From 88d684f6b0bef3d88df99e8d38b5ecb8c4d59973 Mon Sep 17 00:00:00 2001 From: arc Date: Wed, 7 Jan 2026 21:32:20 -0700 Subject: [PATCH] vault backup: 2026-01-07 21:32:20 --- education/physics/PHYS2220/Gauss's Law.md | 6 ++++-- 1 file changed, 4 insertions(+), 2 deletions(-) diff --git a/education/physics/PHYS2220/Gauss's Law.md b/education/physics/PHYS2220/Gauss's Law.md index 952ac00..971158d 100644 --- a/education/physics/PHYS2220/Gauss's Law.md +++ b/education/physics/PHYS2220/Gauss's Law.md @@ -13,10 +13,12 @@ If the area is tilted relative to the field, then the strength of the field is r --- I don't understand what the below section means, but copying it for posterity: The electric flux through any closed surface is proportional to the net charge enclosed by that surface. This would be written mathematically as: -$$ \Phi = \oint \vec{E} \cdot d\vec{A} \alpha q_{enclosed} $$ +$$ \Phi = \oint \vec{E} \cdot d\vec{A} \propto q_{enclosed} $$ +> interjection: $\propto$ means "is proportional to", and $\oint dA$ can *possibly* be treated as the area of the surface. $$ \Phi = \oint \vec{E} \cdot d\vec{A} = \oint EdA \cos\theta$$ - +For a closed sphere, the equation becomes: +$$ \Phi = E(4\pi r^2) $$ --- \ No newline at end of file