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| author | Preston Pan <preston@nullring.xyz> | 2024-05-29 19:24:55 -0700 |
|---|---|---|
| committer | Preston Pan <preston@nullring.xyz> | 2024-05-29 19:24:55 -0700 |
| commit | c35d434272e09256030cb113ec62b72c3dbae84f (patch) | |
| tree | f4cb8599abda34eaaf6cf89d8c603c25e5a9a517 /mindmap/electrostatics.org | |
| parent | e0a4aa29f8ccbc9e86ec202be199756aea2528b6 (diff) | |
new files; more mindmap
Diffstat (limited to 'mindmap/electrostatics.org')
| -rw-r--r-- | mindmap/electrostatics.org | 12 |
1 files changed, 9 insertions, 3 deletions
diff --git a/mindmap/electrostatics.org b/mindmap/electrostatics.org index 6625d4c..d865f86 100644 --- a/mindmap/electrostatics.org +++ b/mindmap/electrostatics.org @@ -1,5 +1,5 @@ :PROPERTIES: -:ID: 32f0b8b1-17bc-4c91-a824-2f2a3bbbdbd1 +:ID: 63713308-0ff7-433f-8103-8b64ba9bdbe1 :END: #+title: electrostatics #+author: Preston Pan @@ -113,10 +113,16 @@ field: \oint\vec{E} \cdot d\vec{l} = \vec{0} \end{align*} -* Electrostatic Potentials +* electrostatic potential +:PROPERTIES: +:ID: 951db9ac-3e8b-49a1-b609-2bbb795be834 +:ROAM_ALIASES: "potential difference" voltage +:END: Because \(\vec{E}\) is a [[id:6f2aba40-5c9f-406b-a1fa-13018de55648][conservative field]]: \begin{align*} \vec{E} = -\vec{\nabla}V \\ \nabla^{2}V = -\frac{\sigma(\vec{r_{1}})}{\epsilon_{0}} \\ -V(\vec{r}) = \frac{1}{4\pi \epsilon_{0}}\int\frac{\sigma(\vec{r_{2}})}{r}dr +V(\vec{r}) = -\frac{1}{4\pi \epsilon_{0}}\int\frac{\sigma(\vec{r_{2}})}{r}dr \end{align*} +Note that the difference of two points in the potential scalar field is also known as potential difference +between those two points, or the voltage between those two points. |