Table of Contents

# Flux

### Prerequisites to Flux

Students need to know how to calculate integrals on surfaces:

- GVC § 1. Surfaces
- GVC § 2. The Cross Product
- GVC § 3. Surface Elements

**Dot Product**(for finding the components of vector field perpendicular to surface)**Cross Product**(for finding unit vector normal to surface)**Electric Field as vector field**(for calculating electric flux)**Surface Element in Rectangular and Curvilinear Coordinates**(finding unit vector normal to surface)**Scalar Surface Integrals**(for finding total flux)

- Reading: GVC § Flux–More Flux through a Cube

## In-class Content

- Recall Flux (SWBQ - 5 min)
- The Concept of Flux (Kinesthetic Activity - 5 min)
- Calculating Flux (Small Group Activity - 30 min) (Optional)
- Visualizing Electric Flux (Maple - 20 min) - plots electric field vectors from a charge in a box and calculates the flux through the surfaces of the box. Leads to a statement of Gauss' law.

## Homework for Static Fields

- (FluxCubeGEM210)
*This problem is an easy, quick follow-up to test your understanding of fluxem activity, from Griffiths E&M book.*A charge $q$ sits at the corner of a cube. Find the flux of $\EE$ through each side of the cube.

**Do not do a long calculation (either by hand or by computer)!** - (FluxCylinderMHG19120)
*This problem is an easy, quick conceptual question about flux, from Hughes Hallett vector calculus book.* - (FluxParaboloid)
*This problem is a long calculation testing whether you can calculate surface elements and flux in a complicated curvilinear coordinate setting.*Find the upward pointing flux of the electric field $\Vec E =E_0\, z\, \hat z$ through the part of the surface $z=-3 s^2 +12$ (cylindrical coordinates) that sits above the $(x, y)$–plane.