کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
727167 | 892706 | 2009 | 6 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Axially symmetric charge distributions and the arithmetic-geometric mean
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
سایر رشته های مهندسی
مهندسی برق و الکترونیک
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چکیده انگلیسی
The potential at an arbitrary point in space due to an axially symmetric charge distribution is related to the arithmetic-geometric mean of the maximum and minimum distances from each annulus of constant charge density. The arithmetic-geometric mean is expressible in terms of the elliptic integral of the first kind, K. Thus the potential of a charged body with cylindrical symmetry is reducible to a double integral over the charge density times K. For conductors the charge resides on the surface, and the potential reduces to a single integral over the surface charge density times K. This result leads to a new proof of the relation between a sum over products of Legendre polynomials and the complete elliptic integral of the first kind, and to new identities for the angular average of Legendre polynomials divided by |rârâ²|. The method also provides a direct route to the capacitance of a slender torus, without the use of toroidal coordinates.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Electrostatics - Volume 67, Issue 6, November 2009, Pages 880-885
Journal: Journal of Electrostatics - Volume 67, Issue 6, November 2009, Pages 880-885
نویسندگان
John Lekner,