Student difficulties with Boundary Conditions in electrodynamics

TL;DR

This study investigates common student difficulties with boundary conditions in electrodynamics through analysis of exam responses, surveys, and interviews, highlighting specific conceptual and mathematical challenges faced by students.

Contribution

It identifies key student misconceptions and difficulties with boundary conditions in electrodynamics, providing insights for targeted teaching strategies.

Findings

Students struggle to activate boundary conditions appropriately.

Students have difficulty constructing and simplifying complex exponential expressions.

Students often fail to verify the physical validity of reflection and transmission coefficients.

Abstract

Boundary conditions (BCs) are considered as an important topic that advanced physics under- graduates are expected to understand and apply. We report findings from an investigation of student difficulties using boundary conditions (BCs) in 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, con- struct, execute, and reflect on boundary conditions. Common student difficulties include: activating boundary conditions in appropriate contexts; constructing a complex expression for the E&M waves; mathematically simplifying complex exponentials and checking if the reflection and transmission co- efficient are physical. We also present potential pedagogical implications based on our observations.