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Physics LibreTexts

5.8.7: Solid Cylinder

( \newcommand{\kernel}{\mathrm{null}\,}\)

Refer to figure V.8. The potential from the elemental disc is

dψ=2πGρδz[(z2+a2)1/2z]

and therefore the potential from the entire cylinder is

ψ=const.2πGρ[h+lh(z2+a2)1/2dzh+1hzdz].

I leave it to the reader to carry out this integration and obtain a final expression. One way to deal with the first integral might be to try z=atanθ. This may lead to sec3θdθ. From there, you could try something like sec3θ=secθdtanθ=secθtanθtanθdsecθ=secθtanθsecθtan2θdθ=secθtanθsec3θ+secθdθ, and so on.


This page titled 5.8.7: Solid Cylinder is shared under a CC BY-NC 4.0 license and was authored, remixed, and/or curated by Jeremy Tatum via source content that was edited to the style and standards of the LibreTexts platform.

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