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 $+2 \pi Gσh$.