diff options
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/electrostatics.org | |
parent | 01ba01763b81a838dcbac4c08243804e068495b9 (diff) |
stuff
Diffstat (limited to 'mindmap/electrostatics.org')
-rw-r--r-- | mindmap/electrostatics.org | 6 |
1 files changed, 3 insertions, 3 deletions
diff --git a/mindmap/electrostatics.org b/mindmap/electrostatics.org index d865f86..7072bf8 100644 --- a/mindmap/electrostatics.org +++ b/mindmap/electrostatics.org @@ -25,14 +25,14 @@ these charges have no mass or volume; we call these /point charges/. The equatio on \( P_{1} \) is as follows: \begin{align*} -\vec{F(\vec{r})} = \frac{1}{4\pi\epsilon_{0}}\frac{qQ}{r^{2}} \hat{r}. +\vec{F(\vec{r})} = \frac{1}{4\pi\epsilon_{0}}\frac{qQ}{r^{2}} \hat{r} \end{align*} Where \( \hat{r} \) is the unit vector pointing in the direction of \( P_{2} \). Note that there are a couple of interesting things about this force. First, it is an [[id:2a543b79-33a0-4bc8-bd1c-e4d693666aba][inverse square]] law, and the formula looks a lot like the one for gravitation, only charge can be negative and mass cannot. Second, it is symmetrical, in the sense that the force felt by \( P_{2} \) is going to be the same, only \( \hat{r} \) -is pointing in the other direction. Also, note that due to linearity, this force calculation follows the /superposition principle/. +is pointing in the other direction. Also, note that due to linearity, this force calculation follows the [[id:422653e2-daa4-422a-9cb7-3983a5a72554][superposition principle]]. That is, if we have different electrostatic forces acting on one particle: \begin{align*} @@ -83,7 +83,7 @@ The result is we find a way to express force in a /test charge independent way/. because we often want to find the force if an arbitrary object with an arbitrary charge is next to the particle in question, instead of focusing specifically on two charges. -Note that it is trivial to prove that \( \vec{E} \) also follows the superposition principle. +Note that it is trivial to prove that \( \vec{E} \) also follows the [[id:422653e2-daa4-422a-9cb7-3983a5a72554][superposition principle]]. ** Continuous Charge Distributions |