From e7dd5245c35d2794f59bcf700a6a92009ec8c478 Mon Sep 17 00:00:00 2001 From: Preston Pan Date: Fri, 28 Jun 2024 21:30:42 -0700 Subject: stuff --- mindmap/inverse square.org | 8 +++++++- 1 file changed, 7 insertions(+), 1 deletion(-) (limited to 'mindmap/inverse square.org') diff --git a/mindmap/inverse square.org b/mindmap/inverse square.org index d55c24a..205c5f7 100644 --- a/mindmap/inverse square.org +++ b/mindmap/inverse square.org @@ -189,4 +189,10 @@ V(\vec{r}) := k\int_{space}\frac{\sigma(r')}{r}d\tau \end{align*} Note that because this field does not require keeping track of vector orientation, it is significantly easier to solve for \(V\) then convert to \(\vec{f}\). Additionally, setting a reference point to something that is not infinity would be valid as well -- we just choose infinity because it cancels off the constant term. However, -the /difference/ in potentials is absolute and does not require any constant adjustment. +the /difference/ in potentials is absolute and does not require any constant adjustment. Then, the divergence of inverse +square fields can be reformulated with the [[id:65004429-a6b7-41f2-8489-07605841da3d][Laplacian]] operator: +\begin{align} +\label{} +\nabla^{2}V(\vec{r''}) = k\sigma(\vec{r''}) +\end{align} + -- cgit