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Unformatted text preview: Electrostatic Potential for Ring of Charge Instructor Guide Keywords: Upper-division, 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. 3-dimensional 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 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) Poster-sized whiteboards markers whiteboards around room. Link to room set-up . 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 poster-sized 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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