# Student Difficulties with Boundary Conditions in Electrodynamics

## TL;DR

This study investigates undergraduate student difficulties with boundary conditions in electrodynamics, revealing common challenges in activation, construction, and manipulation of boundary condition problems, with implications for teaching strategies.

## Contribution

It provides detailed insights into specific student difficulties with boundary conditions in electrodynamics through multiple data sources and analytical frameworks.

## Key findings

- Students struggle to activate boundary conditions appropriately.
- Students have difficulty constructing and simplifying complex expressions.
- Misinterpretation of reflection and transmission coefficients as physical quantities.

## Abstract

Identifying and understanding student difficulties with physics content in a wide variety of topical areas is an active research area within the PER community. In many cases, physics topics appear multiple times in different contexts across the undergraduate physics curriculum. As these common topics reappear, student difficulties can perpetuate from one context to the next, or new difficulties can emerge as students encounter new physical contexts. One example of such a topic is boundary conditions. It is broadly considered to be an important topic that advanced physics undergraduates are expected to understand and apply in multiple topical areas including classical mechanics, quantum mechanics, and throughout electricity and magnetism (EM). We report findings from an investigation of student difficulties using boundary conditions focusing on the context of electrodynamics. Our data sources include student responses to traditional exam questions, conceptual survey questions, and think aloud interviews. The analysis was guided by an analytical framework that characterizes how students activate, construct, execute, and reflect on boundary conditions. Common observed student difficulties include: activating boundary conditions in appropriate contexts; constructing a complex expression for the E&M waves; mathematically simplifying and manipulating complex exponential and, checking if the reflection and transmission coefficient are physical. We also present potential pedagogical implications based on our observations.