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\windowTitle{Multimedia Applications in Studio Physics Courses}
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pdftitle={Multimedia Applications in Studio Physics Courses},
pdfauthor={K. Min, M. Malak, P. Casabella, J. Haus, and J. Wilson},
pdfsubject={Use of computers and multimedia in RPI's Studio Physics II},
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\title{Multimedia Applications in Studio Physics Courses}
\author{K. Min\thanks{Email: mink@rpi.edu}, M. Malak\thanks{Email:
malakm@rpi.edu}, P. Casabella, J. Haus, and J. Wilson\\
Department of Physics, Applied Physics and Astronomy\\
Rensselaer Polytechnic Institute\\
Troy, NY 12180, USA}
\date{July 1998}

\pagestyle{empty}
\thispagestyle{empty}

\begin{document}

\maketitle

\noindent\textbf{Keywords}: Studio Physics Electromagnetism

\begin{abstract}

In the studio format of introductory physics courses at Rensselaer
Polytechnic Institute, a unified teaching method is used in which a
mini-lecture on a specific topic is followed by various classroom
activities related to the topic, such as hands-on experiments,
computer simulations, and spreadsheet exercises.  We will illustrate
this approach using Gauss's Law of electrostatics as an example.

\end{abstract}

\section*{Overview}
\thispagestyle{empty}

At Rensselaer Polytechnic Institute, the introductory physics courses,
Physics I (mechanics) and Physics II (electricity and magnetism,
including optics) are taught in a studio format\cite{wilson_studio}.
The studio format of teaching differs from the traditional
lecture-based format in the assumption that students learn more
effectively from each other and from doing carefully-chosen
small-group activities.  Short lectures, recitations, and class
activities are integrated in a single class session of 110 minutes.
There are two class meetings per week for each of Physics I and II.
One faculty member, one graduate teaching assistant, and one
undergraduate teaching assistant staff each studio class.  Students
work together in groups of two to four in a special studio classroom
equipped with 24 personal computers loaded with Windows applications
and Internet browsers.

A typical studio class is conducted according to the following
schedule:
\begin{itemize}
\setlength{\itemsep}{0 pt}
\item Solving homework problems (30 minutes.)
\item Mini-lecture (20 minutes)
\item Classroom exercises (60 minutes)
\end{itemize}
The students work on the homework assignments individually and hand in
the solutions at the beginning of class before classroom discussion.
The professor or a TA presents a short ``mini-lecture'', perhaps using
a PowerPoint presentation.  The mini-lecture outlines the important
points of a new topic, but avoids any long derivations.  The students
then perform a class exercise.  There are various kinds of exercises;
they include hands-on experiments which may use the computer to gather
data via the Universal Laboratory Interface, computer simulations
using Java applets\cite{links_cip}, spreadsheet calculations, symbolic
mathematical exercises, and paper and pencil worksheet problems.  The
teachers walk about the classroom during the exercise helping the
students, answering their questions, and offering suggestions.  The
students work on the class exercise in groups, and hand in a group
report at the end of class.

We will illustrate this approach using Gauss's Law from electrostatics
as an example.  Gauss's Law states that the electric flux through a
closed surface (the ``Gaussian surface'') is proportional to the net
charge inside the surface.

\subsection{Mini-Lecture}

The mini-lecture introduces the concept of electric flux, and presents
the mathematical formulation of Gauss's Law, $\Phi_{\mathrm{E}} \equiv
\oint \mathbf{E} \cdot \mathrm{d}\mathbf{A} = q/\epsilon_0$, and
discusses its physical interpretation.  To prepare the students for
the computer simulation exercise that follows, it is emphasized that
the flux integral is independent of the shape of the Gaussian surface
and also of the location and distribution of charges enclosed within
the surface.  The mini-lecture includes the discussion of a simple but
important application of Gauss's Law, the case of a uniformly charged
sphere.  Once again, in preparation for the computer simulation
exercise, it is shown that the electric field within a uniformly
charged sphere is proportional to the radial distance, but at points
outside of the sphere, it is inversely proportional to the square of
the distance.

\subsection{Computer simulation}

% I know, this is ugly.  It pains me to think about it.  But it does
% work.  The problem is that with hypertex, you can't line-break the
% anchor text.  With two narrow columns, we have no choice.  We make
% two anchors that link to the same URL, and break the line between
% them.  Now I need to go put a cold compress on my forehead.
(\href{http://links.math.rpi.edu/devmodules/electromagnetism/Gauss/html/gldemo.html}%
{http://links.math.rpi.edu/devmodules/}\urlbreak
\href{http://links.math.rpi.edu/devmodules/electromagnetism/Gauss/html/gldemo.html}%
{electromagnetism/Gauss/html/gldemo.html})

This Java applet opens a rectangular area on the screen in which are
hidden several infinitely long charged objects.  Some are infinitely
thin lines, and some are extended cylinders.  By using combinations of
modifier keys and mouse-button clicks, students can do the following:
\begin{enumerate}
\setlength{\itemsep}{0 pt}
\item Draw electric field lines.
\item Draw rectangular Gaussian surfaces, and evaluate and print the
electric flux through them.
\item Draw cylindrical Gaussian surfaces, and evaluate the flux.
\item Drop arrows indicating the direction and the strength of the field.
\end{enumerate}
An arrow moves with the mouse pointer and shows the direction and the
relative strength of the electric field.  After exploring the
rectangular area, the students are asked to hand in a report answering
the following questions:
\begin{enumerate}
\item How many charged objects are in the rectangular area? 
\item Give the coordinates, magnitudes, and signs of all the hidden
charges.  For a charge that is not a point charge, give the
coordinates of the approximate center of the distributed charge.  The
coordinates of the point where the cursor is located appear in the
browser's status line at the bottom of the window.  If you manage to
put the cursor directly on a line charge, the arrow will disappear,
and a small circle will appear there.
\item Indicate which charges are point charges and which are spread
out over some finite area.
\item For each of the non-point charges, indicate the shape of the
charge distribution.  Is it square, circular, or something else?
\item At how many points in the area is the electric field equal to
zero?
\item Give the coordinates of those points where $E = 0$.
\end{enumerate}

The main features of this simulation exercise are shown below.

\begin{figure}[h]
\begin{center}
% This is 405 pixels wide (4.05 in) and 303 pixels high (3.03 in).
% We need to shrink it.
% A scale of 2/3 will make it 2.70 in (great) x 2.02 in and end up as
% a pair of printer pixels per picture pixel.  (Say six times fast!)
\includegraphics[width=2.70in,height=2.02in]{thkgauss.gif}
\end{center}
\iftechexplorer\else\vspace{-15 pt}\fi
\caption{Gauss's Law Simulation Exercise.  The green circle is the
footprint of a cylindrical Gaussian surface; the surface encloses
$2\,\mu\mathrm{C}$ of charge.  The length of an arrow or the color of
a fieldline indicates the strength of the electric field at a point;
red is strong field, and blue is weak field.  The arrows are tangent
to the field lines and indicate the direction of the electric field.}
\end{figure}

\subsection{Spreadsheet Exercise}

% Here we go again.  Oh, the pain, the pain...
(\href{http://links.math.rpi.edu/devmodules/electromagnetism/Gauss/html/esphere.html}%
{http://links.math.rpi.edu/devmodules/}\urlbreak
\href{http://links.math.rpi.edu/devmodules/electromagnetism/Gauss/html/esphere.html}%
{electromagnetism/Gauss/html/esphere.html})
 
The Excel spreadsheet named ``\texttt{E-sphere.xls}'' uses Gauss's Law
to calculate and graph the strength of the electric field due to a
spherically symmetric charge distribution.  It will calculate the
electric field from the center of the spherical distribution out to
the distance designated as $R_{\mathrm{max}}$; in the spreadsheet,
$R_{\mathrm{max}}= 1.0\,\mathrm{m}$.  When the spreadsheet opens,
there is a uniform positive charge density of $1.0 \times
10^{-6}\,\mathrm{C}/\mathrm{m}^3$ from $R = 0$ to $R =
0.4\,\mathrm{m}$ and no charge beyond that.  The electric field for
this charge distribution is shown in Figure~\ref{hkss1}.
\begin{figure}[tb]
\begin{center}
\includegraphics[scale=0.6666666667]{thk1.gif}
\end{center}
\iftechexplorer\else\vspace{-15 pt}\fi
\caption{Electric Field of Uniformly Charged Sphere}
\label{hkss1}
\end{figure}

\def\sscell#1{\textsf{#1}}

The program sums the charge over spherical shells of thickness
$\mathrm{d}R$, which is given as $0.01\,\mathrm{m}$ in cell
\sscell{B3}. There are 100 shells. The radii of the surfaces of the
shells are listed in cells \sscell{A10} through \sscell{A110}. In
cells \sscell{B10} through \sscell{B109}, the relative charge density
is listed for each shell, next to the value of the radius.  If the
values of the relative charge density in any of the cells \sscell{B10}
through \sscell{B109} are changed, everything is re-calculated
automatically, and the graph is redrawn.

Students are asked to do spreadsheet calculations and turn in the
following report:
\begin{enumerate}
\setlength{\itemsep}{0 pt}
\item A sketch of the graph of $E$ vs.\ $R$ for a hollow sphere with
no charge from $R = 0$ to $R = 0.2\,\mathrm{m}$, and a uniform charge
density from $R = 0.2\,\mathrm{m}$ to $R = 0.4\,\mathrm{m}$.  (See
Figure~\ref{hkss2}.)

\begin{figure}[bt]
\begin{center}
\includegraphics[scale=0.6666666667]{thk2.gif}
\end{center}
\iftechexplorer\else\vspace{-15 pt}\fi
\caption{Electric Field of Hollow Sphere}
\label{hkss2}
\end{figure}

\item The constant relative charge density for the inner region ($R =
0$ to $0.2\,\mathrm{m}$) that produces a field of zero for $R >
0.4\,\mathrm{m}$.
\item A sketch of the graph of $E$ vs.\ $R$ for a sphere with a
negative charge from $R = 0$ to $R = 0.2\,\mathrm{m}$, and positive
charge from $R = 0.2\,\mathrm{m}$ to $R = 0.4\,\mathrm{m}$, such that
$E = 0$ for $R > 0.4\,\mathrm{m}$.  (See Figure~\ref{hkss3}.)

\begin{figure}[b]
\begin{center}
\includegraphics[scale=0.6666666667]{thk3.gif}
\end{center}
\iftechexplorer\else\vspace{-15 pt}\fi
\caption{Electric Field of Nonuniform Sphere}
\label{hkss3}
\end{figure}
\end{enumerate}

\subsection{Classroom Discussion}

In the previous spreadsheet exercises, most students can answer the
questions even with only a qualitative understanding of Gauss's Law.
For example, they are asked to find the constant charge density for
the inner region ($R=0$ to $0.2\,\mathrm{m}$) that produces zero
electric field for $R>0.4\,\mathrm{m}$.  If the student understands
from Gauss's Law that the total charge inside $R=0.4\,\mathrm{m}$ has
to be zero, he can see that the required charge density in the inner
region ($R=0$ to $0.2\,\mathrm{m}$) must be negative.  Most students
then try various negative values while looking at the $E$ vs.\ $R$
plots, until the correct value $\rho = -7 \rho_0$ is obtained.

After the spreadsheet exercise, we ask the students to obtain this
charge density and the corresponding electric field as a function of
distance analytically.

\section*{Summary}

In the studio teaching method illustrated above, we attempt to use
different kinds of activities to illustrate one major physics topic in
one integrated studio class.

We have developed similar applets and spreadsheet exercises for other
topics in Electricity and Magnetism as well as other physics
classes. Further developmental work and classroom applications are
also in progress.

\iftechexplorer
\section*{References}
\fi

\begin{thebibliography}{9}

\bibitem{wilson_studio} Jack M. Wilson, ``The CUPLE Physics Studio'',
\textsl{Physics Teacher} \textbf{32}, 518--523 (1994).

\bibitem{links_cip} William E. Boyce, John B. Brunski, Michael
M. Chen, Kevin Craig, James A. Fairweather, Joseph W. Haus, Joseph
Porter, and William L. Siegmann, ``Interactive Multimedia Modules in
Mathematics, Engineering, and Science'', \textsl{Computers in Physics}
\textbf{11}, 151--156 (1997).  An introduction to Project Links.

\end{thebibliography}

\section*{Acknowledgements}

This work has been developed with Project Links
(\href{http://links.math.rpi.edu/}{http://links.math.rpi.edu/}) and
has been supported in part by National Science Foundation grant
\#DUE--9552465.

\end{document}
