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  "body": "\n## Summary\n\nThe Newtonian capacity of a compact set $K \\subseteq \\R^n$, $n \\ge 3$, measures how much electric charge $K$ can hold at unit potential.\nIt is the least Dirichlet energy of a function that is at least $1$ on $K$ and decays at infinity.\nCapacity is the right notion of size in [[potential theory|9PM8Q2E30Q]]: sets of capacity zero are the negligible sets for harmonic functions and for Sobolev functions.\nIn the plane its role is played by [[logarithmic capacity|DBQXRTC0VN]].\n\n## Explanations\n\n### L1 human\n\nImagine $K$ as a piece of metal held at voltage $1$, with voltage $0$ far away.\nThe capacity is the amount of charge that $K$ then carries, and it depends on the shape of $K$ and not only on its volume.\nA ball of radius $r$ in $\\R^3$ has capacity $4 \\pi r$ in the normalisation used here.\nA single point and a line segment in $\\R^3$ have capacity zero, while a flat disc has positive capacity.\nSo capacity sees thin sets in a different way from volume.\n",
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