The key highlights and insights from the content are:
The interaction between two charged spherical conductors in an electric field is a complex problem involving several factors such as the separation distance, size, charges, and the applied external electric field.
The force expressions involve 10 force coefficients (F1, F2, ..., F10) which are functions of these factors and are represented by 24 infinite series.
As the gap between the two spheres approaches zero, the convergence of these series becomes computationally expensive, requiring numerous terms.
The study employs the method of matched asymptotic expansions to derive the asymptotic expressions for these 24 series, specifically for the scenario involving two equal-sized charged conducting spheres in an external electric field.
The asymptotic expressions are obtained by partitioning the series into "inner" and "outer" expansions, and then matching them within their common area of validity.
The derived asymptotic expressions are used to compute the 10 force coefficients and the electrostatic force for small separations between the charged spherical conductors.
The accuracy of the asymptotic expressions is assessed by comparing them with the actual series and analyzing the percentage errors.
The results show that the asymptotic expressions can accurately capture the electrostatic force behavior, especially in the small separation region, where the series calculations become computationally intensive.
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arxiv.org
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by Natarajan Th... at arxiv.org 10-01-2024
https://arxiv.org/pdf/2409.19106.pdfDeeper Inquiries