From 094e6722457b5499991444e7d5dc540018bd61d2 Mon Sep 17 00:00:00 2001 From: eggy Date: Sat, 28 Jan 2023 19:34:26 -0500 Subject: [PATCH] ece106: attempt flux --- docs/1b/ece106.md | 27 +++++++++++++++++++++++++++ 1 file changed, 27 insertions(+) diff --git a/docs/1b/ece106.md b/docs/1b/ece106.md index e2629d3..4ca3b69 100644 --- a/docs/1b/ece106.md +++ b/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