Common Misunderstandings and Challenges in Learning Gauss’s Law in a Junior Level Electromagnetic Engineering Course

Abstract

Common misunderstandings when learning Gauss’s Law in a college junior level electromagnetic engineering course are identified by observing normal course assessments and conducting one on one student interviews. Additionally, the extent to which students in this course struggle to translate prior mathematics is investigated by codifying student performance on normal assessments using a rubric developed by the authors based on Accreditation Board for Engineering and Technology (ABET) Criterion 3 (a) and (e). Five misconceptions are identified, three of which agree with physics educational literature, as well as a need for better scaffolding the translation of calculus II and multidimensional calculus material. Future work and possible intervention strategies are discussed.

This work has received IRB approval IRB# x16-1616e (i053116) from Michigan State University’s Internal Review Board for research with human subjects.

Appendices

Appendix A: Student Interview Prompt and Line of Questioning

A uniformly charged dielectric material having charge density $\rho _v = 2~C/m^3$ and dielectric constant of $\epsilon _r = 5$ encloses a dielectric sphere with dielectric constant $\epsilon _r = 3$ as shown in the figure. The entire structure is enclosed in a charge shell of total charge Q, and surrounded by free space ($\epsilon _r = 1$). We are interest in $\overrightarrow{E}$ in all regions (Fig. 1).

Fig. 1.

Visualization of described problem in statement.

• 1. Is it clear from the description and figure what is going on in this system?

• 2. If you were asked to solve for the electric field everywhere in this system, what would your approach be to solve the problem. You don’t actually have to solve it just list the steps for solving it.

• 3. Is using Gauss’s Law valid for this problem? Why or why not?

• 4. Can you write Gauss’s Law and tell me what it means? What two fundamental quantities does it allow us to relate?

• 5. If you were asked to find the electric field everywhere, where is everywhere? Please describe the different regions or areas in this system.

• 6. How would you setup the integral for the charge enclosed for each of the regions? Please write the integral setup, you don’t need to take it.

• 7. How would you setup the integral for the Gaussian surface each of the regions? Please write the integral setup, you don’t need to take it.

• 8. Would there be no electric field in any of these regions/spaces? Why or why not?

Appendix B: ABET Based Assessment Rubric

(a) Identify the mathematics, engineering, science, topics in the problem	$\bullet$ Identifies when a major law or formula is applicable $\bullet$ Identifies when relations between fundamental quantities (current, voltage, etc.) can be used $\bullet$ Identify when material property definitions can be applied	$\bullet$ Does not explicitly state the most applicable law in problem setup $\bullet$ Does not explicitly state equation used for fundamental quantity relations (voltage, current, etc.) $\bullet$ Does not explicitly state definitions or picks a suboptimal definition (one that does not quite align with the given information)	$\bullet$ Does not identify a major law or relation $\bullet$ Does not identify when equations for simplification can be applied $\bullet$ Does not identify basic quantity definitions
(b) Formulate an approach	$\bullet$ Shows coherent steps of relations between the given information and the requested information	$\bullet$ Shows some relevant relations	$\bullet$ Does not relate quantities given in the problem to those requested as final answers
(c) Apply this approach to the problem	$\bullet$ Correctly setup the necessary integrations $\bullet$ Correctly setup other mathematical relations with the given quantities	$\bullet$ Sets up the integration with minor errors such as forgetting a term, incorrect sign, incorrect limits $\bullet$ Sets up relations with minor errors such as forgetting a term or incorrect sign	$\bullet$ Incorrectly setup integrations $\bullet$ Incorrectly setup mathematical relationships
(d) Obtain correct results	$\bullet$ Final answer is correct $\bullet$ Appropriate units and vector directions are included	$\bullet$ Final answer has a sign error or is off by a small amount $\bullet$ Included units or vector direction but not both were not quite correct	$\bullet$ No final answer or answer is incorrect $\bullet$ No units or vector directions included