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

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.