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\section*{Electrostatic Field for Ring of Charge}
\section*{Instructor Guide}
Keywords: Upper-division, E and M, Electric Field, Symmetry, Ring

\subsection*{Brief overview of the activity}
In this activity, students work in small groups to find the electric
field everywhere in space due to a charged ring.

\subsection*{This activity brings together student understanding
of:}
\begin{enumerate}
\item Electric Field
\item Spherical and cylindrical coordinates
\item Superposition
\item Integration as "chopping and adding"
\item Understanding of which variables are variable and which are held constant during
integration
\item Linear charge density
\item 3-dimensioinal geometric reasoning
\end{enumerate}
\subsection*{Student prerequisite skills}

This activity was designed to be used following the electrostatic
potential - ring activity.  If this activity is being used on its
own, the instructor should look at the electric potential activity
to understand the types of things students will encounter with this
ring problem.  Students will need understandings of:

\begin{enumerate}
\item The prerequisites addressed in the electrostatic potential -
ring activity.
\item Which variables are variable and which are held
constant during integration. \texttt{Link to helping students
understand what is variable are what is held constant}.
\item Electric field
\end{enumerate}
\subsection*{Props}
\begin{itemize}
\item Hula hoop or other thin ring
\item Balls to represent point
charges
\item Coordinate system (e.g. with straws or Tinkertoys)
\item Poster-sized whiteboards
\item markers
\item whiteboards around room. \texttt{Link to room set-up}.
\end{itemize}
\section*{The activity - Allow 30 minutes.}

\subsection*{Overview}

Students should be assigned to work in groups of three and given the
following instructions using the visual of a hula hoop or other
large ring: ``This is a ring with total charge $Q$ and radius $R$.
Find the electrical field due to this ring in all space.'' Students
do their work collectively with markers on a poster-sized sheet of
whiteboard at their tables. \texttt{Link to worked solution
resulting in an elliptic integral}.

\subsection*{What the students will be challenged by and how to facilitate their
learning}

This description assumes students have already completed the
\texttt{Electrostatic Potential - Ring} activity.  This activity
expands upon and reinforces the concepts from the previous activity.
If students thoroughly understood parts of the previous activity,
they may find this activity fairly easy. On the other hand, if they
received a lot of help during the previous activity and had a weaker
understanding, this will help them to understand those previous
concepts. The instructor can help ``tweak'' and extend the
understanding of the strongest students and can make sure the weaker
students are truly understanding the essential concepts
\begin{enumerate}
\item Students will need to consider the vector nature of the field.
The scalar field in the previous example of electrical potential
requires different geometric arguments and different symmetry
considerations than the electric field. Thinking about these
differences helps students more clearly understand the differences
between electrical potential and electric field. Prior to this
activity, we had a lecture about the vector nature of electric
fields that goes beyond the $V = {kq\over r^2}$ from earlier
courses. \texttt{Link to helping students understand electric field
vectors}.

\item As in the previous activity, this activity also gives students
the opportunity to use curvilinear coordinates and rectangular
coordinates in combination to create an elliptic integral. For a
description of the issues involved, see the electrostatic potential
- ring activity, item 5 under ``what students will be challenged by
and how to facilitate their learning.'' For a worked solution to the
electric field problem see the \texttt{link to the worked solution
resulting in an elliptic integral}.
\end{enumerate}

\subsection*{Debriefing, Whole-Class Discussion, Wrap-up and
Follow-up}
\begin{itemize}
\item Discuss-
\item Maple-Link to Maple worksheet
\item Suggested homework -
\end{itemize}

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