Exploring Gauss's Law and Electric Flux

1. Chapter 22 Gauss’s Law

2. Goals for Chapter 22 • To study electric flux • To calculate electric flux with Gauss’s Law • To consider the electric field of various symmetric charge distributions

3. Introduction • The movement of electrons can be shocking (pardon the pun). • If you look at the girl’s hair (figure to the right), you’ll see the electrons coating each individual hair fiber and then repelling each other. • Gauss imagined a flow through a surface placed around a charge and then considered outcomes that we will study in Chapter 22.

4. Flux as the flow out of an imagined box • If we construct a boundary around a charge or charges, we can think of the flow coming out from the charge like water through a screen surrounding a sprinkler.

5. What happens as I change the conditions? • Consider +1 versus +2 or a box with double the containment dimension.

6. A measurement of flux will be sensitive to measurement • If we considered flux through a rectangle, the flux will change as the rectangle changes orientation to the flow.

7. Flux in a uniform field • Measurement of the flux for a uniform electric field

8. If the field is not uniform—the disk • Refer to Example 22.1 to evaluate flux through a disk. • Figure 22.7 illustrates this example.

9. If the field is not uniform—the cube • Refer to Example 22.2 to evaluate flux through a disk. • Figure 22.8 illustrates this example.

10. If the field is not uniform—the sphere • Refer to Example 22.3 to evaluate flux through a disk. • Figure 22.9 illustrates this example.

11. Gauss’s Law • The expression is an alternative to Coulomb’s Law. • The nifty thing about being a scientist in Gauss’s day is that you got to leave your name on clever work (not to mention the nice painting).

12. Flux through concentric spheres with different radii • Consider the flux as changing the radius of the sphere changes its volume.

13. Projecting flux through other shapes • Consider Figure 22.12 to contemplate flux through nonspherical surfaces.

14. Effect of changing the sign of the charge • Figure 22.14 leads us to consider the effect of changing the sign of our point charge.

15. There are practical applications • Figure 22.17 treats excess charge as residing on the surface of a conductor. • Consider Example 22.5. • Figure 22.18 illustrates Example 22.5.

16. The field of a line or plane of charge • Consider Example 22.6 and Figure 22.19. • See also Example 22.7 and Figure 22.20.

17. A field between parallel plates of opposing charge • The capacitor is the actual device.

18. The field of a uniformly charged sphere • Consider Example 22.9. • Figure 22.22 illustrates the example. • Follow Example 22.10.

19. Charges on conductors • The electric field within a charged conductor may be found. • Consider Figure 22.23. • Follow Example 22.11 and Figure 22.24.

20. Experimental tests of Gauss’s Law • Regard Figure 22.25. • A metal container on an insulating stand.

21. The Van de Graaff generator • The source of all the static on the child’s hair in our introduction. • Consider Figure 22.27 below.

22. A Faraday cage blocks flow • Refer to Figure 22.28 below. • Science-fiction movies always place alien transmitters in these to prevent them from calling for help. • Follow Examples 22.12 and 22.13.