5.8.4: Infinite Plane Lamina

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 \(+2 \pi Gσh\).

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