Which of the following are vectors?
(I) Electric field, (II) Electric flux, and/or (III) Electric charge
1. I only
2. I and II only
3. I and III only
4. II and III only
5. I, II, and II
Note:
* CORRECT ANSWER: A
I spent ... hours on the second homework.
1. 1-2
2. 3-4
3. 5-6
4. 7-8
5. More than 9
## Announcements
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## Gauss' Law
<img src="./images/gauss_pt_charge.png" align="center" style="width: 350px";/>
$$\oint_S \mathbf{E}\cdot d\mathbf{A} = \int_V \dfrac{\rho}{\varepsilon_0}d\tau$$
<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
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