<img src="./images/cubical_box.png" align="right" style="width: 350px";/>
The space in and around a cubical box (edge length $L$) is filled with a constant uniform electric field, $\mathbf{E} = E_0 \hat{y}$. What is the TOTAL electric flux $\oint_S \mathbf{E} \cdot d\mathbf{A}$ through this closed surface?
1. 0
2. $E_0L^2$
3. $2E_0L^2$
4. $6E_0L^2$
5. We don't know $\rho(r)$, so can't answer.
Note:
* CORRECT ANSWER: A
* All the incoming flux on the left side comes out the right side
## Announcements
* Starting to 'grade' clickers on Monday!
* GRE Prep (SPS and WAMPS)
- [Information on PA webpage](https://www.pa.msu.edu/academics/undergraduate-program/graduate-school-preparation/)
- First meeting: Wednesday 5-6pm in 1300 BPS
A positive point charge $+q$ is placed outside a closed cylindrical surface as shown. The closed surface consists of the flat end caps (labeled A and B) and the curved side surface (C). What is the sign of the electric flux through surface C?
<img src="./images/ABC_cylinder.png" align="center" style="width: 600px";/>
1. positive
2. negative
3. zero
4. not enough information given to decide
Note:
* CORRECT ANSWER: B
* This is meant to be hard to visualize, next slide illustrates it better.
Let's get a better look at the side view.
<img src="./images/ABC_cylinder_side.png" align="center" style="width: 350px";/>
A positive point charge $+q$ is placed outside a closed cylindrical surface as shown. The closed surface consists of the flat end caps (labeled A and B) and the curved side surface (C). What is the sign of the electric flux through surface C?
<img src="./images/ABC_cylinder.png" align="center" style="width: 600px";/>
1. positive
2. negative
3. zero
4. not enough information given to decide
Note:
* CORRECT ANSWER: B
* Some of the incoming flux through C goes out A and B.
Which of the following two fields has zero divergence?
| I | II |
|:-:|:-:|
| <img src ="./images/cq_left_field.png" align="center" style="width: 400px";/> | <img src ="./images/cq_right_field.png" align="center" style="width: 400px";/> |
1. Both do.
2. Only I is zero
3. Only II is zero
4. Neither is zero
5. ???
Note:
* CORRECT ANSWER: B
* Think about dE/dx and dE/dy
* Fall 2016: 7 [34] 13 43 3; (Asked them to consider dvx/dx and dvy/dy) 3 [90] 3 4 0
What is the divergence in the boxed region?
<img src ="./images/pt_charge_red_box.png" align="right" style="width: 400px";/>
1. Zero
2. Not zero
3. ???
Note:
* CORRECT ANSWER: A
* Lines in; lines out - harder to see dE/dx and dE/dy
* One of those curious ones where the 2D picture might get in the way; think 3D
**Activity:** For a the electric field of a point charge, $\mathbf{E}(\mathbf{r}) = \dfrac{1}{4\pi\varepsilon_0}\dfrac{q}{r^2}\hat{r}$, compute $\nabla \cdot \mathbf{E}$.
*Hint: The front fly leaf of Griffiths suggests that the we take:*
$$\dfrac{1}{r^2}\dfrac{\partial}{\partial r}\left(r^2 E_r\right)$$
Note:
* You get zero! Motivates delta function
Remember this?
<img src ="./images/pt_charge_red_box.png" align="center" style="width: 400px";/>