What is the total charge for this distribution? $$\rho(\mathbf{r}) = \sum_{k=0}^2 (1+k)\,q\,\delta^3(\mathbf{r}-k\mathbf{a})$$ 1. q 2. 2 q 3. 4 q 4. 6 q 5. Something else Note: * Correct Answer: D (write it out) * Follow up what does it look like?

## Announcements * Make sure you are on Slack; there's HW solutions there * [phy481msuf2018.slack.com](https://phy481msuf2018.slack.com/) * Exam 1 is coming up! October 3rd (More details next week!) * And I will post practice exams to Slack!

A Gaussian surface which is *not* a sphere has a single charge (q) inside it, *not* at the center. There are more charges outside. What can we say about total electric flux through this surface $\oint_S \mathbf{E} \cdot d\mathbf{A}$? 1. It is $q/\varepsilon_0$. 2. We know what it is, but it is NOT $q/\varepsilon_0$. 3. Need more info/details to figure it out. Note: * CORRECT ANSWER: A

A Gaussian surface which is *not* a sphere has a single charge (q) inside it, *not* at the center. There are more charges outside. Can we use Gauss's Law ($\oint_S \mathbf{E} \cdot d\mathbf{A}$) to find $|\mathbf{E}|$? 1. Yes 2. No 3. Maybe? Note: * CORRECT ANSWER: B

<img src ="./images/dipole_gauss.png" align="right" style="width: 300px";/> An electric dipole ($+q$ and $–q$, small distance $d$ apart) sits centered in a Gaussian sphere. What can you say about the flux of $\mathbf{E}$ through the sphere, and $|\mathbf{E}|$ on the sphere? 1. Flux = 0, E = 0 everywhere on sphere surface 2. Flux = 0, E need not be zero *everywhere* on sphere 3. Flux is not zero, E = 0 everywhere on sphere 4. Flux is not zero, E need not be zero... Note: * CORRECT ANSWER: B * Think about Q enclosed; what can we say about E though?

SLAC (Stanford Linear Accelerator Center) is where quarks (including the charm quark), and the tauon (like a heavier electron) were discovered. <img src ="./images/slac_overhead.jpg" align="center" style="width: 700px";/> Note: Charged particles are accelerated inside a long metal cylindrical pipe, which is 2 miles long and has a radius R = 6 cm. All the air is pumped out of this pipe, known as the "beam line."

<img src ="./images/cylinder_slac.png" align="left" style="width: 300px";/> One afternoon, the beam line is struck by lightning, which gives it a uniform surface charge density $+\sigma$. Does that affect the experiment?! What is the infinitesimal area, $dA$, of a small patch on a cylindrical shell centered on the z-axis? 1. $d\phi\,dz$ 2. $s\,d\phi\,dz$ 3. $s\,ds\,d\phi$ 4. $ds\,dz$ 5. Something else Note: Correct answer B

Which way does the electric field due to the positive charges resting on the beam line point for locations _outside the pipe_ far from the ends? 1. Roughly radially outward 2. Exactly radially outward 3. Roughly radially inward 4. Exactly radially inward 5. It varies too much to tell Note: Correct answers A and B; talk about models and modeling

Which way does the electric field due to the positive charges resting on the beam line point for locations _inside the pipe_ far from the ends? 1. Exactly radially outward 2. Exactly radially inward 3. It varies too much to tell 4. Something else Note: Correct answer D; it zero