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 to contemplate flux through nonspherical surfaces.

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

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

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

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 illustrates the example.
Follow Example

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

20. Experimental tests of Gauss’s Law
Regard Figure
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 below.

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