• scalar fields
• electrostatic potentials

Approximate Time: 20 minutes

Use a pre-made Maple worksheet to visualize the electrostatic potential of several distributions of charges. The Maple worksheet has several different ways of plotting the potential.

We find it valuable to use this activity AFTER students have done an activity drawing equipotential surfaces (see the Equipotential Surfaces Activity ). This pair of activities bolster students' geometric sensemaking of potentials.

Sometimes, we have students do this activity after they have had practice calculating electrostatic potentials (see the Electrostatic Potentials Due to Two Point Charges Activity ). We have also used this activity BEFORE the two point charges activity. This also works quite well.

• Computers with Maple/Mathematica

This activity starts with prompting the students to brainstorm different ways to represent a three dimensional scalar field on a 2-D surface (like their paper or a whiteboard). (  5 minutes, can be done as a whole class discussion or in small groups)

It is a good idea to put the least confident member of each group at the keyboard. This helps to ensure that everyone is comfortable with the technology. Do not hesitate to encourage a group to change its typist if the current one is typing too quickly.

This activity can be used very effectively in a context where students are asked to brainstorm about ways in which they might graphically represent the electrostatic potential. They should be reminded to think about the fact that the electrostatic potential is a scalar field, i.e. it is a number (with appropriate units) at every point in THREE dimensional space. As the students generate ideas, the instructor projects each choice from the Maple worksheet for the students to examine/discuss.

A pedagogically useful representation is for each number at a point to be represented by a color. Then the students can imagine how they would try to show this “sea” of colors on a two-dimensional graph.

If using Mathematica, it is well worth showing students how to create a new line so they can enter new mathematical input. This requires moving the mouse between existing blocks; the pointer should change to a horizontal line.

No particular wrap-up is necessary.

A Mathematica notebook that draws nice 3d contour plots of each of the 5 potentials in this worksheet can be found here.

This activity is part of a sequence of activities addressing Representations of Scalar Fields in the context of electrostatics.

• Prerequisite activities:
  • Electrostatic Potential due to a Point Charge: This small whiteboard question asks students to recall the electrostatic potential due to a point charge which results in discussions likely to include notation of the distance from the origin to a point charge.
  • Drawing Equipotential Surfaces: This small group activity has students construct a contour plot of the electrostatic potential, level curves of equipotential, in the plane of four point charges.

• Follow-up activities:
  • Electric Potential Due to a Ring Mathematica Extension: This small group activity begins with students solving for the electrostatic potential due to a charged ring everywhere in space, an elliptic integral, and then use power series to approximate the potential at various locations in the scalar field. As an extension, students use a Mathematica notebook to visualize the electrostatic potential over all space in various representations.