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PIER PIER B PIER C PIER M PIER Letters PIER Photonics
2026-10-10
Analytical Calculation of the Electrostatic Field of a Charged Conducting Spherical Shell with a Circular Aperture
By
Hanyu Wu,

    Dr. Hanyu Wu

    North China Electric Power University

    China

    Homepage

Herui Cheng,

    Dr. Herui Cheng

    North China Electric Power University

    China

    Homepage

Xinyi Jiang,

    Dr. Xinyi Jiang

    North China Electric Power University

    China

    Homepage

Chongqing Jiao

    Professor Chongqing Jiao

    North China Electric Power University

    China

    Homepage

Progress In Electromagnetics Research Letters, Vol. 132, 16-23, 2026
doi:10.2528/PIERL26072301 | Google Scholar

Abstract
In electrostatic shielding, previous studies have focused on shielding external electric fields using electrically neutral shielding shells. Here, we consider a new situation in which the electric field generated by the charge on the shielding shell penetrates the shield's interior through the shell's apertures. As a preliminary exploration of this situation, we started with relatively simple yet analytically solvable configurations. Specifically, we focus on configuring a thin-walled conducting spherical shell that is charged and has a circular aperture. For this configuration, we derive a series-form analytical solution for the potential distribution using the method of variable separation and present simplified solutions for the potential and electric-field strength along the central axis. Based on this analytical solution, we analyzed the characteristics of the potential and electric field distributions inside the spherical shell for different aperture sizes and found that, compared with a single aperture, placing two apertures at diametrically opposite positions on the spherical shell can significantly reduce the electric field strength in the region near the center of the sphere.
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Citation
Hanyu Wu, Herui Cheng, Xinyi Jiang, and Chongqing Jiao, "Analytical Calculation of the Electrostatic Field of a Charged Conducting Spherical Shell with a Circular Aperture," Progress In Electromagnetics Research Letters, Vol. 132, 16-23, 2026.
doi:10.2528/PIERL26072301
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