane of a circular coil with a radius of 0.98\,m. The magnetic field is spatially uniform but decays in time according to $$(4.5)e^{-\alpha t}$$ at time t = 0.045 seconds, and $$\alpha=$$8.6\,s\textsuperscript{$$-$$1}. What is the current in the coil if the impedance of the coil is 7.5\,\textOmega\ ?
\begin{choices} %%%%%%% begin choices
\choice  7.221E+00\,A
\choice  7.943E+00\,A
\choice  8.738E+00\,A
\choice  9.611E+00\,A
\CorrectChoice 1.057E+01\,A
\end{choices} %%% end choices

\question A time dependent magnetic field is directed  perpendicular to the plane of a circular coil with a radius of 0.53\,m. The magnetic field is spatially uniform but decays in time according to $$(2.0)e^{-\alpha t}$$ at time t = 0.077 seconds, and $$\alpha=$$7.5\,s\textsuperscript{$$-$$1}. What is the current in the coil if the impedance of the coil is 67.0\,\textOmega\ ?
\begin{choices} %%%%%%% begin choices
\CorrectChoice 1.109E-01\,A
\choice  1.220E-01\,A
\choice  1.342E-01\,A
\choice  1.476E-01\,A
\choice  1.624E-01\,A
\end{choices} %%% end choices

\question A time dependent magnetic field is directed  perpendicular to the plane of a circular coil with a radius of 0.65\,m. The magnetic field is spatially uniform but decays in time according to $$(5.7)e^{-\alpha t}$$ at time t = 0.073 seconds, and $$\alpha=$$8.2\,s\textsuperscript{$$-$$1}. What is the current in the coil if the impedance of the coil is 51.0\,\textOmega\ ?
\begin{choices} %%%%%%% begin choices
\choice  5.525E-01\,A
\choice  6.078E-01\,A
\CorrectChoice 6.685E-01\,A
\choice  7.354E-01\,A
\choice  8.089E-01\,A
\end{choices} %%% end choices

\question A time dependent magnetic field is directed  perpendicular to the plane of a circular coil with a radius of 0.77\,m. The magnetic field is spatially uniform but decays in time according to $$(2.7)e^{-\alpha t}$$ at time t = 0.035 seconds, and $$\alpha=$$5.5\,s\textsuperscript{$$-$$1}. What is the current in the coil if the impedance of the coil is 38.0\,\textOmega\ ?
\begin{choices} %%%%%%% begin choices
\choice  4.511E-01\,A
\choice  4.962E-01\,A
\choice  5.459E-01\,A
\CorrectChoice 6.004E-01\,A
\choice  6.605E-01\,A
\end{choices} %%% end choices

\question A time dependent magnetic field is directed  perpendicular to the plane of a circular coil with a radius of 0.68\,m. The magnetic field is spatially uniform but decays in time according to $$(2.6)e^{-\alpha t}$$ at time t = 0.061 seconds, and $$\alpha=$$9.5\,s\textsuperscript{$$-$$1}. What is the current in the coil if the impedance of the coil is 13.0\,\textOmega\ ?
\begin{choices} %%%%%%% begin choices
\choice  1.278E+00\,A
\choice  1.406E+00\,A
\CorrectChoice 1.546E+00\,A
\choice  1.701E+00\,A
\choice  1.871E+00\,A
\end{choices} %%% end choices

\question A time dependent magnetic field is directed  perpendicular to the plane of a circular coil with a radius of 0.42\,m. The magnetic field is spatially uniform but decays in time according to $$(4.7)e^{-\alpha t}$$ at time t = 0.033 seconds, and $$\alpha=$$5.7\,s\textsuperscript{$$-$$1}. What is the current in the coil if the impedance of the coil is 25.0\,\textOmega\ ?
\begin{choices} %%%%%%% begin choices
\choice  3.697E-01\,A
\choice  4.066E-01\,A
\choice  4.473E-01\,A
\CorrectChoice 4.920E-01\,A
\choice  5.412E-01\,A
\end{choices} %%% end choices

\question A time dependent magnetic field is directed  perpendicular to the plane of a circular coil with a radius of 0.73\,m. The magnetic field is spatially uniform but decays in time according to $$(1.2)e^{-\alpha t}$$ at time t = 0.058 seconds, and $$\alpha=$$7.1\,s\textsuperscript{$$-$$1}. What is the current in the coil if the impedance of the coil is 54.0\,\textOmega\ ?
\begin{choices} %%%%%%% begin choices
\CorrectChoice 1.750E-01\,A
\choice  1.925E-01\,A
\choice  2.117E-01\,A
\choice  2.329E-01\,A
\choice  2.562E-01\,A
\end{choices} %%% end choices

\question A time dependent magnetic field is directed  perpendicular to the plane of a circular coil with a radius of 0.97\,m. The magnetic field is spatially uniform but decays in time according to $$(1.6)e^{-\alpha t}$$ at time t = 0.035 seconds, and $$\alpha=$$7.5\,s\textsuperscript{$$-$$1}. What is the current in the coil if the impedance of the coil is 97.0\,\textOmega\ ?
\begin{choices} %%%%%%% begin choices
\choice  2.113E-01\,A
\choice  2.324E-01\,A
\choice  2.557E-01\,A
\CorrectChoice 2.813E-01\,A
\choice  3.094E-01\,A
\end{choices} %%% end choices

\question A time dependent magnetic field is directed  perpendicular to the plane of a circular coil with a radius of 0.75\,m. The magnetic field is spatially uniform but decays in time according to $$(5.2)e^{-\alpha t}$$ at time t = 0.067 seconds, and $$\alpha=$$9.6\,s\textsuperscript{$$-$$1}. What is the current in the coil if the impedance of the coil is 71.0\,\textOmega\ ?
\begin{choices} %%%%%%% begin choices
\choice  5.937E-01\,A
\CorrectChoice 6.531E-01\,A
\choice  7.184E-01\,A
\choice  7.902E-01\,A
\choice  8.692E-01\,A
\end{choices} %%% end choices

\question A time dependent magnetic field is directed  perpendicular to the plane of a circular coil with a radius of 0.73\,m. The magnetic field is spatially uniform but decays in time according to $$(3.3)e^{-\alpha t}$$ at time t = 0.062 seconds, and $$\alpha=$$8.1\,s\textsuperscript{$$-$$1}. What is the current in the coil if the impedance of the coil is 53.0\,\textOmega\ ?
\begin{choices} %%%%%%% begin choices
\choice  4.645E-01\,A
\CorrectChoice 5.110E-01\,A
\choice  5.621E-01\,A
\choice  6.183E-01\,A
\choice  6.801E-01\,A
\end{choices} %%% end choices

\question A time dependent magnetic field is directed  perpendicular to the plane of a circular coil with a radius of 0.68\,m. The magnetic field is spatially uniform but decays in time according to $$(1.8)e^{-\alpha t}$$ at time t = 0.038 seconds, and $$\alpha=$$5.3\,s\textsuperscript{$$-$$1}. What is the current in the coil if the impedance of the coil is 91.0\,\textOmega\ ?
\begin{choices} %%%%%%% begin choices
\CorrectChoice 1.245E-01\,A
\choice  1.370E-01\,A
\choice  1.507E-01\,A
\choice  1.657E-01\,A
\choice  1.823E-01\,A
\end{choices} %%% end choices

\question A time dependent magnetic field is directed  perpendicular to the plane of a circular coil with a radius of 0.92\,m. The magnetic field is spatially uniform but decays in time according to $$(2.8)e^{-\alpha t}$$ at time t = 0.032 seconds, and $$\alpha=$$6.6\,s\textsuperscript{$$-$$1}. What is the current in the coil if the impedance of the coil is 88.0\,\textOmega\ ?
\begin{choices} %%%%%%% begin choices
\choice  3.397E-01\,A
\choice  3.736E-01\,A
\choice  4.110E-01\,A
\CorrectChoice 4.521E-01\,A
\choice  4.973E-01\,A
\end{choices} %%% end choices

\question A time dependent magnetic field is directed  perpendicular to the plane of a circular coil with a radius of 0.48\,m. The magnetic field is spatially uniform but decays in time according to $$(3.8)e^{-\alpha t}$$ at time t = 0.036 seconds, and $$\alpha=$$9.3\,s\textsuperscript{$$-$$1}. What is the current in the coil if the impedance of the coil is 68.0\,\textOmega\ ?
\begin{choices} %%%%%%% begin choices
\choice  2.022E-01\,A
\choice  2.224E-01\,A
\choice  2.447E-01\,A
\CorrectChoice 2.691E-01\,A
\choice  2.961E-01\,A
\end{choices} %%% end choices

\question A time dependent magnetic field is directed  perpendicular to the plane of a circular coil with a radius of 0.59\,m. The magnetic field is spatially uniform but decays in time according to $$(2.6)e^{-\alpha t}$$ at time t = 0.051 seconds, and $$\alpha=$$9.1\,s\textsuperscript{$$-$$1}. What is the current in the coil if the impedance of the coil is 63.0\,\textOmega\ ?
\begin{choices} %%%%%%% begin choices
\choice  1.940E-01\,A
\choice  2.134E-01\,A
\choice  2.347E-01\,A
\CorrectChoice 2.582E-01\,A
\choice  2.840E-01\,A
\end{choices} %%% end choices

\question A time dependent magnetic field is directed  perpendicular to the plane of a circular coil with a radius of 0.4\,m. The magnetic field is spatially uniform but decays in time according to $$(2.3)e^{-\alpha t}$$ at time t = 0.051 seconds, and $$\alpha=$$4.1\,s\textsuperscript{$$-$$1}. What is the current in the coil if the impedance of the coil is 1.7\,\textOmega\ ?
\begin{choices} %%%%%%% begin choices
\choice  1.545E+00\,A
\choice  1.700E+00\,A
\choice  1.870E+00\,A
\choice  2.057E+00\,A
\CorrectChoice 2.262E+00\,A
\end{choices} %%% end choices

\question A time dependent magnetic field is directed  perpendicular to the plane of a circular coil with a radius of 0.38\,m. The magnetic field is spatially uniform but decays in time according to $$(1.5)e^{-\alpha t}$$ at time t = 0.032 seconds, and $$\alpha=$$4.4\,s\textsuperscript{$$-$$1}. What is the current in the coil if the impedance of the coil is 7.6\,\textOmega\ ?
\begin{choices} %%%%%%% begin choices
\choice  2.571E-01\,A
\choice  2.828E-01\,A
\choice  3.111E-01\,A
\CorrectChoice 3.422E-01\,A
\choice  3.764E-01\,A
\end{choices} %%% end choices
%\pagebreak
%\end{choices}%??????????????
\end{questions}%%%%%%%% end questions

\subsection{}%%%% subsection 3

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

\question The current through the windings of a solenoid with n= 2.120E+03 turns per meter is changing at a rate dI/dt=4\,A/s.  The solenoid is 94\,cm long and has a cross-sectional diameter of 2.56\,cm.  A small coil consisting of N=30turns wraped in a circle of diameter 1.15\,cm is placed in the middle of the solenoid such that the plane of the coil is perpendicular to the central axis of the solenoid. Assume that the infinite-solenoid approximation is valid inside the small coil.  What is the emf induced in the coil?
\begin{choices} %%%%%%% begin choices
\choice  3.019E-05\,V
\CorrectChoice 3.321E-05\,V
\choice  3.653E-05\,V
\choice  4.018E-05\,V
\choice  4.420E-05\,V
\end{choices} %%% end choices

\question The current through the windings of a solenoid with n= 2.460E+03 turns per meter is changing at a rate dI/dt=7\,A/s.  The solenoid is 87\,cm long and has a cross-sectional diameter of 3.32\,cm.  A small coil consisting of N=38turns wraped in a circle of diameter 1.29\,cm is placed in the middle of the solenoid such that the plane of the coil is perpendicular to the central axis of the solenoid. Assume that the infinite-solenoid approximation is valid inside the small coil.  What is the emf induced in the coil?
\begin{choices} %%%%%%% begin choices
\choice  7.340E-05\,V
\choice  8.075E-05\,V
\choice  8.882E-05\,V
\choice  9.770E-05\,V
\CorrectChoice 1.075E-04\,V
\end{choices} %%% end choices

\question The current through the windings of a solenoid with n= 2.100E+03 turns per meter is changing at a rate dI/dt=7\,A/s.  The solenoid is 91\,cm long and has a cross-sectional diameter of 3.24\,cm.  A small coil consisting of N=22turns wraped in a circle of diameter 1.22\,cm is placed in the middle of the solenoid such that the plane of the coil is perpendicular to the central axis of the solenoid. Assume that the infinite-solenoid approximation is valid inside the small coil.  What is the emf induced in the coil?
\begin{choices} %%%%%%% begin choices
\choice  3.245E-05\,V
\choice  3.569E-05\,V
\choice  3.926E-05\,V
\choice  4.319E-05\,V
\CorrectChoice 4.751E-05\,V
\end{choices} %%% end choices

\question The current through the windings of a solenoid with n= 2.220E+03 turns per meter is changing at a rate dI/dt=10\,A/s.  The solenoid is 70\,cm long and has a cross-sectional diameter of 2.73\,cm.  A small coil consisting of N=28turns wraped in a circle of diameter 1.45\,cm is placed in the middle of the solenoid such that the plane of the coil is perpendicular to the central axis of the solenoid. Assume that the infinite-solenoid approximation is valid inside the small coil.  What is the emf induced in the coil?
\begin{choices} %%%%%%% begin choices
\choice  1.066E-04\,V
\choice  1.173E-04\,V
\CorrectChoice 1.290E-04\,V
\choice  1.419E-04\,V
\choice  1.561E-04\,V
\end{choices} %%% end choices

\question The current through the windings of a solenoid with n= 2.840E+03 turns per meter is changing at a rate dI/dt=19\,A/s.  The solenoid is 65\,cm long and has a cross-sectional diameter of 2.18\,cm.  A small coil consisting of N=25turns wraped in a circle of diameter 1.35\,cm is placed in the middle of the solenoid such that the plane of the coil is perpendicular to the central axis of the solenoid. Assume that the infinite-solenoid approximation is valid inside the small coil.  What is the emf induced in the coil?
\begin{choices} %%%%%%% begin choices
\choice  2.206E-04\,V
\CorrectChoice 2.426E-04\,V
\choice  2.669E-04\,V
\choice  2.936E-04\,V
\choice  3.230E-04\,V
\end{choices} %%% end choices

\question The current through the windings of a solenoid with n= 2.040E+03 turns per meter is changing at a rate dI/dt=19\,A/s.  The solenoid is 76\,cm long and has a cross-sectional diameter of 3.23\,cm.  A small coil consisting of N=25turns wraped in a circle of diameter 1.67\,cm is placed in the middle of the solenoid such that the plane of the coil is perpendicular to the central axis of the solenoid. Assume that the infinite-solenoid approximation is valid inside the small coil.  What is the emf induced in the coil?
\begin{choices} %%%%%%% begin choices
\choice  2.204E-04\,V
\choice  2.425E-04\,V
\CorrectChoice 2.667E-04\,V
\choice  2.934E-04\,V
\choice  3.227E-04\,V
\end{choices} %%% end choices

\question The current through the windings of a solenoid with n= 2.970E+03 turns per meter is changing at a rate dI/dt=15\,A/s.  The solenoid is 89\,cm long and has a cross-sectional diameter of 3.48\,cm.  A small coil consisting of N=28turns wraped in a circle of diameter 1.5\,cm is placed in the middle of the solenoid such that the plane of the coil is perpendicular to the central axis of the solenoid. Assume that the infinite-solenoid approximation is valid inside the small coil.  What is the emf induced in the coil?
\begin{choices} %%%%%%% begin choices
\choice  2.081E-04\,V
\choice  2.289E-04\,V
\choice  2.518E-04\,V
\CorrectChoice 2.770E-04\,V
\choice  3.047E-04\,V
\end{choices} %%% end choices

\question The current through the windings of a solenoid with n= 1.820E+03 turns per meter is changing at a rate dI/dt=7\,A/s.  The solenoid is 78\,cm long and has a cross-sectional diameter of 3.26\,cm.  A small coil consisting of N=35turns wraped in a circle of diameter 1.68\,cm is placed in the middle of the solenoid such that the plane of the coil is perpendicular to the central axis of the solenoid. Assume that the infinite-solenoid approximation is valid inside the small coil.  What is the emf induced in the coil?
\begin{choices} %%%%%%% begin choices
\CorrectChoice 1.242E-04\,V
\choice  1.366E-04\,V
\choice  1.503E-04\,V
\choice  1.653E-04\,V
\choice  1.819E-04\,V
\end{choices} %%% end choices

\question The current through the windings of a solenoid with n= 2.210E+03 turns per meter is changing at a rate dI/dt=18\,A/s.  The solenoid is 65\,cm long and has a cross-sectional diameter of 2.2\,cm.  A small coil consisting of N=36turns wraped in a circle of diameter 1.29\,cm is placed in the middle of the solenoid such that the plane of the coil is perpendicular to the central axis of the solenoid. Assume that the infinite-solenoid approximation is valid inside the small coil.  What is the emf induced in the coil?
\begin{choices} %%%%%%% begin choices
\CorrectChoice 2.352E-04\,V
\choice  2.587E-04\,V
\choice  2.846E-04\,V
\choice  3.131E-04\,V
\choice  3.444E-04\,V
\end{choices} %%% end choices

\question The current through the windings of a solenoid with n= 2.760E+03 turns per meter is changing at a rate dI/dt=8\,A/s.  The solenoid is 74\,cm long and has a cross-sectional diameter of 2.57\,cm.  A small coil consisting of N=32turns wraped in a circle of diameter 1.49\,cm is placed in the middle of the solenoid such that the plane of the coil is perpendicular to the central axis of the solenoid. Assume that the infinite-solenoid approximation is valid inside the small coil.  What is the emf induced in the coil?
\begin{choices} %%%%%%% begin choices
\choice  1.407E-04\,V
\CorrectChoice 1.548E-04\,V
\choice  1.703E-04\,V
\choice  1.873E-04\,V
\choice  2.061E-04\,V
\end{choices} %%% end choices

\question The current through the windings of a solenoid with n= 2.060E+03 turns per meter is changing at a rate dI/dt=12\,A/s.  The solenoid is 68\,cm long and has a cross-sectional diameter of 2.96\,cm.  A small coil consisting of N=29turns wraped in a circle of diameter 1.74\,cm is placed in the middle of the solenoid such that the plane of the coil is perpendicular to the central axis of the solenoid. Assume that the infinite-solenoid approximation is valid inside the small coil.  What is the emf induced in the coil?
\begin{choices} %%%%%%% begin choices
\choice  1.463E-04\,V
\choice  1.609E-04\,V
\choice  1.770E-04\,V
\choice  1.947E-04\,V
\CorrectChoice 2.142E-04\,V
\end{choices} %%% end choices

\question The current through the windings of a solenoid with n= 1.830E+03 turns per meter is changing at a rate dI/dt=14\,A/s.  The solenoid is 87\,cm long and has a cross-sectional diameter of 2.5\,cm.  A small coil consisting of N=30turns wraped in a circle of diameter 1.34\,cm is placed in the middle of the solenoid such that the plane of the coil is perpendicular to the central axis of the solenoid. Assume that the infinite-solenoid approximation is valid inside the small coil.  What is the emf induced in the coil?
\begin{choices} %%%%%%% begin choices
\choice  1.126E-04\,V
\choice  1.238E-04\,V
\CorrectChoice 1.362E-04\,V
\choice  1.498E-04\,V
\choice  1.648E-04\,V
\end{choices} %%% end choices

\question The current through the windings of a solenoid with n= 2.260E+03 turns per meter is changing at a rate dI/dt=12\,A/s.  The solenoid is 62\,cm long and has a cross-sectional diameter of 3.37\,cm.  A small coil consisting of N=23turns wraped in a circle of diameter 1.7\,cm is placed in the middle of the solenoid such that the plane of the coil is perpendicular to the central axis of the solenoid. Assume that the infinite-solenoid approximation is valid inside the small coil.  What is the emf induced in the coil?
\begin{choices} %%%%%%% begin choices
\choice  1.215E-04\,V
\choice  1.337E-04\,V
\choice  1.470E-04\,V
\choice  1.617E-04\,V
\CorrectChoice 1.779E-04\,V
\end{choices} %%% end choices

\question The current through the windings of a solenoid with n= 2.500E+03 turns per meter is changing at a rate dI/dt=4\,A/s.  The solenoid is 96\,cm long and has a cross-sectional diameter of 2.39\,cm.  A small coil consisting of N=22turns wraped in a circle of diameter 1.44\,cm is placed in the middle of the solenoid such that the plane of the coil is perpendicular to the central axis of the solenoid. Assume that the infinite-solenoid approximation is valid inside the small coil.  What is the emf induced in the coil?
\begin{choices} %%%%%%% begin choices
\choice  3.721E-05\,V
\choice  4.093E-05\,V
\CorrectChoice 4.502E-05\,V
\choice  4.953E-05\,V
\choice  5.448E-05\,V
\end{choices} %%% end choices

\question The current through the windings of a solenoid with n= 2.590E+03 turns per meter is changing at a rate dI/dt=11\,A/s.  The solenoid is 95\,cm long and has a cross-sectional diameter of 2.29\,cm.  A small coil consisting of N=25turns wraped in a circle of diameter 1.15\,cm is placed in the middle of the solenoid such that the plane of the coil is perpendicular to the central axis of the solenoid. Assume that the infinite-solenoid approximation is valid inside the small coil.  What is the emf induced in the coil?
\begin{choices} %%%%%%% begin choices
\choice  6.985E-05\,V
\choice  7.683E-05\,V
\choice  8.452E-05\,V
\CorrectChoice 9.297E-05\,V
\choice  1.023E-04\,V
\end{choices} %%% end choices

\question The current through the windings of a solenoid with n= 2.960E+03 turns per meter is changing at a rate dI/dt=10\,A/s.  The solenoid is 85\,cm long and has a cross-sectional diameter of 3.12\,cm.  A small coil consisting of N=32turns wraped in a circle of diameter 1.44\,cm is placed in the middle of the solenoid such that the plane of the coil is perpendicular to the central axis of the solenoid. Assume that the infinite-solenoid approximation is valid inside the small coil.  What is the emf induced in the coil?
\begin{choices} %%%%%%% begin choices
\choice  1.602E-04\,V
\choice  1.762E-04\,V
\CorrectChoice 1.939E-04\,V
\choice  2.132E-04\,V
\choice  2.346E-04\,V
\end{choices} %%% end choices

\question The current through the windings of a solenoid with n= 1.850E+03 turns per meter is changing at a rate dI/dt=17\,A/s.  The solenoid is 98\,cm long and has a cross-sectional diameter of 3.38\,cm.  A small coil consisting of N=23turns wraped in a circle of diameter 1.72\,cm is placed in the middle of the solenoid such that the plane of the coil is perpendicular to the central axis of the solenoid. Assume that the infinite-solenoid approximation is valid inside the small coil.  What is the emf induced in the coil?
\begin{choices} %%%%%%% begin choices
\choice  1.587E-04\,V
\choice  1.745E-04\,V
\choice  1.920E-04\,V
\CorrectChoice 2.112E-04\,V
\choice  2.323E-04\,V
\end{choices} %%% end choices

\question The current through the windings of a solenoid with n= 2.980E+03 turns per meter is changing at a rate dI/dt=9\,A/s.  The solenoid is 88\,cm long and has a cross-sectional diameter of 2.69\,cm.  A small coil consisting of N=28turns wraped in a circle of diameter 1.64\,cm is placed in the middle of the solenoid such that the plane of the coil is perpendicular to the central axis of the solenoid. Assume that the infinite-solenoid approximation is valid inside the small coil.  What is the emf induced in the coil?
\begin{choices} %%%%%%% begin choices
\choice  1.498E-04\,V
\choice  1.647E-04\,V
\choice  1.812E-04\,V
\CorrectChoice 1.993E-04\,V
\choice  2.193E-04\,V
\end{choices} %%% end choices

\question The current through the windings of a solenoid with n= 2.400E+03 turns per meter is changing at a rate dI/dt=3\,A/s.  The solenoid is 93\,cm long and has a cross-sectional diameter of 2.13\,cm.  A small coil consisting of N=30turns wraped in a circle of diameter 1.35\,cm is placed in the middle of the solenoid such that the plane of the coil is perpendicular to the central axis of the solenoid. Assume that the infinite-solenoid approximation is valid inside the small coil.  What is the emf induced in the coil?
\begin{choices} %%%%%%% begin choices
\CorrectChoice 3.885E-05\,V
\choice  4.274E-05\,V
\choice  4.701E-05\,V
\choice  5.171E-05\,V
\choice  5.688E-05\,V
\end{choices} %%% end choices
%\pagebreak
%\end{choices}%??????????????
\end{questions}%%%%%%%% end questions

\subsection{}%%%% subsection 4

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

\question Calculate the motional emf induced along a 40.1\,km conductor moving at an orbital speed of 7.85\,km/s perpendicular to Earth's 5.160E-05\,Tesla magnetic field.
\begin{choices} %%%%%%% begin choices
\choice  1.477E+04\,V
\CorrectChoice 1.624E+04\,V
\choice  1.787E+04\,V
\choice  1.965E+04\,V
\choice  2.162E+04\,V
\end{choices} %%% end choices

\question Calculate the motional emf induced along a 24.9\,km conductor moving at an orbital speed of 7.82\,km/s perpendicular to Earth's 5.040E-05\,Tesla magnetic field.
\begin{choices} %%%%%%% begin choices
\choice  8.111E+03\,V
\choice  8.922E+03\,V
\CorrectChoice 9.814E+03\,V
\choice  1.080E+04\,V
\choice  1.187E+04\,V
\end{choices} %%% end choices

\question Calculate the motional emf induced along a 27.5\,km conductor moving at an orbital speed of 7.86\,km/s perpendicular to Earth's 4.520E-05\,Tesla magnetic field.
\begin{choices} %%%%%%% begin choices
\choice  8.074E+03\,V
\choice  8.882E+03\,V
\CorrectChoice 9.770E+03\,V
\choice  1.075E+04\,V
\choice  1.182E+04\,V
\end{choices} %%% end choices

\question Calculate the motional emf induced along a 42.1\,km conductor moving at an orbital speed of 7.77\,km/s perpendicular to Earth's 4.730E-05\,Tesla magnetic field.
\begin{choices} %%%%%%% begin choices
\choice  1.279E+04\,V
\choice  1.407E+04\,V
\CorrectChoice 1.547E+04\,V
\choice  1.702E+04\,V
\choice  1.872E+04\,V
\end{choices} %%% end choices

\question Calculate the motional emf induced along a 11.9\,km conductor moving at an orbital speed of 7.8\,km/s perpendicular to Earth's 4.870E-05\,Tesla magnetic field.
\begin{choices} %%%%%%% begin choices
\choice  3.736E+03\,V
\choice  4.109E+03\,V
\CorrectChoice 4.520E+03\,V
\choice  4.972E+03\,V
\choice  5.470E+03\,V
\end{choices} %%% end choices

\question Calculate the motional emf induced along a 24.7\,km conductor moving at an orbital speed of 7.77\,km/s perpendicular to Earth's 5.410E-05\,Tesla magnetic field.
\begin{choices} %%%%%%% begin choices
\choice  7.801E+03\,V
\choice  8.581E+03\,V
\choice  9.439E+03\,V
\CorrectChoice 1.038E+04\,V
\choice  1.142E+04\,V
\end{choices} %%% end choices

\question Calculate the motional emf induced along a 37.9\,km conductor moving at an orbital speed of 7.84\,km/s perpendicular to Earth's 5.410E-05\,Tesla magnetic field.
\begin{choices} %%%%%%% begin choices
\choice  1.208E+04\,V
\choice  1.329E+04\,V
\choice  1.461E+04\,V
\CorrectChoice 1.608E+04\,V
\choice  1.768E+04\,V
\end{choices} %%% end choices

\question Calculate the motional emf induced along a 50.7\,km conductor moving at an orbital speed of 7.88\,km/s perpendicular to Earth's 4.930E-05\,Tesla magnetic field.
\begin{choices} %%%%%%% begin choices
\choice  1.791E+04\,V
\CorrectChoice 1.970E+04\,V
\choice  2.167E+04\,V
\choice  2.383E+04\,V
\choice  2.622E+04\,V
\end{choices} %%% end choices

\question Calculate the motional emf induced along a 25.2\,km conductor moving at an orbital speed of 7.72\,km/s perpendicular to Earth's 4.900E-05\,Tesla magnetic field.
\begin{choices} %%%%%%% begin choices
\choice  7.162E+03\,V
\choice  7.878E+03\,V
\choice  8.666E+03\,V
\CorrectChoice 9.533E+03\,V
\choice  1.049E+04\,V
\end{choices} %%% end choices

\question Calculate the motional emf induced along a 49.5\,km conductor moving at an orbital speed of 7.77\,km/s perpendicular to Earth's 5.310E-05\,Tesla magnetic field.
\begin{choices} %%%%%%% begin choices
\choice  1.395E+04\,V
\choice  1.534E+04\,V
\choice  1.688E+04\,V
\choice  1.857E+04\,V
\CorrectChoice 2.042E+04\,V
\end{choices} %%% end choices

\question Calculate the motional emf induced along a 34.3\,km conductor moving at an orbital speed of 7.86\,km/s perpendicular to Earth's 4.780E-05\,Tesla magnetic field.
\begin{choices} %%%%%%% begin choices
\choice  8.802E+03\,V
\choice  9.682E+03\,V
\choice  1.065E+04\,V
\choice  1.172E+04\,V
\CorrectChoice 1.289E+04\,V
\end{choices} %%% end choices

\question Calculate the motional emf induced along a 30.3\,km conductor moving at an orbital speed of 7.76\,km/s perpendicular to Earth's 5.100E-05\,Tesla magnetic field.
\begin{choices} %%%%%%% begin choices
\choice  1.090E+04\,V
\CorrectChoice 1.199E+04\,V
\choice  1.319E+04\,V
\choice  1.451E+04\,V
\choice  1.596E+04\,V
\end{choices} %%% end choices

\question Calculate the motional emf induced along a 48.8\,km conductor moving at an orbital speed of 7.88\,km/s perpendicular to Earth's 4.660E-05\,Tesla magnetic field.
\begin{choices} %%%%%%% begin choices
\choice  1.224E+04\,V
\choice  1.346E+04\,V
\choice  1.481E+04\,V
\choice  1.629E+04\,V
\CorrectChoice 1.792E+04\,V
\end{choices} %%% end choices

\question Calculate the motional emf induced along a 14.1\,km conductor moving at an orbital speed of 7.8\,km/s perpendicular to Earth's 4.910E-05\,Tesla magnetic field.
\begin{choices} %%%%%%% begin choices
\choice  3.688E+03\,V
\choice  4.057E+03\,V
\choice  4.463E+03\,V
\choice  4.909E+03\,V
\CorrectChoice 5.400E+03\,V
\end{choices} %%% end choices

\question Calculate the motional emf induced along a 21.3\,km conductor moving at an orbital speed of 7.75\,km/s perpendicular to Earth's 5.320E-05\,Tesla magnetic field.
\begin{choices} %%%%%%% begin choices
\choice  6.598E+03\,V
\choice  7.258E+03\,V
\choice  7.984E+03\,V
\CorrectChoice 8.782E+03\,V
\choice  9.660E+03\,V
\end{choices} %%% end choices

\question Calculate the motional emf induced along a 46.2\,km conductor moving at an orbital speed of 7.9\,km/s perpendicular to Earth's 4.630E-05\,Tesla magnetic field.
\begin{choices} %%%%%%% begin choices
\choice  1.536E+04\,V
\CorrectChoice 1.690E+04\,V
\choice  1.859E+04\,V
\choice  2.045E+04\,V
\choice  2.249E+04\,V
\end{choices} %%% end choices

\question Calculate the motional emf induced along a 24.4\,km conductor moving at an orbital speed of 7.79\,km/s perpendicular to Earth's 4.790E-05\,Tesla magnetic field.
\begin{choices} %%%%%%% begin choices
\choice  6.840E+03\,V
\choice  7.524E+03\,V
\choice  8.277E+03\,V
\CorrectChoice 9.105E+03\,V
\choice  1.002E+04\,V
\end{choices} %%% end choices

\question Calculate the motional emf induced along a 32.1\,km conductor moving at an orbital speed of 7.8\,km/s perpendicular to Earth's 5.280E-05\,Tesla magnetic field.
\begin{choices} %%%%%%% begin choices
\choice  1.093E+04\,V
\choice  1.202E+04\,V
\CorrectChoice 1.322E+04\,V
\choice  1.454E+04\,V
\choice  1.600E+04\,V
\end{choices} %%% end choices

\question Calculate the motional emf induced along a 24.6\,km conductor moving at an orbital speed of 7.89\,km/s perpendicular to Earth's 5.180E-05\,Tesla magnetic field.
\begin{choices} %%%%%%% begin choices
\choice  9.140E+03\,V
\CorrectChoice 1.005E+04\,V
\choice  1.106E+04\,V
\choice  1.217E+04\,V
\choice  1.338E+04\,V
\end{choices} %%% end choices
%\pagebreak
%\end{choices}%??????????????
\end{questions}%%%%%%%% end questions

\subsection{}%%%% subsection 5

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

\question \includegraphics[width=0.12\textwidth]{Wikiversity-wedge.png}A cylinder of height 1.98\,cm and radius 2.62\,cm is cut into a wedge as shown. Now imagine that the volume grows as \straighttheta\  increases while the radius R and height h remains constant.  What is the volume's rate of change if point P is 1.33\,cm from point O and moves at a speed of 2.0\,cm/s? Assume that the wedge grows in such a way as the front face moves by rotating around the axis (that contains point O.)
\begin{choices} %%%%%%% begin choices
\choice  6.980E+00\,cm\textsuperscript{3}/s
\choice  7.678E+00\,cm\textsuperscript{3}/s
\choice  8.446E+00\,cm\textsuperscript{3}/s
\choice  9.290E+00\,cm\textsuperscript{3}/s
\CorrectChoice 1.022E+01\,cm\textsuperscript{3}/s
\end{choices} %%% end choices

\question \includegraphics[width=0.12\textwidth]{Wikiversity-wedge.png}A cylinder of height 3.5\,cm and radius 5.36\,cm is cut into a wedge as shown. Now imagine that the volume grows as \straighttheta\  increases while the radius R and height h remains constant.  What is the volume's rate of change if point P is 2.79\,cm from point O and moves at a speed of 3.24\,cm/s? Assume that the wedge grows in such a way as the front face moves by rotating around the axis (that contains point O.)
\begin{choices} %%%%%%% begin choices
\choice  5.308E+01\,cm\textsuperscript{3}/s
\CorrectChoice 5.839E+01\,cm\textsuperscript{3}/s
\choice  6.422E+01\,cm\textsuperscript{3}/s
\choice  7.065E+01\,cm\textsuperscript{3}/s
\choice  7.771E+01\,cm\textsuperscript{3}/s
\end{choices} %%% end choices

\question \includegraphics[width=0.12\textwidth]{Wikiversity-wedge.png}A cylinder of height 2.58\,cm and radius 9.47\,cm is cut into a wedge as shown. Now imagine that the volume grows as \straighttheta\  increases while the radius R and height h remains constant.  What is the volume's rate of change if point P is 3.62\,cm from point O and moves at a speed of 4.7\,cm/s? Assume that the wedge grows in such a way as the front face moves by rotating around the axis (that contains point O.)
\begin{choices} %%%%%%% begin choices
\choice  1.128E+02\,cm\textsuperscript{3}/s
\choice  1.241E+02\,cm\textsuperscript{3}/s
\choice  1.365E+02\,cm\textsuperscript{3}/s
\CorrectChoice 1.502E+02\,cm\textsuperscript{3}/s
\choice  1.652E+02\,cm\textsuperscript{3}/s
\end{choices} %%% end choices

\question \includegraphics[width=0.12\textwidth]{Wikiversity-wedge.png}A cylinder of height 1.3\,cm and radius 6.01\,cm is cut into a wedge as shown. Now imagine that the volume grows as \straighttheta\  increases while the radius R and height h remains constant.  What is the volume's rate of change if point P is 3.61\,cm from point O and moves at a speed of 2.11\,cm/s? Assume that the wedge grows in such a way as the front face moves by rotating around the axis (that contains point O.)
\begin{choices} %%%%%%% begin choices
\CorrectChoice 1.372E+01\,cm\textsuperscript{3}/s
\choice  1.509E+01\,cm\textsuperscript{3}/s
\choice  1.660E+01\,cm\textsuperscript{3}/s
\choice  1.826E+01\,cm\textsuperscript{3}/s
\choice  2.009E+01\,cm\textsuperscript{3}/s
\end{choices} %%% end choices

\question \includegraphics[width=0.12\textwidth]{Wikiversity-wedge.png}A cylinder of height 2.63\,cm and radius 6.27\,cm is cut into a wedge as shown. Now imagine that the volume grows as \straighttheta\  increases while the radius R and height h remains constant.  What is the volume's rate of change if point P is 2.35\,cm from point O and moves at a speed of 2.7\,cm/s? Assume that the wedge grows in such a way as the front face moves by rotating around the axis (that contains point O.)
\begin{choices} %%%%%%% begin choices
\choice  4.057E+01\,cm\textsuperscript{3}/s
\choice  4.463E+01\,cm\textsuperscript{3}/s
\choice  4.909E+01\,cm\textsuperscript{3}/s
\choice  5.400E+01\,cm\textsuperscript{3}/s
\CorrectChoice 5.940E+01\,cm\textsuperscript{3}/s
\end{choices} %%% end choices

\question \includegraphics[width=0.12\textwidth]{Wikiversity-wedge.png}A cylinder of height 2.12\,cm and radius 2.28\,cm is cut into a wedge as shown. Now imagine that the volume grows as \straighttheta\  increases while the radius R and height h remains constant.  What is the volume's rate of change if point P is 1.52\,cm from point O and moves at a speed of 8.21\,cm/s? Assume that the wedge grows in such a way as the front face moves by rotating around the axis (that contains point O.)
\begin{choices} %%%%%%% begin choices
\CorrectChoice 2.976E+01\,cm\textsuperscript{3}/s
\choice  3.274E+01\,cm\textsuperscript{3}/s
\choice  3.601E+01\,cm\textsuperscript{3}/s
\choice  3.961E+01\,cm\textsuperscript{3}/s
\choice  4.358E+01\,cm\textsuperscript{3}/s
\end{choices} %%% end choices

\question \includegraphics[width=0.12\textwidth]{Wikiversity-wedge.png}A cylinder of height 2.42\,cm and radius 6.94\,cm is cut into a wedge as shown. Now imagine that the volume grows as \straighttheta\  increases while the radius R and height h remains constant.  What is the volume's rate of change if point P is 2.59\,cm from point O and moves at a speed of 4.87\,cm/s? Assume that the wedge grows in such a way as the front face moves by rotating around the axis (that contains point O.)
\begin{choices} %%%%%%% begin choices
\choice  9.962E+01\,cm\textsuperscript{3}/s
\CorrectChoice 1.096E+02\,cm\textsuperscript{3}/s
\choice  1.205E+02\,cm\textsuperscript{3}/s
\choice  1.326E+02\,cm\textsuperscript{3}/s
\choice  1.459E+02\,cm\textsuperscript{3}/s
\end{choices} %%% end choices

\question \includegraphics[width=0.12\textwidth]{Wikiversity-wedge.png}A cylinder of height 2.94\,cm and radius 5.05\,cm is cut into a wedge as shown. Now imagine that the volume grows as \straighttheta\  increases while the radius R and height h remains constant.  What is the volume's rate of change if point P is 2.37\,cm from point O and moves at a speed of 7.29\,cm/s? Assume that the wedge grows in such a way as the front face moves by rotating around the axis (that contains point O.)
\begin{choices} %%%%%%% begin choices
\CorrectChoice 1.153E+02\,cm\textsuperscript{3}/s
\choice  1.268E+02\,cm\textsuperscript{3}/s
\choice  1.395E+02\,cm\textsuperscript{3}/s
\choice  1.535E+02\,cm\textsuperscript{3}/s
\choice  1.688E+02\,cm\textsuperscript{3}/s
\end{choices} %%% end choices

\question \includegraphics[width=0.12\textwidth]{Wikiversity-wedge.png}A cylinder of height 2.15\,cm and radius 7.03\,cm is cut into a wedge as shown. Now imagine that the volume grows as \straighttheta\  increases while the radius R and height h remains constant.  What is the volume's rate of change if point P is 3.83\,cm from point O and moves at a speed of 5.7\,cm/s? Assume that the wedge grows in such a way as the front face moves by rotating around the axis (that contains point O.)
\begin{choices} %%%%%%% begin choices
\choice  6.534E+01\,cm\textsuperscript{3}/s
\choice  7.188E+01\,cm\textsuperscript{3}/s
\CorrectChoice 7.907E+01\,cm\textsuperscript{3}/s
\choice  8.697E+01\,cm\textsuperscript{3}/s
\choice  9.567E+01\,cm\textsuperscript{3}/s
\end{choices} %%% end choices

\question \includegraphics[width=0.12\textwidth]{Wikiversity-wedge.png}A cylinder of height 1.27\,cm and radius 8.63\,cm is cut into a wedge as shown. Now imagine that the volume grows as \straighttheta\  increases while the radius R and height h remains constant.  What is the volume's rate of change if point P is 3.15\,cm from point O and moves at a speed of 1.26\,cm/s? Assume that the wedge grows in such a way as the front face moves by rotating around the axis (that contains point O.)
\begin{choices} %%%%%%% begin choices
\CorrectChoice 1.892E+01\,cm\textsuperscript{3}/s
\choice  2.081E+01\,cm\textsuperscript{3}/s
\choice  2.289E+01\,cm\textsuperscript{3}/s
\choice  2.518E+01\,cm\textsuperscript{3}/s
\choice  2.770E+01\,cm\textsuperscript{3}/s
\end{choices} %%% end choices

\question \includegraphics[width=0.12\textwidth]{Wikiversity-wedge.png}A cylinder of height 1.34\,cm and radius 2.47\,cm is cut into a wedge as shown. Now imagine that the volume grows as \straighttheta\  increases while the radius R and height h remains constant.  What is the volume's rate of change if point P is 1.23\,cm from point O and moves at a speed of 6.23\,cm/s? Assume that the wedge grows in such a way as the front face moves by rotating around the axis (that contains point O.)
\begin{choices} %%%%%%% begin choices
\choice  1.414E+01\,cm\textsuperscript{3}/s
\choice  1.556E+01\,cm\textsuperscript{3}/s
\choice  1.711E+01\,cm\textsuperscript{3}/s
\choice  1.882E+01\,cm\textsuperscript{3}/s
\CorrectChoice 2.070E+01\,cm\textsuperscript{3}/s
\end{choices} %%% end choices

\question \includegraphics[width=0.12\textwidth]{Wikiversity-wedge.png}A cylinder of height 1.68\,cm and radius 3.44\,cm is cut into a wedge as shown. Now imagine that the volume grows as \straighttheta\  increases while the radius R and height h remains constant.  What is the volume's rate of change if point P is 1.28\,cm from point O and moves at a speed of 1.41\,cm/s? Assume that the wedge grows in such a way as the front face moves by rotating around the axis (that contains point O.)
\begin{choices} %%%%%%% begin choices
\choice  7.479E+00\,cm\textsuperscript{3}/s
\choice  8.227E+00\,cm\textsuperscript{3}/s
\choice  9.049E+00\,cm\textsuperscript{3}/s
\choice  9.954E+00\,cm\textsuperscript{3}/s
\CorrectChoice 1.095E+01\,cm\textsuperscript{3}/s
\end{choices} %%% end choices

\question \includegraphics[width=0.12\textwidth]{Wikiversity-wedge.png}A cylinder of height 1.19\,cm and radius 4.51\,cm is cut into a wedge as shown. Now imagine that the volume grows as \straighttheta\  increases while the radius R and height h remains constant.  What is the volume's rate of change if point P is 2.7\,cm from point O and moves at a speed of 8.35\,cm/s? Assume that the wedge grows in such a way as the front face moves by rotating around the axis (that contains point O.)
\begin{choices} %%%%%%% begin choices
\choice  3.093E+01\,cm\textsuperscript{3}/s
\choice  3.403E+01\,cm\textsuperscript{3}/s
\CorrectChoice 3.743E+01\,cm\textsuperscript{3}/s
\choice  4.117E+01\,cm\textsuperscript{3}/s
\choice  4.529E+01\,cm\textsuperscript{3}/s
\end{choices} %%% end choices

\question \includegraphics[width=0.12\textwidth]{Wikiversity-wedge.png}A cylinder of height 1.68\,cm and radius 2.74\,cm is cut into a wedge as shown. Now imagine that the volume grows as \straighttheta\  increases while the radius R and height h remains constant.  What is the volume's rate of change if point P is 1.78\,cm from point O and moves at a speed of 3.44\,cm/s? Assume that the wedge grows in such a way as the front face moves by rotating around the axis (that contains point O.)
\begin{choices} %%%%%%% begin choices
\choice  8.324E+00\,cm\textsuperscript{3}/s
\choice  9.157E+00\,cm\textsuperscript{3}/s
\choice  1.007E+01\,cm\textsuperscript{3}/s
\choice  1.108E+01\,cm\textsuperscript{3}/s
\CorrectChoice 1.219E+01\,cm\textsuperscript{3}/s
\end{choices} %%% end choices

\question \includegraphics[width=0.12\textwidth]{Wikiversity-wedge.png}A cylinder of height 3.82\,cm and radius 5.6\,cm is cut into a wedge as shown. Now imagine that the volume grows as \straighttheta\  increases while the radius R and height h remains constant.  What is the volume's rate of change if point P is 2.89\,cm from point O and moves at a speed of 4.25\,cm/s? Assume that the wedge grows in such a way as the front face moves by rotating around the axis (that contains point O.)
\begin{choices} %%%%%%% begin choices
\choice  7.280E+01\,cm\textsuperscript{3}/s
\choice  8.008E+01\,cm\textsuperscript{3}/s
\CorrectChoice 8.808E+01\,cm\textsuperscript{3}/s
\choice  9.689E+01\,cm\textsuperscript{3}/s
\choice  1.066E+02\,cm\textsuperscript{3}/s
\end{choices} %%% end choices

\question \includegraphics[width=0.12\textwidth]{Wikiversity-wedge.png}A cylinder of height 2.91\,cm and radius 8.33\,cm is cut into a wedge as shown. Now imagine that the volume grows as \straighttheta\  increases while the radius R and height h remains constant.  What is the volume's rate of change if point P is 3.7\,cm from point O and moves at a speed of 9.14\,cm/s? Assume that the wedge grows in such a way as the front face moves by rotating around the axis (that contains point O.)
\begin{choices} %%%%%%% begin choices
\choice  2.061E+02\,cm\textsuperscript{3}/s
\choice  2.267E+02\,cm\textsuperscript{3}/s
\CorrectChoice 2.494E+02\,cm\textsuperscript{3}/s
\choice  2.743E+02\,cm\textsuperscript{3}/s
\choice  3.018E+02\,cm\textsuperscript{3}/s
\end{choices} %%% end choices

\question \includegraphics[width=0.12\textwidth]{Wikiversity-wedge.png}A cylinder of height 1.48\,cm and radius 7.74\,cm is cut into a wedge as shown. Now imagine that the volume grows as \straighttheta\  increases while the radius R and height h remains constant.  What is the volume's rate of change if point P is 3.76\,cm from point O and moves at a speed of 3.09\,cm/s? Assume that the wedge grows in such a way as the front face moves by rotating around the axis (that contains point O.)
\begin{choices} %%%%%%% begin choices
\choice  3.312E+01\,cm\textsuperscript{3}/s
\CorrectChoice 3.643E+01\,cm\textsuperscript{3}/s
\choice  4.008E+01\,cm\textsuperscript{3}/s
\choice  4.408E+01\,cm\textsuperscript{3}/s
\choice  4.849E+01\,cm\textsuperscript{3}/s
\end{choices} %%% end choices

\question \includegraphics[width=0.12\textwidth]{Wikiversity-wedge.png}A cylinder of height 2.25\,cm and radius 6.77\,cm is cut into a wedge as shown. Now imagine that the volume grows as \straighttheta\  increases while the radius R and height h remains constant.  What is the volume's rate of change if point P is 3.27\,cm from point O and moves at a speed of 4.07\,cm/s? Assume that the wedge grows in such a way as the front face moves by rotating around the axis (that contains point O.)
\begin{choices} %%%%%%% begin choices
\choice  5.834E+01\,cm\textsuperscript{3}/s
\CorrectChoice 6.418E+01\,cm\textsuperscript{3}/s
\choice  7.059E+01\,cm\textsuperscript{3}/s
\choice  7.765E+01\,cm\textsuperscript{3}/s
\choice  8.542E+01\,cm\textsuperscript{3}/s
\end{choices} %%% end choices

\question \includegraphics[width=0.12\textwidth]{Wikiversity-wedge.png}A cylinder of height 1.69\,cm and radius 4.56\,cm is cut into a wedge as shown. Now imagine that the volume grows as \straighttheta\  increases while the radius R and height h remains constant.  What is the volume's rate of change if point P is 2.33\,cm from point O and moves at a speed of 4.9\,cm/s? Assume that the wedge grows in such a way as the front face moves by rotating around the axis (that contains point O.)
\begin{choices} %%%%%%% begin choices
\choice  3.054E+01\,cm\textsuperscript{3}/s
\choice  3.359E+01\,cm\textsuperscript{3}/s
\CorrectChoice 3.695E+01\,cm\textsuperscript{3}/s
\choice  4.065E+01\,cm\textsuperscript{3}/s
\choice  4.471E+01\,cm\textsuperscript{3}/s
\end{choices} %%% end choices
%\pagebreak
%\end{choices}%??????????????
\end{questions}%%%%%%%% end questions

\subsection{}%%%% subsection 6

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

\question A recangular coil with an area of 0.371\,m\textsuperscript{2} and 20\,turns is placed in a uniform magnetic field of 2.51\,T.  The coil is rotated about an axis that is perpendicular to this field. At time t=0 the normal to the coil is oriented parallel to the magnetic field and the coil is rotating with a constant angular frequency of 3.060E+03\,s\textsuperscript{$$-$$1}.  What is the ''magnitude'' (absolute value) of the induced emf at t\,=\,88\,s?
\begin{choices} %%%%%%% begin choices
\CorrectChoice 5.694E+04\,V
\choice  6.263E+04\,V
\choice  6.889E+04\,V
\choice  7.578E+04\,V
\choice  8.336E+04\,V
\end{choices} %%% end choices

\question A recangular coil with an area of 0.479\,m\textsuperscript{2} and 11\,turns is placed in a uniform magnetic field of 1.34\,T.  The coil is rotated about an axis that is perpendicular to this field. At time t=0 the normal to the coil is oriented parallel to the magnetic field and the coil is rotating with a constant angular frequency of 4.200E+03\,s\textsuperscript{$$-$$1}.  What is the ''magnitude'' (absolute value) of the induced emf at t\,=\,38\,s?
\begin{choices} %%%%%%% begin choices
\CorrectChoice 2.148E+04\,V
\choice  2.363E+04\,V
\choice  2.599E+04\,V
\choice  2.859E+04\,V
\choice  3.145E+04\,V
\end{choices} %%% end choices

\question A recangular coil with an area of 0.39\,m\textsuperscript{2} and 16\,turns is placed in a uniform magnetic field of 3.07\,T.  The coil is rotated about an axis that is perpendicular to this field. At time t=0 the normal to the coil is oriented parallel to the magnetic field and the coil is rotating with a constant angular frequency of 3.320E+03\,s\textsuperscript{$$-$$1}.  What is the ''magnitude'' (absolute value) of the induced emf at t\,=\,44\,s?
\begin{choices} %%%%%%% begin choices
\choice  3.792E+04\,V
\choice  4.172E+04\,V
\choice  4.589E+04\,V
\CorrectChoice 5.048E+04\,V
\choice  5.552E+04\,V
\end{choices} %%% end choices

\question A recangular coil with an area of 0.137\,m\textsuperscript{2} and 18\,turns is placed in a uniform magnetic field of 1.18\,T.  The coil is rotated about an axis that is perpendicular to this field. At time t=0 the normal to the coil is oriented parallel to the magnetic field and the coil is rotating with a constant angular frequency of 4.120E+03\,s\textsuperscript{$$-$$1}.  What is the ''magnitude'' (absolute value) of the induced emf at t\,=\,47\,s?
\begin{choices} %%%%%%% begin choices
\choice  1.086E+04\,V
\CorrectChoice 1.195E+04\,V
\choice  1.314E+04\,V
\choice  1.446E+04\,V
\choice  1.590E+04\,V
\end{choices} %%% end choices

\question A recangular coil with an area of 0.219\,m\textsuperscript{2} and 14\,turns is placed in a uniform magnetic field of 3.71\,T.  The coil is rotated about an axis that is perpendicular to this field. At time t=0 the normal to the coil is oriented parallel to the magnetic field and the coil is rotating with a constant angular frequency of 7.540E+03\,s\textsuperscript{$$-$$1}.  What is the ''magnitude'' (absolute value) of the induced emf at t\,=\,15\,s?
\begin{choices} %%%%%%% begin choices
\choice  2.959E+04\,V
\choice  3.255E+04\,V
\choice  3.581E+04\,V
\CorrectChoice 3.939E+04\,V
\choice  4.332E+04\,V
\end{choices} %%% end choices

\question A recangular coil with an area of 0.449\,m\textsuperscript{2} and 20\,turns is placed in a uniform magnetic field of 3.58\,T.  The coil is rotated about an axis that is perpendicular to this field. At time t=0 the normal to the coil is oriented parallel to the magnetic field and the coil is rotating with a constant angular frequency of 4.990E+03\,s\textsuperscript{$$-$$1}.  What is the ''magnitude'' (absolute value) of the induced emf at t\,=\,66\,s?
\begin{choices} %%%%%%% begin choices
\choice  7.734E+04\,V
\CorrectChoice 8.507E+04\,V
\choice  9.358E+04\,V
\choice  1.029E+05\,V
\choice  1.132E+05\,V
\end{choices} %%% end choices

\question A recangular coil with an area of 0.157\,m\textsuperscript{2} and 17\,turns is placed in a uniform magnetic field of 3.64\,T.  The coil is rotated about an axis that is perpendicular to this field. At time t=0 the normal to the coil is oriented parallel to the magnetic field and the coil is rotating with a constant angular frequency of 5.890E+03\,s\textsuperscript{$$-$$1}.  What is the ''magnitude'' (absolute value) of the induced emf at t\,=\,9\,s?
\begin{choices} %%%%%%% begin choices
\choice  4.464E+04\,V
\choice  4.911E+04\,V
\CorrectChoice 5.402E+04\,V
\choice  5.942E+04\,V
\choice  6.536E+04\,V
\end{choices} %%% end choices

\question A recangular coil with an area of 0.315\,m\textsuperscript{2} and 20\,turns is placed in a uniform magnetic field of 3.45\,T.  The coil is rotated about an axis that is perpendicular to this field. At time t=0 the normal to the coil is oriented parallel to the magnetic field and the coil is rotating with a constant angular frequency of 9.480E+03\,s\textsuperscript{$$-$$1}.  What is the ''magnitude'' (absolute value) of the induced emf at t\,=\,26\,s?
\begin{choices} %%%%%%% begin choices
\CorrectChoice 1.342E+04\,V
\choice  1.476E+04\,V
\choice  1.624E+04\,V
\choice  1.786E+04\,V
\choice  1.965E+04\,V
\end{choices} %%% end choices

\question A recangular coil with an area of 0.23\,m\textsuperscript{2} and 20\,turns is placed in a uniform magnetic field of 1.66\,T.  The coil is rotated about an axis that is perpendicular to this field. At time t=0 the normal to the coil is oriented parallel to the magnetic field and the coil is rotating with a constant angular frequency of 1.380E+03\,s\textsuperscript{$$-$$1}.  What is the ''magnitude'' (absolute value) of the induced emf at t\,=\,4\,s?
\begin{choices} %%%%%%% begin choices
\CorrectChoice 2.317E+03\,V
\choice  2.549E+03\,V
\choice  2.804E+03\,V
\choice  3.084E+03\,V
\choice  3.393E+03\,V
\end{choices} %%% end choices

\question A recangular coil with an area of 0.178\,m\textsuperscript{2} and 17\,turns is placed in a uniform magnetic field of 2.62\,T.  The coil is rotated about an axis that is perpendicular to this field. At time t=0 the normal to the coil is oriented parallel to the magnetic field and the coil is rotating with a constant angular frequency of 4.380E+03\,s\textsuperscript{$$-$$1}.  What is the ''magnitude'' (absolute value) of the induced emf at t\,=\,45\,s?
\begin{choices} %%%%%%% begin choices
\choice  1.068E+04\,V
\choice  1.175E+04\,V
\CorrectChoice 1.293E+04\,V
\choice  1.422E+04\,V
\choice  1.564E+04\,V
\end{choices} %%% end choices

\question A recangular coil with an area of 0.412\,m\textsuperscript{2} and 18\,turns is placed in a uniform magnetic field of 3.81\,T.  The coil is rotated about an axis that is perpendicular to this field. At time t=0 the normal to the coil is oriented parallel to the magnetic field and the coil is rotating with a constant angular frequency of 2.120E+03\,s\textsuperscript{$$-$$1}.  What is the ''magnitude'' (absolute value) of the induced emf at t\,=\,79\,s?
\begin{choices} %%%%%%% begin choices
\choice  4.465E+04\,V
\choice  4.912E+04\,V
\choice  5.403E+04\,V
\CorrectChoice 5.943E+04\,V
\choice  6.538E+04\,V
\end{choices} %%% end choices

\question A recangular coil with an area of 0.815\,m\textsuperscript{2} and 11\,turns is placed in a uniform magnetic field of 3.62\,T.  The coil is rotated about an axis that is perpendicular to this field. At time t=0 the normal to the coil is oriented parallel to the magnetic field and the coil is rotating with a constant angular frequency of 4.700E+03\,s\textsuperscript{$$-$$1}.  What is the ''magnitude'' (absolute value) of the induced emf at t\,=\,59\,s?
\begin{choices} %%%%%%% begin choices
\choice  1.197E+05\,V
\CorrectChoice 1.316E+05\,V
\choice  1.448E+05\,V
\choice  1.593E+05\,V
\choice  1.752E+05\,V
\end{choices} %%% end choices

\question A recangular coil with an area of 0.432\,m\textsuperscript{2} and 16\,turns is placed in a uniform magnetic field of 3.7\,T.  The coil is rotated about an axis that is perpendicular to this field. At time t=0 the normal to the coil is oriented parallel to the magnetic field and the coil is rotating with a constant angular frequency of 5.020E+03\,s\textsuperscript{$$-$$1}.  What is the ''magnitude'' (absolute value) of the induced emf at t\,=\,55\,s?
\begin{choices} %%%%%%% begin choices
\choice  1.055E+05\,V
\CorrectChoice 1.161E+05\,V
\choice  1.277E+05\,V
\choice  1.405E+05\,V
\choice  1.545E+05\,V
\end{choices} %%% end choices

\question A recangular coil with an area of 0.446\,m\textsuperscript{2} and 13\,turns is placed in a uniform magnetic field of 3.17\,T.  The coil is rotated about an axis that is perpendicular to this field. At time t=0 the normal to the coil is oriented parallel to the magnetic field and the coil is rotating with a constant angular frequency of 5.060E+03\,s\textsuperscript{$$-$$1}.  What is the ''magnitude'' (absolute value) of the induced emf at t\,=\,54\,s?
\begin{choices} %%%%%%% begin choices
\CorrectChoice 1.957E+03\,V
\choice  2.153E+03\,V
\choice  2.368E+03\,V
\choice  2.605E+03\,V
\choice  2.865E+03\,V
\end{choices} %%% end choices

\question A recangular coil with an area of 0.897\,m\textsuperscript{2} and 8\,turns is placed in a uniform magnetic field of 2.83\,T.  The coil is rotated about an axis that is perpendicular to this field. At time t=0 the normal to the coil is oriented parallel to the magnetic field and the coil is rotating with a constant angular frequency of 8.740E+03\,s\textsuperscript{$$-$$1}.  What is the ''magnitude'' (absolute value) of the induced emf at t\,=\,3\,s?
\begin{choices} %%%%%%% begin choices
\CorrectChoice 4.695E+04\,V
\choice  5.165E+04\,V
\choice  5.681E+04\,V
\choice  6.249E+04\,V
\choice  6.874E+04\,V
\end{choices} %%% end choices

\question A recangular coil with an area of 0.45\,m\textsuperscript{2} and 18\,turns is placed in a uniform magnetic field of 2.68\,T.  The coil is rotated about an axis that is perpendicular to this field. At time t=0 the normal to the coil is oriented parallel to the magnetic field and the coil is rotating with a constant angular frequency of 3.730E+03\,s\textsuperscript{$$-$$1}.  What is the ''magnitude'' (absolute value) of the induced emf at t\,=\,87\,s?
\begin{choices} %%%%%%% begin choices
\choice  4.861E+04\,V
\choice  5.347E+04\,V
\CorrectChoice 5.882E+04\,V
\choice  6.470E+04\,V
\choice  7.117E+04\,V
\end{choices} %%% end choices

\question A recangular coil with an area of 0.182\,m\textsuperscript{2} and 5\,turns is placed in a uniform magnetic field of 2.74\,T.  The coil is rotated about an axis that is perpendicular to this field. At time t=0 the normal to the coil is oriented parallel to the magnetic field and the coil is rotating with a constant angular frequency of 2.390E+03\,s\textsuperscript{$$-$$1}.  What is the ''magnitude'' (absolute value) of the induced emf at t\,=\,79\,s?
\begin{choices} %%%%%%% begin choices
\CorrectChoice 1.656E+03\,V
\choice  1.821E+03\,V
\choice  2.003E+03\,V
\choice  2.204E+03\,V
\choice  2.424E+03\,V
\end{choices} %%% end choices

\question A recangular coil with an area of 0.291\,m\textsuperscript{2} and 6\,turns is placed in a uniform magnetic field of 2.63\,T.  The coil is rotated about an axis that is perpendicular to this field. At time t=0 the normal to the coil is oriented parallel to the magnetic field and the coil is rotating with a constant angular frequency of 7.130E+03\,s\textsuperscript{$$-$$1}.  What is the ''magnitude'' (absolute value) of the induced emf at t\,=\,35\,s?
\begin{choices} %%%%%%% begin choices
\choice  1.490E+04\,V
\choice  1.639E+04\,V
\choice  1.803E+04\,V
\choice  1.983E+04\,V
\CorrectChoice 2.181E+04\,V
\end{choices} %%% end choices

\question A recangular coil with an area of 0.587\,m\textsuperscript{2} and 13\,turns is placed in a uniform magnetic field of 1.62\,T.  The coil is rotated about an axis that is perpendicular to this field. At time t=0 the normal to the coil is oriented parallel to the magnetic field and the coil is rotating with a constant angular frequency of 3.800E+03\,s\textsuperscript{$$-$$1}.  What is the ''magnitude'' (absolute value) of the induced emf at t\,=\,93\,s?
\begin{choices} %%%%%%% begin choices
\choice  2.512E+04\,V
\choice  2.763E+04\,V
\choice  3.039E+04\,V
\choice  3.343E+04\,V
\CorrectChoice 3.677E+04\,V
\end{choices} %%% end choices
%\pagebreak
%\end{choices}%??????????????
\end{questions}%%%%%%%% end questions

\subsection{}%%%% subsection 7

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

\question A spatially uniform magnetic points in the z-direction and oscilates with time as $$\vec B(t) = B_0\sin\omega t$$ where $$B_0=$$3.26\,T and $$\omega=$$9.250E+03\,s\textsuperscript{$$-$$1}. Suppose the electric field is always zero at point $$\mathcal O$$, and consider a circle of radius 0.385\,m that is centered at that point and oriented in a plane perpendicular to the magnetic field. Evaluate the maximum value of the line integral  $$\oint \vec E\cdot d\vec s$$ around the circle.
\begin{choices} %%%%%%% begin choices
\choice  6.029E+04\,V
\choice  6.631E+04\,V
\CorrectChoice 7.295E+04\,V
\choice  8.024E+04\,V
\choice  8.826E+04\,V
\end{choices} %%% end choices

\question A spatially uniform magnetic points in the z-direction and oscilates with time as $$\vec B(t) = B_0\sin\omega t$$ where $$B_0=$$3.29\,T and $$\omega=$$4.720E+03\,s\textsuperscript{$$-$$1}. Suppose the electric field is always zero at point $$\mathcal O$$, and consider a circle of radius 0.658\,m that is centered at that point and oriented in a plane perpendicular to the magnetic field. Evaluate the maximum value of the line integral  $$\oint \vec E\cdot d\vec s$$ around the circle.
\begin{choices} %%%%%%% begin choices
\CorrectChoice 6.420E+04\,V
\choice  7.062E+04\,V
\choice  7.768E+04\,V
\choice  8.545E+04\,V
\choice  9.400E+04\,V
\end{choices} %%% end choices

\question A spatially uniform magnetic points in the z-direction and oscilates with time as $$\vec B(t) = B_0\sin\omega t$$ where $$B_0=$$1.89\,T and $$\omega=$$1.710E+03\,s\textsuperscript{$$-$$1}. Suppose the electric field is always zero at point $$\mathcal O$$, and consider a circle of radius 0.476\,m that is centered at that point and oriented in a plane perpendicular to the magnetic field. Evaluate the maximum value of the line integral  $$\oint \vec E\cdot d\vec s$$ around the circle.
\begin{choices} %%%%%%% begin choices
\choice  7.262E+03\,V
\choice  7.988E+03\,V
\choice  8.787E+03\,V
\CorrectChoice 9.666E+03\,V
\choice  1.063E+04\,V
\end{choices} %%% end choices

\question A spatially uniform magnetic points in the z-direction and oscilates with time as $$\vec B(t) = B_0\sin\omega t$$ where $$B_0=$$3.71\,T and $$\omega=$$6.600E+03\,s\textsuperscript{$$-$$1}. Suppose the electric field is always zero at point $$\mathcal O$$, and consider a circle of radius 0.31\,m that is centered at that point and oriented in a plane perpendicular to the magnetic field. Evaluate the maximum value of the line integral  $$\oint \vec E\cdot d\vec s$$ around the circle.
\begin{choices} %%%%%%% begin choices
\CorrectChoice 4.769E+04\,V
\choice  5.246E+04\,V
\choice  5.771E+04\,V
\choice  6.348E+04\,V
\choice  6.983E+04\,V
\end{choices} %%% end choices

\question A spatially uniform magnetic points in the z-direction and oscilates with time as $$\vec B(t) = B_0\sin\omega t$$ where $$B_0=$$2.18\,T and $$\omega=$$4.840E+03\,s\textsuperscript{$$-$$1}. Suppose the electric field is always zero at point $$\mathcal O$$, and consider a circle of radius 0.387\,m that is centered at that point and oriented in a plane perpendicular to the magnetic field. Evaluate the maximum value of the line integral  $$\oint \vec E\cdot d\vec s$$ around the circle.
\begin{choices} %%%%%%% begin choices
\choice  1.928E+04\,V
\choice  2.120E+04\,V
\choice  2.332E+04\,V
\CorrectChoice 2.566E+04\,V
\choice  2.822E+04\,V
\end{choices} %%% end choices

\question A spatially uniform magnetic points in the z-direction and oscilates with time as $$\vec B(t) = B_0\sin\omega t$$ where $$B_0=$$3.7\,T and $$\omega=$$8.100E+03\,s\textsuperscript{$$-$$1}. Suppose the electric field is always zero at point $$\mathcal O$$, and consider a circle of radius 0.827\,m that is centered at that point and oriented in a plane perpendicular to the magnetic field. Evaluate the maximum value of the line integral  $$\oint \vec E\cdot d\vec s$$ around the circle.
\begin{choices} %%%%%%% begin choices
\choice  1.416E+05\,V
\CorrectChoice 1.557E+05\,V
\choice  1.713E+05\,V
\choice  1.884E+05\,V
\choice  2.073E+05\,V
\end{choices} %%% end choices

\question A spatially uniform magnetic points in the z-direction and oscilates with time as $$\vec B(t) = B_0\sin\omega t$$ where $$B_0=$$2.34\,T and $$\omega=$$2.670E+03\,s\textsuperscript{$$-$$1}. Suppose the electric field is always zero at point $$\mathcal O$$, and consider a circle of radius 0.646\,m that is centered at that point and oriented in a plane perpendicular to the magnetic field. Evaluate the maximum value of the line integral  $$\oint \vec E\cdot d\vec s$$ around the circle.
\begin{choices} %%%%%%% begin choices
\choice  1.905E+04\,V
\choice  2.096E+04\,V
\choice  2.305E+04\,V
\CorrectChoice 2.536E+04\,V
\choice  2.790E+04\,V
\end{choices} %%% end choices

\question A spatially uniform magnetic points in the z-direction and oscilates with time as $$\vec B(t) = B_0\sin\omega t$$ where $$B_0=$$3.84\,T and $$\omega=$$4.410E+03\,s\textsuperscript{$$-$$1}. Suppose the electric field is always zero at point $$\mathcal O$$, and consider a circle of radius 0.379\,m that is centered at that point and oriented in a plane perpendicular to the magnetic field. Evaluate the maximum value of the line integral  $$\oint \vec E\cdot d\vec s$$ around the circle.
\begin{choices} %%%%%%% begin choices
\choice  3.333E+04\,V
\choice  3.666E+04\,V
\CorrectChoice 4.033E+04\,V
\choice  4.436E+04\,V
\choice  4.879E+04\,V
\end{choices} %%% end choices

\question A spatially uniform magnetic points in the z-direction and oscilates with time as $$\vec B(t) = B_0\sin\omega t$$ where $$B_0=$$3.54\,T and $$\omega=$$1.860E+03\,s\textsuperscript{$$-$$1}. Suppose the electric field is always zero at point $$\mathcal O$$, and consider a circle of radius 0.642\,m that is centered at that point and oriented in a plane perpendicular to the magnetic field. Evaluate the maximum value of the line integral  $$\oint \vec E\cdot d\vec s$$ around the circle.
\begin{choices} %%%%%%% begin choices
\choice  2.415E+04\,V
\CorrectChoice 2.656E+04\,V
\choice  2.922E+04\,V
\choice  3.214E+04\,V
\choice  3.535E+04\,V
\end{choices} %%% end choices

\question A spatially uniform magnetic points in the z-direction and oscilates with time as $$\vec B(t) = B_0\sin\omega t$$ where $$B_0=$$2.25\,T and $$\omega=$$8.280E+03\,s\textsuperscript{$$-$$1}. Suppose the electric field is always zero at point $$\mathcal O$$, and consider a circle of radius 0.227\,m that is centered at that point and oriented in a plane perpendicular to the magnetic field. Evaluate the maximum value of the line integral  $$\oint \vec E\cdot d\vec s$$ around the circle.
\begin{choices} %%%%%%% begin choices
\CorrectChoice 2.657E+04\,V
\choice  2.923E+04\,V
\choice  3.215E+04\,V
\choice  3.537E+04\,V
\choice  3.890E+04\,V
\end{choices} %%% end choices

\question A spatially uniform magnetic points in the z-direction and oscilates with time as $$\vec B(t) = B_0\sin\omega t$$ where $$B_0=$$3.75\,T and $$\omega=$$1.740E+03\,s\textsuperscript{$$-$$1}. Suppose the electric field is always zero at point $$\mathcal O$$, and consider a circle of radius 0.417\,m that is centered at that point and oriented in a plane perpendicular to the magnetic field. Evaluate the maximum value of the line integral  $$\oint \vec E\cdot d\vec s$$ around the circle.
\begin{choices} %%%%%%% begin choices
\choice  1.168E+04\,V
\choice  1.284E+04\,V
\choice  1.413E+04\,V
\choice  1.554E+04\,V
\CorrectChoice 1.710E+04\,V
\end{choices} %%% end choices

\question A spatially uniform magnetic points in the z-direction and oscilates with time as $$\vec B(t) = B_0\sin\omega t$$ where $$B_0=$$3.75\,T and $$\omega=$$9.800E+03\,s\textsuperscript{$$-$$1}. Suppose the electric field is always zero at point $$\mathcal O$$, and consider a circle of radius 0.22\,m that is centered at that point and oriented in a plane perpendicular to the magnetic field. Evaluate the maximum value of the line integral  $$\oint \vec E\cdot d\vec s$$ around the circle.
\begin{choices} %%%%%%% begin choices
\choice  4.198E+04\,V
\choice  4.618E+04\,V
\CorrectChoice 5.080E+04\,V
\choice  5.588E+04\,V
\choice  6.147E+04\,V
\end{choices} %%% end choices

\question A spatially uniform magnetic points in the z-direction and oscilates with time as $$\vec B(t) = B_0\sin\omega t$$ where $$B_0=$$3.79\,T and $$\omega=$$7.280E+03\,s\textsuperscript{$$-$$1}. Suppose the electric field is always zero at point $$\mathcal O$$, and consider a circle of radius 0.668\,m that is centered at that point and oriented in a plane perpendicular to the magnetic field. Evaluate the maximum value of the line integral  $$\oint \vec E\cdot d\vec s$$ around the circle.
\begin{choices} %%%%%%% begin choices
\choice  7.910E+04\,V
\choice  8.701E+04\,V
\choice  9.571E+04\,V
\choice  1.053E+05\,V
\CorrectChoice 1.158E+05\,V
\end{choices} %%% end choices

\question A spatially uniform magnetic points in the z-direction and oscilates with time as $$\vec B(t) = B_0\sin\omega t$$ where $$B_0=$$1.8\,T and $$\omega=$$1.530E+03\,s\textsuperscript{$$-$$1}. Suppose the electric field is always zero at point $$\mathcal O$$, and consider a circle of radius 0.519\,m that is centered at that point and oriented in a plane perpendicular to the magnetic field. Evaluate the maximum value of the line integral  $$\oint \vec E\cdot d\vec s$$ around the circle.
\begin{choices} %%%%%%% begin choices
\choice  7.422E+03\,V
\choice  8.164E+03\,V
\CorrectChoice 8.981E+03\,V
\choice  9.879E+03\,V
\choice  1.087E+04\,V
\end{choices} %%% end choices

\question A spatially uniform magnetic points in the z-direction and oscilates with time as $$\vec B(t) = B_0\sin\omega t$$ where $$B_0=$$1.97\,T and $$\omega=$$5.410E+03\,s\textsuperscript{$$-$$1}. Suppose the electric field is always zero at point $$\mathcal O$$, and consider a circle of radius 0.244\,m that is centered at that point and oriented in a plane perpendicular to the magnetic field. Evaluate the maximum value of the line integral  $$\oint \vec E\cdot d\vec s$$ around the circle.
\begin{choices} %%%%%%% begin choices
\choice  1.485E+04\,V
\CorrectChoice 1.634E+04\,V
\choice  1.797E+04\,V
\choice  1.977E+04\,V
\choice  2.175E+04\,V
\end{choices} %%% end choices

\question A spatially uniform magnetic points in the z-direction and oscilates with time as $$\vec B(t) = B_0\sin\omega t$$ where $$B_0=$$3.31\,T and $$\omega=$$8.360E+03\,s\textsuperscript{$$-$$1}. Suppose the electric field is always zero at point $$\mathcal O$$, and consider a circle of radius 0.547\,m that is centered at that point and oriented in a plane perpendicular to the magnetic field. Evaluate the maximum value of the line integral  $$\oint \vec E\cdot d\vec s$$ around the circle.
\begin{choices} %%%%%%% begin choices
\choice  7.145E+04\,V
\choice  7.860E+04\,V
\choice  8.646E+04\,V
\CorrectChoice 9.510E+04\,V
\choice  1.046E+05\,V
\end{choices} %%% end choices

\question A spatially uniform magnetic points in the z-direction and oscilates with time as $$\vec B(t) = B_0\sin\omega t$$ where $$B_0=$$3.58\,T and $$\omega=$$4.310E+03\,s\textsuperscript{$$-$$1}. Suppose the electric field is always zero at point $$\mathcal O$$, and consider a circle of radius 0.879\,m that is centered at that point and oriented in a plane perpendicular to the magnetic field. Evaluate the maximum value of the line integral  $$\oint \vec E\cdot d\vec s$$ around the circle.
\begin{choices} %%%%%%% begin choices
\choice  7.043E+04\,V
\choice  7.747E+04\,V
\CorrectChoice 8.522E+04\,V
\choice  9.374E+04\,V
\choice  1.031E+05\,V
\end{choices} %%% end choices

\question A spatially uniform magnetic points in the z-direction and oscilates with time as $$\vec B(t) = B_0\sin\omega t$$ where $$B_0=$$3.11\,T and $$\omega=$$1.150E+03\,s\textsuperscript{$$-$$1}. Suppose the electric field is always zero at point $$\mathcal O$$, and consider a circle of radius 0.171\,m that is centered at that point and oriented in a plane perpendicular to the magnetic field. Evaluate the maximum value of the line integral  $$\oint \vec E\cdot d\vec s$$ around the circle.
\begin{choices} %%%%%%% begin choices
\choice  2.887E+03\,V
\choice  3.176E+03\,V
\choice  3.493E+03\,V
\CorrectChoice 3.843E+03\,V
\choice  4.227E+03\,V
\end{choices} %%% end choices

\question A spatially uniform magnetic points in the z-direction and oscilates with time as $$\vec B(t) = B_0\sin\omega t$$ where $$B_0=$$1.71\,T and $$\omega=$$4.780E+03\,s\textsuperscript{$$-$$1}. Suppose the electric field is always zero at point $$\mathcal O$$, and consider a circle of radius 0.294\,m that is centered at that point and oriented in a plane perpendicular to the magnetic field. Evaluate the maximum value of the line integral  $$\oint \vec E\cdot d\vec s$$ around the circle.
\begin{choices} %%%%%%% begin choices
\CorrectChoice 1.510E+04\,V
\choice  1.661E+04\,V
\choice  1.827E+04\,V
\choice  2.010E+04\,V
\choice  2.211E+04\,V
\end{choices} %%% end choices
%\pagebreak
%\end{choices}%??????????????
\end{questions}%%%%%%%% end questions

\subsection{}%%%% subsection 8

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

\question A long solenoid has a radius of 0.442\,m and 63\,turns per meter; its current decreases with time according to $$I_0e^{-\alpha t}$$, where $$I_0=$$7\,A and $$\alpha=$$22\,s\textsuperscript{$$-$$1}.What is the induced electric fied at a distance 1.94\,m from the axis at time t=0.0331\,s ?
\begin{choices} %%%%%%% begin choices
\CorrectChoice 2.964E-04\,V/m
\choice  3.260E-04\,V/m
\choice  3.586E-04\,V/m
\choice  3.945E-04\,V/m
\choice  4.339E-04\,V/m
\end{choices} %%% end choices

\question A long solenoid has a radius of 0.521\,m and 46\,turns per meter; its current decreases with time according to $$I_0e^{-\alpha t}$$, where $$I_0=$$1\,A and $$\alpha=$$30\,s\textsuperscript{$$-$$1}.What is the induced electric fied at a distance 2.42\,m from the axis at time t=0.0449\,s ?
\begin{choices} %%%%%%% begin choices
\CorrectChoice 2.529E-05\,V/m
\choice  2.782E-05\,V/m
\choice  3.060E-05\,V/m
\choice  3.366E-05\,V/m
\choice  3.703E-05\,V/m
\end{choices} %%% end choices

\question A long solenoid has a radius of 0.8\,m and 77\,turns per meter; its current decreases with time according to $$I_0e^{-\alpha t}$$, where $$I_0=$$5\,A and $$\alpha=$$28\,s\textsuperscript{$$-$$1}.What is the induced electric fied at a distance 2.2\,m from the axis at time t=0.0757\,s ?
\begin{choices} %%%%%%% begin choices
\choice  1.616E-04\,V/m
\choice  1.778E-04\,V/m
\choice  1.955E-04\,V/m
\choice  2.151E-04\,V/m
\CorrectChoice 2.366E-04\,V/m
\end{choices} %%% end choices

\question A long solenoid has a radius of 0.413\,m and 17\,turns per meter; its current decreases with time according to $$I_0e^{-\alpha t}$$, where $$I_0=$$1\,A and $$\alpha=$$21\,s\textsuperscript{$$-$$1}.What is the induced electric fied at a distance 2.25\,m from the axis at time t=0.0689\,s ?
\begin{choices} %%%%%%% begin choices
\choice  3.006E-06\,V/m
\choice  3.307E-06\,V/m
\choice  3.637E-06\,V/m
\CorrectChoice 4.001E-06\,V/m
\choice  4.401E-06\,V/m
\end{choices} %%% end choices

\question A long solenoid has a radius of 0.644\,m and 20\,turns per meter; its current decreases with time according to $$I_0e^{-\alpha t}$$, where $$I_0=$$7\,A and $$\alpha=$$27\,s\textsuperscript{$$-$$1}.What is the induced electric fied at a distance 2.84\,m from the axis at time t=0.083\,s ?
\begin{choices} %%%%%%% begin choices
\choice  3.353E-05\,V/m
\CorrectChoice 3.689E-05\,V/m
\choice  4.058E-05\,V/m
\choice  4.463E-05\,V/m
\choice  4.910E-05\,V/m
\end{choices} %%% end choices

\question A long solenoid has a radius of 0.45\,m and 35\,turns per meter; its current decreases with time according to $$I_0e^{-\alpha t}$$, where $$I_0=$$1\,A and $$\alpha=$$28\,s\textsuperscript{$$-$$1}.What is the induced electric fied at a distance 2.35\,m from the axis at time t=0.0709\,s ?
\begin{choices} %%%%%%% begin choices
\choice  5.475E-06\,V/m
\choice  6.023E-06\,V/m
\choice  6.625E-06\,V/m
\CorrectChoice 7.288E-06\,V/m
\choice  8.017E-06\,V/m
\end{choices} %%% end choices

\question A long solenoid has a radius of 0.716\,m and 96\,turns per meter; its current decreases with time according to $$I_0e^{-\alpha t}$$, where $$I_0=$$9\,A and $$\alpha=$$23\,s\textsuperscript{$$-$$1}.What is the induced electric fied at a distance 2.67\,m from the axis at time t=0.0226\,s ?
\begin{choices} %%%%%%% begin choices
\CorrectChoice 1.426E-03\,V/m
\choice  1.568E-03\,V/m
\choice  1.725E-03\,V/m
\choice  1.897E-03\,V/m
\choice  2.087E-03\,V/m
\end{choices} %%% end choices

\question A long solenoid has a radius of 0.806\,m and 41\,turns per meter; its current decreases with time according to $$I_0e^{-\alpha t}$$, where $$I_0=$$2\,A and $$\alpha=$$21\,s\textsuperscript{$$-$$1}.What is the induced electric fied at a distance 2.67\,m from the axis at time t=0.0701\,s ?
\begin{choices} %%%%%%% begin choices
\CorrectChoice 6.040E-05\,V/m
\choice  6.644E-05\,V/m
\choice  7.309E-05\,V/m
\choice  8.039E-05\,V/m
\choice  8.843E-05\,V/m
\end{choices} %%% end choices

\question A long solenoid has a radius of 0.786\,m and 60\,turns per meter; its current decreases with time according to $$I_0e^{-\alpha t}$$, where $$I_0=$$2\,A and $$\alpha=$$21\,s\textsuperscript{$$-$$1}.What is the induced electric fied at a distance 1.98\,m from the axis at time t=0.049\,s ?
\begin{choices} %%%%%%% begin choices
\choice  1.605E-04\,V/m
\CorrectChoice 1.766E-04\,V/m
\choice  1.942E-04\,V/m
\choice  2.136E-04\,V/m
\choice  2.350E-04\,V/m
\end{choices} %%% end choices

\question A long solenoid has a radius of 0.578\,m and 34\,turns per meter; its current decreases with time according to $$I_0e^{-\alpha t}$$, where $$I_0=$$7\,A and $$\alpha=$$27\,s\textsuperscript{$$-$$1}.What is the induced electric fied at a distance 2.63\,m from the axis at time t=0.0462\,s ?
\begin{choices} %%%%%%% begin choices
\CorrectChoice 1.473E-04\,V/m
\choice  1.621E-04\,V/m
\choice  1.783E-04\,V/m
\choice  1.961E-04\,V/m
\choice  2.157E-04\,V/m
\end{choices} %%% end choices

\question A long solenoid has a radius of 0.777\,m and 67\,turns per meter; its current decreases with time according to $$I_0e^{-\alpha t}$$, where $$I_0=$$6\,A and $$\alpha=$$20\,s\textsuperscript{$$-$$1}.What is the induced electric fied at a distance 2.39\,m from the axis at time t=0.0399\,s ?
\begin{choices} %%%%%%% begin choices
\choice  3.924E-04\,V/m
\choice  4.317E-04\,V/m
\choice  4.748E-04\,V/m
\choice  5.223E-04\,V/m
\CorrectChoice 5.745E-04\,V/m
\end{choices} %%% end choices

\question A long solenoid has a radius of 0.434\,m and 41\,turns per meter; its current decreases with time according to $$I_0e^{-\alpha t}$$, where $$I_0=$$9\,A and $$\alpha=$$28\,s\textsuperscript{$$-$$1}.What is the induced electric fied at a distance 2.28\,m from the axis at time t=0.0392\,s ?
\begin{choices} %%%%%%% begin choices
\choice  1.479E-04\,V/m
\choice  1.627E-04\,V/m
\CorrectChoice 1.789E-04\,V/m
\choice  1.968E-04\,V/m
\choice  2.165E-04\,V/m
\end{choices} %%% end choices

\question A long solenoid has a radius of 0.845\,m and 65\,turns per meter; its current decreases with time according to $$I_0e^{-\alpha t}$$, where $$I_0=$$6\,A and $$\alpha=$$30\,s\textsuperscript{$$-$$1}.What is the induced electric fied at a distance 2.63\,m from the axis at time t=0.0561\,s ?
\begin{choices} %%%%%%% begin choices
\choice  3.371E-04\,V/m
\CorrectChoice 3.709E-04\,V/m
\choice  4.079E-04\,V/m
\choice  4.487E-04\,V/m
\choice  4.936E-04\,V/m
\end{choices} %%% end choices

\question A long solenoid has a radius of 0.583\,m and 38\,turns per meter; its current decreases with time according to $$I_0e^{-\alpha t}$$, where $$I_0=$$6\,A and $$\alpha=$$24\,s\textsuperscript{$$-$$1}.What is the induced electric fied at a distance 2.09\,m from the axis at time t=0.0388\,s ?
\begin{choices} %%%%%%% begin choices
\choice  1.655E-04\,V/m
\choice  1.821E-04\,V/m
\choice  2.003E-04\,V/m
\CorrectChoice 2.203E-04\,V/m
\choice  2.424E-04\,V/m
\end{choices} %%% end choices

\question A long solenoid has a radius of 0.394\,m and 13\,turns per meter; its current decreases with time according to $$I_0e^{-\alpha t}$$, where $$I_0=$$9\,A and $$\alpha=$$28\,s\textsuperscript{$$-$$1}.What is the induced electric fied at a distance 1.8\,m from the axis at time t=0.0757\,s ?
\begin{choices} %%%%%%% begin choices
\CorrectChoice 2.132E-05\,V/m
\choice  2.345E-05\,V/m
\choice  2.579E-05\,V/m
\choice  2.837E-05\,V/m
\choice  3.121E-05\,V/m
\end{choices} %%% end choices

\question A long solenoid has a radius of 0.887\,m and 43\,turns per meter; its current decreases with time according to $$I_0e^{-\alpha t}$$, where $$I_0=$$7\,A and $$\alpha=$$28\,s\textsuperscript{$$-$$1}.What is the induced electric fied at a distance 2.66\,m from the axis at time t=0.0332\,s ?
\begin{choices} %%%%%%% begin choices
\CorrectChoice 6.182E-04\,V/m
\choice  6.801E-04\,V/m
\choice  7.481E-04\,V/m
\choice  8.229E-04\,V/m
\choice  9.052E-04\,V/m
\end{choices} %%% end choices

\question A long solenoid has a radius of 0.624\,m and 84\,turns per meter; its current decreases with time according to $$I_0e^{-\alpha t}$$, where $$I_0=$$6\,A and $$\alpha=$$20\,s\textsuperscript{$$-$$1}.What is the induced electric fied at a distance 1.78\,m from the axis at time t=0.0579\,s ?
\begin{choices} %%%%%%% begin choices
\choice  3.597E-04\,V/m
\choice  3.956E-04\,V/m
\CorrectChoice 4.352E-04\,V/m
\choice  4.787E-04\,V/m
\choice  5.266E-04\,V/m
\end{choices} %%% end choices

\question A long solenoid has a radius of 0.306\,m and 98\,turns per meter; its current decreases with time according to $$I_0e^{-\alpha t}$$, where $$I_0=$$6\,A and $$\alpha=$$22\,s\textsuperscript{$$-$$1}.What is the induced electric fied at a distance 2.52\,m from the axis at time t=0.0246\,s ?
\begin{choices} %%%%%%% begin choices
\choice  1.598E-04\,V/m
\CorrectChoice 1.758E-04\,V/m
\choice  1.934E-04\,V/m
\choice  2.127E-04\,V/m
\choice  2.340E-04\,V/m
\end{choices} %%% end choices

\question A long solenoid has a radius of 0.757\,m and 90\,turns per meter; its current decreases with time according to $$I_0e^{-\alpha t}$$, where $$I_0=$$7\,A and $$\alpha=$$30\,s\textsuperscript{$$-$$1}.What is the induced electric fied at a distance 2.08\,m from the axis at time t=0.0442\,s ?
\begin{choices} %%%%%%% begin choices
\choice  6.527E-04\,V/m
\choice  7.180E-04\,V/m
\choice  7.898E-04\,V/m
\CorrectChoice 8.688E-04\,V/m
\choice  9.556E-04\,V/m
\end{choices} %%% end choices
%\pagebreak
%\end{choices}%??????????????
\end{questions}%%%%%%%% end questions

\subsection{}%%%% subsection 9

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

\question A long solenoid has a radius of 0.508\,m and 90\,turns per meter; its current decreases with time according to $$I_0e^{-\alpha t}$$, where $$I_0=$$7\,A and $$\alpha=$$25\,s\textsuperscript{$$-$$1}.What is the induced electric fied at a distance 0.145\,m from the axis at time t=0.0643\,s ?
\begin{choices} %%%%%%% begin choices
\choice  2.614E-04\,V/m
\CorrectChoice 2.875E-04\,V/m
\choice  3.163E-04\,V/m
\choice  3.479E-04\,V/m
\choice  3.827E-04\,V/m
\end{choices} %%% end choices

\question A long solenoid has a radius of 0.732\,m and 55\,turns per meter; its current decreases with time according to $$I_0e^{-\alpha t}$$, where $$I_0=$$9\,A and $$\alpha=$$25\,s\textsuperscript{$$-$$1}.What is the induced electric fied at a distance 0.203\,m from the axis at time t=0.0448\,s ?
\begin{choices} %%%%%%% begin choices
\CorrectChoice 5.150E-04\,V/m
\choice  5.665E-04\,V/m
\choice  6.232E-04\,V/m
\choice  6.855E-04\,V/m
\choice  7.540E-04\,V/m
\end{choices} %%% end choices

\question A long solenoid has a radius of 0.682\,m and 38\,turns per meter; its current decreases with time according to $$I_0e^{-\alpha t}$$, where $$I_0=$$2\,A and $$\alpha=$$27\,s\textsuperscript{$$-$$1}.What is the induced electric fied at a distance 0.16\,m from the axis at time t=0.0736\,s ?
\begin{choices} %%%%%%% begin choices
\choice  2.571E-05\,V/m
\CorrectChoice 2.828E-05\,V/m
\choice  3.111E-05\,V/m
\choice  3.422E-05\,V/m
\choice  3.764E-05\,V/m
\end{choices} %%% end choices

\question A long solenoid has a radius of 0.887\,m and 45\,turns per meter; its current decreases with time according to $$I_0e^{-\alpha t}$$, where $$I_0=$$3\,A and $$\alpha=$$25\,s\textsuperscript{$$-$$1}.What is the induced electric fied at a distance 0.169\,m from the axis at time t=0.072\,s ?
\begin{choices} %%%%%%% begin choices
\choice  4.896E-05\,V/m
\choice  5.385E-05\,V/m
\CorrectChoice 5.924E-05\,V/m
\choice  6.516E-05\,V/m
\choice  7.168E-05\,V/m
\end{choices} %%% end choices

\question A long solenoid has a radius of 0.845\,m and 78\,turns per meter; its current decreases with time according to $$I_0e^{-\alpha t}$$, where $$I_0=$$3\,A and $$\alpha=$$20\,s\textsuperscript{$$-$$1}.What is the induced electric fied at a distance 0.214\,m from the axis at time t=0.0655\,s ?
\begin{choices} %%%%%%% begin choices
\choice  1.160E-04\,V/m
\choice  1.276E-04\,V/m
\choice  1.403E-04\,V/m
\choice  1.544E-04\,V/m
\CorrectChoice 1.698E-04\,V/m
\end{choices} %%% end choices

\question A long solenoid has a radius of 0.851\,m and 12\,turns per meter; its current decreases with time according to $$I_0e^{-\alpha t}$$, where $$I_0=$$3\,A and $$\alpha=$$30\,s\textsuperscript{$$-$$1}.What is the induced electric fied at a distance 0.14\,m from the axis at time t=0.0531\,s ?
\begin{choices} %%%%%%% begin choices
\choice  1.319E-05\,V/m
\choice  1.451E-05\,V/m
\choice  1.596E-05\,V/m
\choice  1.756E-05\,V/m
\CorrectChoice 1.932E-05\,V/m
\end{choices} %%% end choices

\question A long solenoid has a radius of 0.447\,m and 85\,turns per meter; its current decreases with time according to $$I_0e^{-\alpha t}$$, where $$I_0=$$7\,A and $$\alpha=$$23\,s\textsuperscript{$$-$$1}.What is the induced electric fied at a distance 0.212\,m from the axis at time t=0.0819\,s ?
\begin{choices} %%%%%%% begin choices
\choice  1.893E-04\,V/m
\choice  2.082E-04\,V/m
\choice  2.290E-04\,V/m
\choice  2.519E-04\,V/m
\CorrectChoice 2.771E-04\,V/m
\end{choices} %%% end choices

\question A long solenoid has a radius of 0.596\,m and 19\,turns per meter; its current decreases with time according to $$I_0e^{-\alpha t}$$, where $$I_0=$$5\,A and $$\alpha=$$29\,s\textsuperscript{$$-$$1}.What is the induced electric fied at a distance 0.209\,m from the axis at time t=0.0604\,s ?
\begin{choices} %%%%%%% begin choices
\CorrectChoice 6.277E-05\,V/m
\choice  6.904E-05\,V/m
\choice  7.595E-05\,V/m
\choice  8.354E-05\,V/m
\choice  9.190E-05\,V/m
\end{choices} %%% end choices

\question A long solenoid has a radius of 0.645\,m and 37\,turns per meter; its current decreases with time according to $$I_0e^{-\alpha t}$$, where $$I_0=$$9\,A and $$\alpha=$$23\,s\textsuperscript{$$-$$1}.What is the induced electric fied at a distance 0.189\,m from the axis at time t=0.0698\,s ?
\begin{choices} %%%%%%% begin choices
\choice  1.372E-04\,V/m
\choice  1.509E-04\,V/m
\choice  1.660E-04\,V/m
\CorrectChoice 1.826E-04\,V/m
\choice  2.009E-04\,V/m
\end{choices} %%% end choices

\question A long solenoid has a radius of 0.857\,m and 58\,turns per meter; its current decreases with time according to $$I_0e^{-\alpha t}$$, where $$I_0=$$1\,A and $$\alpha=$$21\,s\textsuperscript{$$-$$1}.What is the induced electric fied at a distance 0.144\,m from the axis at time t=0.0898\,s ?
\begin{choices} %%%%%%% begin choices
\choice  1.256E-05\,V/m
\choice  1.382E-05\,V/m
\choice  1.520E-05\,V/m
\CorrectChoice 1.672E-05\,V/m
\choice  1.839E-05\,V/m
\end{choices} %%% end choices

\question A long solenoid has a radius of 0.436\,m and 87\,turns per meter; its current decreases with time according to $$I_0e^{-\alpha t}$$, where $$I_0=$$4\,A and $$\alpha=$$27\,s\textsuperscript{$$-$$1}.What is the induced electric fied at a distance 0.153\,m from the axis at time t=0.02\,s ?
\begin{choices} %%%%%%% begin choices
\choice  4.785E-04\,V/m
\CorrectChoice 5.264E-04\,V/m
\choice  5.790E-04\,V/m
\choice  6.369E-04\,V/m
\choice  7.006E-04\,V/m
\end{choices} %%% end choices

\question A long solenoid has a radius of 0.793\,m and 45\,turns per meter; its current decreases with time according to $$I_0e^{-\alpha t}$$, where $$I_0=$$2\,A and $$\alpha=$$29\,s\textsuperscript{$$-$$1}.What is the induced electric fied at a distance 0.216\,m from the axis at time t=0.0208\,s ?
\begin{choices} %%%%%%% begin choices
\choice  1.456E-04\,V/m
\choice  1.601E-04\,V/m
\choice  1.762E-04\,V/m
\CorrectChoice 1.938E-04\,V/m
\choice  2.132E-04\,V/m
\end{choices} %%% end choices

\question A long solenoid has a radius of 0.517\,m and 23\,turns per meter; its current decreases with time according to $$I_0e^{-\alpha t}$$, where $$I_0=$$1\,A and $$\alpha=$$30\,s\textsuperscript{$$-$$1}.What is the induced electric fied at a distance 0.162\,m from the axis at time t=0.0679\,s ?
\begin{choices} %%%%%%% begin choices
\choice  6.256E-06\,V/m
\choice  6.882E-06\,V/m
\choice  7.570E-06\,V/m
\choice  8.327E-06\,V/m
\CorrectChoice 9.160E-06\,V/m
\end{choices} %%% end choices

\question A long solenoid has a radius of 0.861\,m and 28\,turns per meter; its current decreases with time according to $$I_0e^{-\alpha t}$$, where $$I_0=$$1\,A and $$\alpha=$$20\,s\textsuperscript{$$-$$1}.What is the induced electric fied at a distance 0.106\,m from the axis at time t=0.055\,s ?
\begin{choices} %%%%%%% begin choices
\choice  1.026E-05\,V/m
\choice  1.129E-05\,V/m
\CorrectChoice 1.242E-05\,V/m
\choice  1.366E-05\,V/m
\choice  1.502E-05\,V/m
\end{choices} %%% end choices

\question A long solenoid has a radius of 0.749\,m and 62\,turns per meter; its current decreases with time according to $$I_0e^{-\alpha t}$$, where $$I_0=$$9\,A and $$\alpha=$$25\,s\textsuperscript{$$-$$1}.What is the induced electric fied at a distance 0.139\,m from the axis at time t=0.071\,s ?
\begin{choices} %%%%%%% begin choices
\CorrectChoice 2.065E-04\,V/m
\choice  2.271E-04\,V/m
\choice  2.499E-04\,V/m
\choice  2.748E-04\,V/m
\choice  3.023E-04\,V/m
\end{choices} %%% end choices

\question A long solenoid has a radius of 0.591\,m and 41\,turns per meter; its current decreases with time according to $$I_0e^{-\alpha t}$$, where $$I_0=$$1\,A and $$\alpha=$$30\,s\textsuperscript{$$-$$1}.What is the induced electric fied at a distance 0.234\,m from the axis at time t=0.0208\,s ?
\begin{choices} %%%%%%% begin choices
\choice  6.618E-05\,V/m
\choice  7.280E-05\,V/m
\choice  8.008E-05\,V/m
\choice  8.809E-05\,V/m
\CorrectChoice 9.689E-05\,V/m
\end{choices} %%% end choices

\question A long solenoid has a radius of 0.603\,m and 51\,turns per meter; its current decreases with time according to $$I_0e^{-\alpha t}$$, where $$I_0=$$2\,A and $$\alpha=$$26\,s\textsuperscript{$$-$$1}.What is the induced electric fied at a distance 0.105\,m from the axis at time t=0.0659\,s ?
\begin{choices} %%%%%%% begin choices
\choice  2.154E-05\,V/m
\choice  2.369E-05\,V/m
\choice  2.606E-05\,V/m
\choice  2.867E-05\,V/m
\CorrectChoice 3.154E-05\,V/m
\end{choices} %%% end choices

\question A long solenoid has a radius of 0.613\,m and 75\,turns per meter; its current decreases with time according to $$I_0e^{-\alpha t}$$, where $$I_0=$$2\,A and $$\alpha=$$22\,s\textsuperscript{$$-$$1}.What is the induced electric fied at a distance 0.206\,m from the axis at time t=0.0387\,s ?
\begin{choices} %%%%%%% begin choices
\choice  1.370E-04\,V/m
\choice  1.507E-04\,V/m
\choice  1.657E-04\,V/m
\CorrectChoice 1.823E-04\,V/m
\choice  2.005E-04\,V/m
\end{choices} %%% end choices

\question A long solenoid has a radius of 0.442\,m and 41\,turns per meter; its current decreases with time according to $$I_0e^{-\alpha t}$$, where $$I_0=$$4\,A and $$\alpha=$$20\,s\textsuperscript{$$-$$1}.What is the induced electric fied at a distance 0.2\,m from the axis at time t=0.0833\,s ?
\begin{choices} %%%%%%% begin choices
\choice  6.438E-05\,V/m
\choice  7.082E-05\,V/m
\CorrectChoice 7.790E-05\,V/m
\choice  8.569E-05\,V/m
\choice  9.426E-05\,V/m
\end{choices} %%% end choices
\end{questions}
\pagebreak