# Recall the Electrostatic Potential Due to a Point Charge

## Prompt

“Write down what the potential is due to a point charge.”

## Context

This SWBQ can be used as a transition between the Star Trek Activity, where students are learning about how to describe (algebraically) the geometric distance between two points, and the Two Charges Activity, where students are using these results and the superposition principle to find the electrostatic potential due to two point charges.

Moreover, this activity is the initial activity on the sequence addressing the Representations of Scalar Fields in the context of electrostatics.

• Follow-up activities:
• 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.
• Visualizing Electrostatic Potentials: 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.
• 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.

This activity also has an accompanying narrative, The Potential of a Point Charge.

## Wrap Up

##### Answers you're likely to see
• Two Charges

$V=\frac{kq_{1}q_{2}}{r}$

• Distance squared

$V=\frac{kq}{r^2}$

• Vectors

$V=\frac{kq\vec r}{r^2}$

• Various constants

$V=\frac{kq}{r}$

$V=\frac{1}{4\pi\epsilon_0}\frac{q}{r}$

##### Possible Conversations
• Which function falls off faster: $1/r$ or $1/r^2$?
• Which function is the derivative of the other: $1/r$ or $1/r^2$?
• What is the electric potential conceptually?
• What are the dimensions of potential? Units?
• Where is the zero of potential?
• You may need to talk about how a voltmeter actually works, rather than idealizing it.
• Students often want to know about the “ground” lead. We often tie a long string to it (to symbolize making a really long wire) and send the TA out of the room with the string, “headed off to infinity” while discussing the importance of setting the zero of potential. The extra minute or two of byplay gives the importance of the zero of potential a chance to sink in.

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