ece106: attempt flux

docs/1b/ece106.md

@@ -221,3 +221,30 @@ $$dQ=\rho_s dS$$
 4. Create a right-angle triangle with $A$, the desired point, and usually the origin
 5. Attempt to find symmetry
 6. Solve
+
+## Gauss's law
+
+!!! definition
+    - A **closed surface** is any closed three-dimensional object.
+    - **Electric flux** represents the number of electric field lines going through a surface.
+
+At an arbitrary surface, the **normal** to the plane is its vector form:
+
+$$\vec{dS}=\vec n\cdot dS$$
+
+The **electric flux density** $\vec D$ is an alternate representation of electric field strength. In a vacuum:
+
+$$\vec D = \epsilon_0\vec E$$
+
+**Electric flux** is the electric flux density multiplied by the surface area at every point of an object.
+
+$$\phi_e=\epsilon_0\int_s\vec E\bullet\vec{dS}$$
+
+The flux from charges outside a closed surface will **always be zero at the surface**. A point charge in the centre of a closed space has a flux equal to its charge. Regardless of the charge distribution or shape, the **total flux** through a closed surface is equal to the **total charge within** the closed surface.
+
+$$\oint \vec D\bullet\vec{dS}=Q_\text{enclosed}$$
+
+This implies $\phi_e>0$ is a net positive charge enclosed.
+
+!!! warning
+    Gauss's law only applies when $\vec E$ is from all charges in the system