Electrostatic Potential for Ring of Charge
Instructor Guide
Keywords:
Upperdivision, E and M, Electrostatic Potential, Symmetry,
Ring
Brief overview of the activity
In this activity, students work in small groups to write the electrostatic po
tential everywhere in space due to a charged ring.
This activity brings together student understanding of:
1. Electrostatic potential
2. Spherical and cylindrical coordinates
3. Superposition
4. Integration as ”chopping and adding”
5. Linear charge density
6. 3dimensional geometric reasoning
7. Power series expansion
Student prerequisite skills
This activity is may be used as the second in a sequence, following the elec
trostatic potential  discrete charges activity, or may be used on its own.
Students will need understandings of:
1. The prerequisites addressed in the
electrostatic potential  discrete
charges activity
.
2. Spherical and cylindrical coordinates.
Link to spherical and cylindrical
coordinates activity
.
3. Integration as chopping and adding.
Link to Integration activity.
1
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4. Linear charge density
Props
•
Hula hoop or other thin ring
•
Balls to represent point charges
•
Voltmeter
•
Coordinate system (e.g. with straws or Tinkertoys)
•
Postersized whiteboards
•
markers
•
whiteboards around room.
Link to room setup
.
The activity  Allow 50 minutes.
Overview
Part I
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 potential due to
this ring in all space.” Students do their work collectively with markers on a
postersized sheet of whiteboard at their tables.
Link to worked solution
resulting in an elliptic integral
.
Part II
Students determine the power series expansion to represent the electrostatic
potential due to the charged ring along a particular axis.
Link to worked
solutions for power series expansions.
Note:
students should not be told
about part II until they have completed part I.
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 Fall '06
 Culbertson
 Charge, Work

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