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  "body": "\n## Summary\n\nThe logarithmic capacity of a compact set $K$ in the plane measures how large $K$ is from the point of view of [[potential theory|9PM8Q2E30Q]].\nIt is defined from the least possible logarithmic energy of a unit charge distributed on $K$.\nA disc of radius $r$ has capacity $r$, and a line segment of length $L$ has capacity $L/4$.\nSets of capacity zero, the polar sets, are negligible for many questions on harmonic and holomorphic functions.\nExamples are removable singularities and the solvability of the [[Dirichlet problem|8D56GQ4AG8]].\n\n## Explanations\n\n### L1 human\n\nSpread one unit of electric charge on a conducting plate shaped like $K$, in a two-dimensional world where the potential of a point charge is logarithmic.\nThe charge arranges itself to make the energy as small as possible.\nThe smaller that minimal energy, the larger the capacity.\nA finite set of points cannot hold any charge with finite energy, so it has capacity $0$, while a disc of radius $r$ has capacity $r$.\n",
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