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  "body": "\n## Summary\n\nThe logarithmic potential of a finite measure $\\mu$ with compact support in the plane is $p_\\mu(z) = \\int \\log(1/\\abs{z - w}) \\, d\\mu(w)$.\nIt is the [[potential of the measure|JHKSF3XFY2]] $\\mu$ with respect to the [[logarithmic kernel|VDZ5FKYC2T]].\nIt is harmonic off the support of $\\mu$ and superharmonic on the whole plane.\nLogarithmic potentials connect potential theory with complex analysis.\nFor a polynomial $p$ with zeros $z_1, \\dots, z_d$, $\\log(1/\\abs{p})$ is, up to a constant, the logarithmic potential of the point masses at the zeros.\n\n## Explanations\n\n### L1 human\n\nIn the plane a point charge creates a potential that changes like the logarithm of the distance.\nSpread charge along a curve or over a region, and add up the logarithmic contributions: this is the logarithmic potential.\nFor one unit charge at the origin it is $\\log(1/\\abs{z})$.\nFor a monic polynomial $p(z) = (z - z_1)\\cdots(z - z_d)$, the potential of unit charges at the roots is $-\\log\\abs{p(z)}$.\n",
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