Chapter 22 Gauss’s Law

Our approach Look at why to study Gauss’s Law Give attention to Electric Flux Grasp Gauss’s Law Grasp when and how to use it Grasp making use of symmetry Master calculating Electric Fields through Gauss’s Law

Why study Gauss’s Law? To get experience with mathematical elegance To make powerful use of symmetry to get quantitative results To gain familiarity with Electric Field behavior and gain qualitative clarity

Electric Flux (on whiteboards) What is electric flux (in words)? What is the electric flux if the electric field is uniform (in words & mathematically)? What is the general mathematical expression for electric flux? Exercises –from Mastering Physics: Flux through a cube –make one up

Gauss’s Law (on whiteboards) What (in words) two things does Gauss’s Law say are proportional? What is the general mathematical expression of Gauss’s Law? Make a sketch illustrating Gauss’s Law.

To solve for E directly, one must (1) be able to determine from the symmetry of the charge distribution what direction E points and on what variables E depends on so that one can (2) create a Gaussian surface on which E·dA is a constant. Once such a Gaussian surface has been created, one can then (3) solve for E by pulling it out of the integral. –Rachel Pepper, et. al. PERC Proceedings 2010

When there’s sufficient symmetry… Identify the position at which you want to determine the E-field from a specific charge distribution. Make a judicious “Gaussian surface” through that point, so that there and elsewhere E·dA = E dA, E a constant, and possibly elsewhere E·dA = 0. Use symmetry of charge distribution to find such a surface. (What symmetries….?)

Symmetry… From a superposition standpoint (we’ve been introduced to it with Coulomb’s Law) From a geometric standpoint (very powerful) Examples

Compound use of Gauss’s Law Extending beyond the direct calculation of E is sometimes possible. Examples

Sample problems Let’s make one up in our groups and share with the class Work out as groups/class

the end review these lecture notes to refresh your memory of what we did, what you learned during our classes, and what is left to understand on chapter 22 subject matter