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Drawing Equipotential Surfaces for a Quadrupole: Instructor's Guide

Main Ideas

Students are asked to draw equipotential surfaces due to several simple charge configurations starting with the formula for the electrostatic potential due to a point charge and the superposition principle.

  1. They must clarify, in their own minds, the differences between the electric field $\Vec E$ and the electrostatic potential $V$. The electrostatic potential, $V$, is a scalar, not a vector.
  2. What does the superposition principle mean?
  3. The electrostatic potential, $V$, exists in three-dimensions, not just two.

Students' Task

Approximate Time: 45 minutes

Students are asked to draw lines of constant electrostatic potential due to a quadrupole distribution of charges. The prompt should ask them to use the formula for the potential due to a point charge and the superposition principle and not to use reasoning from other courses.

Prerequisites

None

Props/Equipment

Activity: Introduction

Introduce the formula for the electrostatic potential due to a point charge: $$V(\Vec r)=\frac{1}{4\pi\epsilon_0} \frac{q}{|\Vec r - \Vec r'|}$$ and introduce the idea of the superposition principle.

Activity: Student Conversations

Most students find this activity very challenging, even though these students had already done an activity in which they considered two point charges and were required to find the series expansion for the electric potential along an axis.

The types of things that were common for students to do:

Activity: Wrap-up

Emphasize what information about the equipotential surfaces comes from the formula $$V(\Vec r)=\frac{1}{4\pi\epsilon_0} \frac{q}{|\Vec r - \Vec r'|}$$ together with the superposition principle, and what information comes from other things that they may have learned in intro courses about the electric field $\Vec E$.

Extensions

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