From 6de29052077fa51ccaa452ad7432dd64dc806bd2 Mon Sep 17 00:00:00 2001 From: Preston Pan Date: Fri, 30 Jan 2026 20:50:09 -0800 Subject: add more stuff to my monorepo --- mindmap/central force.org | 4 ++-- mindmap/continuity equation.org | 2 +- 2 files changed, 3 insertions(+), 3 deletions(-) (limited to 'mindmap') diff --git a/mindmap/central force.org b/mindmap/central force.org index 99751fc..f341837 100644 --- a/mindmap/central force.org +++ b/mindmap/central force.org @@ -16,8 +16,8 @@ Central fields have the following properties: 4. If you draw a straight line between the two points, the force vector has to be parallel to that line. 5. The force works in the same no matter where in the universe you are. -Where these five properties are all common attributes of everyday forces. What these properties are basically saying is that we want -a function only dependent on the vector between two particles \(P_{1}\) and \(P_{2}\) that are experiencing the force, and it is +These five properties are all common attributes of everyday forces. What these properties are basically saying is that we want +a function only depending on the vector between two particles \(P_{1}\) and \(P_{2}\) that are experiencing the force, and it is also parallel to this vector, as well as some symmetry constraints. Therefore, we can define a central force: * Definition diff --git a/mindmap/continuity equation.org b/mindmap/continuity equation.org index 579e09a..c12ffa1 100644 --- a/mindmap/continuity equation.org +++ b/mindmap/continuity equation.org @@ -15,7 +15,7 @@ $Q_{enc} = \int_{V} \rho(r')d\tau$ or $Q_{enc}$ is the total amount of particles \begin{align*} \oint_{S} \vec{J} \cdot d\vec{a} = -\frac{\partial Q_{enc}}{\partial t}, \end{align*} -or in other words, the amount that the current goes through some closed surface must be proportional to the loss of particles +or in other words, the current flowing through some closed surface must be proportional to the loss of particles inside of the enclosure. This is of course because of conservation of mass (which is in and of itself conservation of energy). Using the [[id:44e65b69-e5d5-464a-b1f3-8a914e1b7e9e][divergence theorem]]: \begin{align*} -- cgit v1.3