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.
What do you think will be the flux through the cylindrical surface that is placed as shown in the constant vector field in the figure on the left? What if the cylinder is placed upright, as shown in the figure on the right? Explain.
- (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.