Revisiting the displacement current: Two key examples showing when and why it can be neglected

TL;DR

This paper examines the significance of displacement current beyond capacitors, demonstrating when it can be neglected and emphasizing its importance in dynamic electromagnetic systems through two illustrative examples.

Contribution

It provides a detailed analysis of conditions where displacement current is negligible, extending understanding beyond traditional capacitor scenarios and clarifying its role in dynamic regimes.

Findings

Displacement current is negligible at low frequencies in coaxial cables and resistors.

In dynamic regimes, displacement current is essential for accurate electromagnetic descriptions.

Simplified models like Biot-Savart are valid only under specific conditions.

Abstract

This work explores the role of the displacement current in systems beyond capacitors, focusing on coaxial cables and resistors with alternating currents. Although its contribution, compared to that of the conduction current, is negligible at low frequencies, the displacement current becomes essential for accurately describing electromagnetic fields in dynamic regimes. Introductory physics textbooks typically restrict the discussion of displacement currents to capacitor charging, which can limit the students' understanding of its broader relevance and the interdependence of Maxwell's equations. By analyzing two specific cases, we clarify the conditions under which the displacement current can be neglected, when simplified laws like Biot-Savart are valid, and where coupled electromagnetic equations are essential. This approach highlights the boundaries of common models and promotes a deeper understanding of dynamic field interactions.