Skip to main content
\(\require{cancel}\)
Physics LibreTexts

5.8.4: Infinite Plane Lamina

  • Page ID
    8148
  • \( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \) \( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)\(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\) \(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\)

    The field above an infinite uniform plane lamina of surface density \(σ\) is \(−2 \pi Gσ\). Let \(\text{A}\) be a point at a distance a from the lamina and \(\text{B}\) be a point at a distance \(b\) from the lamina (with \(b > a\)), the potential difference between \(\text{B}\) and \(\text{A}\) is

    \[ψ_{\text{B}} - ψ_{\text{A}} = 2 \pi G σ (b-a). \label{5.8.14} \tag{5.8.14}\]

    If we elect to call the potential zero at the surface of the lamina, then, at a distance \(h\) from the lamina, the potential will be \(+2 \pi Gσh\).


    This page titled 5.8.4: Infinite Plane Lamina 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; a detailed edit history is available upon request.

    • Was this article helpful?