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  "body": "\n## Summary\n\nA condenser is a pair $(K, \\Omega)$ of a compact set $K$ inside an open set $\\Omega \\subseteq \\R^n$.\nIts capacity is the least Dirichlet energy $\\int_\\Omega \\abs{\\nabla u}^2 \\, dx$ of a function that is at least $1$ on $K$ and vanishes near the boundary of $\\Omega$.\nIt is the case $p = 2$ of the [[variational capacity|A1KWT817JX]].\nCondenser capacity works in every dimension, including the plane.\nIt is a basic tool in the theory of quasiconformal maps through the conformal modulus of ring domains.\n\n## Explanations\n\n### L1 human\n\nA physical capacitor has two conductors: an inner plate $K$ and an outer shell, the boundary of $\\Omega$.\nHold $K$ at voltage $1$ and the shell at voltage $0$.\nThe capacity is the charge needed to keep this voltage difference, and it equals the energy of the electric field between the plates.\nFor two concentric spheres of radii $r \u003c R$ in space, the capacity is $4 \\pi r R / (R - r)$, which grows without bound as the two spheres come close.\nAs $R$ tends to infinity it tends to $4 \\pi r$, the [[capacity|4YZVFGJVSZ]] of a single ball.\n",
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