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| author | Preston Pan <preston@nullring.xyz> | 2024-06-28 21:30:42 -0700 |
|---|---|---|
| committer | Preston Pan <preston@nullring.xyz> | 2024-06-28 21:30:42 -0700 |
| commit | e7dd5245c35d2794f59bcf700a6a92009ec8c478 (patch) | |
| tree | 0d0e81552f0426f8b715bd5bd3bdd0856058db2c /mindmap/inverse square.org | |
| parent | 01ba01763b81a838dcbac4c08243804e068495b9 (diff) | |
stuff
Diffstat (limited to 'mindmap/inverse square.org')
| -rw-r--r-- | mindmap/inverse square.org | 8 |
1 files changed, 7 insertions, 1 deletions
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} + |