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## Superposition of Electrostatic Potential due to Point Charges

This sequence of activities can directly follow the Representations of Two-Dimensional Scalar Fields sequence.

### Activities

**Recall the Electrostatic Potential due to a Point Charge***(Estimated time: 5 minutes)*: This small whiteboard question asks students to write a formula for the electrostatic potential everywhere in space due to a point charge. Discussions which will likely arise include notation of the distance from the origin to the point charge, the constants in the equation, and the dimensions of the equation. The representation used by students is predictably algebraic in form, however, the discussion can include other representations of a one-dimensional electrostatic potential.

**Lecture on Electrostatic Potential and Superposition of Charges***(Estimated time: 20 minutes)*: This lecture introduces students to the electrostatic potential by discussing how to measure the potential, what the formulas generated from Recall the Electrostatic Potential due to a Point Charge mean, and the potential at the location of the point charge and infinity. Next, the principle of superposition is introduced by discussing superposing the electrostatic potential due to point charges.

**Drawing Equipotential Surfaces***(Estimated time: 45 minutes)*: This small group activity encourages students to work in the plane of four point charges arranged in a square to find level curves of equipotential. Students construct a contour plot of the electrostatic potential in the plane of the four charges and explore the constructed scalar field close to the charges, far from the charges, and at important points in the field. Most students are familiar with the elementary equation of the electrostatic potential but few reconcile the equation with the geometry of a scalar field. This small group activity forces students to explicitly work out the geometry of the potential of a quadrupole, allowing them to realize what's “scalar” about the electrostatic potential.

**PhET: Charges and Fields 2.04***(Estimated time: )*: http://phet.colorado.edu/sims/charges-and-fields_en.html

**Visualizing Electrostatic Potentials***(Estimated time: 20 minutes)*: Students begin by brainstorming ways in which to represent three-dimensional scalar fields in two-dimensions and then use a Mathematica notebook to explore various representations for a distribution of point charges. This activity allows students to check their solutions to Drawing Equipotential Surfaces as well as explore other representations. Students recognize that the electrostatic potential is a function of three spatial variables which requires an alternative way to represent the potential such as the use of color and plotting equipotential surfaces. This activity can be used exclusively with the quadrupole to extend Drawing Equipotential Surfaces by drawing on more representations of the configuration of point charges without taking up much more class time.