Paschen’s law for non-uniform fields using a rod-plane gap

Abstract Paschen’s law describes the breakdown voltage of a gas as a function of gap distance and gas pressure. This fundamental principle of high-voltage physics and engineering significantly impacts the operation, design, and safety of various electrical and plasma-based technologies, including air ionizers, aircraft, and satellites. Originally developed for uniform electric fields, such as those between two parallel plates or spheres, Paschen’s law determines the voltage required to initiate an electric arc. It predicts that the breakdown voltage is a unique function of the pressure-distance product p · d , with a minimum value occurring at a specific p · d . This work proposes a practical laboratory session or guided project for physics or engineering courses to determine Paschen’s law based on laboratory measurements for non-uniform electrode geometries under a 50 Hz sinusoidal supply. A rod-plane gap geometry produces a highly non-uniform electric field distribution, enabling corona discharges to occur before complete breakdown of the air gap. The experimental results presented here indicate that partial discharges tend to occur at higher p · d values for a rod-plane geometry than predicted by Paschen’s law. However, the results approach Paschen’s values as the p · d product decreases. Additionally, the results show that corona discharges occur well before complete air gap breakdown at high p · d values, and that each pressure has a unique curve relating breakdown voltage to the p · d product. Therefore, the results deviate from original Paschen’s law. This paper analyzes the concepts of partial discharges and complete breakdown and discusses the conditions leading to one or the other. The discharges were detected by remotely controlling a smartphone camera via open-source software. A complete dataset is provided that can be used directly for developing practical or guided projects. Students also have the option of acquiring their own data using the simple experimental setup outlined in this paper.