Students examine a plastic "surface" graph of the electric potential due to two changes plates (near the center of the plates) and explore the properties of the electric potential.
What Students Learn:
- How to interpret a surface plot (plastic surface model) of the potential due to a parallel plate capacitor
- The potential near the center of two charged plates is a plane (constant slope)
- Equipotential curves represent a single value of potential
- Equipotential curves for the center of two charged plates are equally spaced horizontally
- The height of zero potential is arbitrary/chosen for convenience
Time estimate: 15 minutes
Equipment:
- Yellow plastic surface
- Big Whiteboard (1 per group)
- Contour map for a parallel plate capacitor in a plastic sleeve (1 per group)
- Ruler (1 per group)
- Dry-erase pens and erasers (1 each per student)
- Student handout (1 per student)
Introduction
- Try doing this activity BEFORE you talk about the electric field of a parallel plate capacitor and follow up with the “Electric Potential of a Parallel Plate Capacitor” surface activity.
- Students should know that a parallel plate capacitor is two charged planes separated by a distance.
- Students should be familiar with the term “potential” and maybe know the potential due to a point charge (not required but useful for one of the challenge questions).
- NOTE: We chose to have a uniform charge density on the plates rather than make the plates conductors. Therefore, the equipotential curves intersect the plates far from the center.
Whole Class Discussion / Wrap Up:
- Introduce the term “equipotential”
- Have the students propose an equation to describe the electric potential as a function of the distance, x, from the negative plate: \(V_{-\rightarrow +} = m\;x\) It's linear! Students will learn later that the slope, \(m\), is the magnitude of the electric field.
Before you is a plastic surface representing the electric potential between two charged plates. A 1 cm height difference corresponds to an electric potential difference of 1 V.
This question is very straightforward and intuitive for students.
Mark three points on the surface that are separated by equal (non-zero!) changes in potential.
Points should represent equal changes in height. They need not be along a straight line!
Answer: Students should notice that the points with the same potential are straight lines that are equally spaced horizontally.
Extension: What shape of surface would yield lines not equally spaced horizontally? Curved?
Answer: The surface should be in the middle of the capacitor with the lower end of the surface at the negative plate.
Discussion: Ask students to share their alignment strategies:
Extension: Is the value of the potential negative at the location of the negatively charged plate?
- Matching Contours: Each contour represents a single value of potential. The surface should go in the region where the contours are parallel and equally spaced on the contour map.
- Negative Plate: Students might know or have intuition that the lowest potential will be aligned with the negative plate.
Extension: Write a symbolic equation for the potential.
Extension: What do you think the potential is not negative near the negative plate?
Extension: Why is it reasonable that the curves of constant potential are straight lines?