Focused Reading Guide
Chapter 24: Gauss’ Law and Flux
In this chapter (24.1-4), you will first be reading a description of the general idea of Electric Flux. This correlates to the notes given in class on 2/9 about:
 the GENERAL idea of Flux
 the definition of Flux
 the definition of Mass Flux and Volume Flux
 the definition of an “Area Vector”.

The definition of Electric Flux

Gauss’ Law in integral form and Examples related to it.
Then, you will see a few examples worked to demonstrate this idea of Gauss’ Law. Then, Gauss’ Law
Integral will be used to derive a simpler version of electric flux based on charge. Remember! This idea comes from some complicated math in the “divergence theorem” in Calculus 3. We just need to know how to use it. Think of this- you can learn how to use an electric drill fairly easily, but you don’t need to know how each part is made.
When finished you should know and be able to:
1) Define mass flux, volume flux, and electric flux and give examples of each.
2) Define an area vector and a dot product.
3) Understand why a dot product is used for flux. (Hint: Vectors)
4) Know 2 cases when a closed surface has no “net flux”.
5) Know 2 conditions when a closed surface has a “net flux”
6) Know all symbols in Gauss’ Law (Integral Form)
7) Understand the role symmetry plays in making the integral solvable. (Know why E-Field is constant)
8) Know how to derive the E-Field for uniform charge distributions using a symmetrical Gaussian Surface for objects like: a) A cube b) A sphere c) A cylinder d) A plane.
**9) Solve problems involving an E-field function for various shapes. (FUTURE)

From the Class Notes on Flux and the BOOK, answer the following (pp.684-686, notes):
1) In physics, FLUX means more than just “flow”. What is the equation for (also define each symbol in the equation) of: 1) Volume Flux? 2) Mass Flux? 3) Electric Flux?
2) An Area Vector is sort of a new idea. It has the magnitude of the little piece of area you choose. Yet, the direction is the new part. a) What is the definition of an Area Vector? b) How do you know which direction it points for a closed surface? c) What must be the angle between the surface and the vector always? d) What is

A compared to the Total surface area of a closed surface? e) What is “dA” vector? What are the units? f) In equation 24.3 on page 686, what is the “i” subscript on the E and

A vectors for? g) When is there a + electric flux through a surface? How about a negative electric flux?
3) The electric flux is sort of how many “lines of force” “pierce” a surface in space. a) Which two vectors, multiplied together via a “dot product”, give the Electric Flux? b) The angle in the dot product uses which trig function? c) What 2 vectors is this angle always between? d) To get the MOST flux through a surface, the angle should be equal to what degrees/radians? e) For anything (mass, volume, electric field) to not FLUX through a surface, what angle must it
have relative to the surface?
4) This integral nonsense. . . a) On page 686, what does the circle on the integral sign represent? b) If the E Field varied in a complex way (not a simple shape, not a constant magnitude, the angles changed based on position, etc.), this integral could require 3 dimensional vector calculus or more! According to the book, when is the calculation of the integral “ . . . straightforward”? c) In class today, you will see Examples 24.1 and 24.2 done and explained. Follow back through them in your book. I want to you to point out 3 differences in each example between Mr. Mac’s way of solving and the way the book shows it. d) The entire integral for Gauss’ Law (Electric Flux) reduces to a simple ratio. What do the two symbols mean in that ratio in equation 24.6. e) If a surface has a net flux not equal to zero, what MUST be the case inside that surface? f) If a Gaussian surface is in a region of constant E-Field, where net flux is zero, how much charge must be enclosed by it?

7) Use the statements in the margin of page 688 to answer this: When is the net flux through a closed surface zero?
8) Why is the net flux NOT equal to zero if a charge is enclosed by a surface? (See figure 24.7)
9) On page 689, when is the technique of Gauss’ Law useful?
10) What is a Gaussian Surface?
11) For conceptual example 24.2 on page 689, give an example that proves that a and c are not correct.
DRAW them.