From e36ec113ae7f9ee3e980534b4c6e73d599d8ced9 Mon Sep 17 00:00:00 2001
From: Nathan Nguyen <159226326+Indigo5684@users.noreply.github.com>
Date: Mon, 4 Nov 2024 10:54:25 -0600
Subject: [PATCH] Electrostatics Ohm's Law

---
 docs/physics/electrostatics/5-moving-charges.md | 13 +++++++++++++
 1 file changed, 13 insertions(+)
 create mode 100644 docs/physics/electrostatics/5-moving-charges.md

diff --git a/docs/physics/electrostatics/5-moving-charges.md b/docs/physics/electrostatics/5-moving-charges.md
new file mode 100644
index 0000000..9376772
--- /dev/null
+++ b/docs/physics/electrostatics/5-moving-charges.md
@@ -0,0 +1,13 @@
+# Chapter 5 - Electrodynamics with Moving Charges
+
+## Section 5.1 - Currents in Steady-State Regine
+
+We want to work in a steady-state system. Thus, we restrict ourselves to currents that do not change in time.
+
+With math, we see that $\div \vb{J}(\vb{r}) = -\frac{\partial \rho(\vb{r})}{\partial t}$. Since we are only considering a steady-state system, $\div \vb{J}_e = \div \vb{J}_m = 0$.
+
+**Definition**. The *conductance* of a material is $G = \frac{1}{R}$, where $R$ is the resistance of a material.
+
+For a wire of uniform cross-sectional area, we see that $G = \sigma \frac{A}{L}$, where $A$ is the cross-sectional area, $L$ is the length of the wire, and $\sigma$ is the conductivity of a wire. Inverted, we see that $R$ = $\rho \frac{L}{A}$, where $\rho = \frac{1}{\sigma}$ is the resistivity of the wire.
+
+**Definition**. *Ohm's Law* can be written as $I = G V$, or inverted, $V = IR$. In a wire, we see that current density $\vb{} = \frac{I}{A} = \sigma \frac{V}{L} = \sigma \vb{E}$
\ No newline at end of file