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  "body": "\n## Summary\n\nThe fundamental solution of the Laplacian is a radial function $\\Phi$ on $\\R^n \\setminus \\set{0}$ with $-\\Delta \\Phi = \\delta$, the Dirac delta at the origin.\nIt equals $-\\frac{1}{2\\pi} \\log \\abs{x}$ in the plane and $\\frac{1}{n(n-2)\\omega_n} \\abs{x}^{2-n}$ in dimension $n \\ge 3$, where $\\omega_n$ is the volume of the unit ball.\nIt is the [[fundamental solution|K2NK9A8M5F]] of the Laplace operator that is used throughout potential theory, up to sign.\nConvolving it with a source $f$ solves Poisson's equation, and it is the building block of Green's functions and of the Newtonian and logarithmic potentials.\n\n## Explanations\n\n### L1 human\n\nThink of a single unit point charge at the origin of space.\nThe electrostatic potential it creates is proportional to one over the distance to the origin, and this is the fundamental solution in three dimensions.\nIn the plane the potential of a point source grows like the logarithm of the distance instead.\nAway from the origin the function is harmonic; all of its \"source\" sits at the origin.\nFor example, in $\\R^3$ it is $\\Phi(x) = \\frac{1}{4\\pi \\abs{x}}$.\n",
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