= Gravitational field of an infinite plane sheet
{title2=$|g|=2\pi G\Sigma$}
An infinite plane sheet of surface <mass density> $\Sigma$ has constant gravitational-field magnitude $2\pi G\Sigma$ on either side, directed toward the sheet. A Gaussian pillbox has equal inward <flux> on its two caps and enclosed <mass> $\Sigma A$, so $-2gA=-4\pi G\Sigma A$. A uniform infinite slab has the same exterior formula with $\Sigma=\rho h$. Translating an infinite sheet does not change its exterior field, whereas adding a slab changes its surface <mass density>.
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