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

<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?

*Tutorial follow-up*: Does the charge $\sigma$ on the beam line affect the particles being accelerated inside it? 1. Yes 2. No 3. ??? *Think: Why? Or why not?* Note: * CORRECT ANSWER: B * There's no field inside

*Tutorial follow-up*: Could the charge $\sigma$ affect the electronic equipment outside the tunnel? 1. Yes 2. No 3. ??? *Think: Why? Or why not?* Note: * CORRECT ANSWER: A * Definitely a field outside