<img src="./images/capacitor_pull_apart.png" align="center" style="width: 500px";/> A parallel-plate capacitor has $+Q$ on one plate, $-Q$ on the other. The plates are isolated so the charge $Q$ cannot change. As the plates are pulled apart, the total electrostatic energy stored in the capacitor: 1. increases 2. decreases 3. remains constant. Note: * CORRECT ANSWER: A * Same E; constant; larger volume where it is non-zero

<img src="./images/pt_charges_energy.png" align="center" style="width: 300px";/> Two charges, $+q$ and $-q$, are a distance $r$ apart. As the charges are slowly moved together, the total field energy $$\dfrac{\varepsilon_0}{2}\int E^2 d\tau$$ 1. increases 2. decreases 3. remains constant Note: * CORRECT ANSWER: B * Consider when they overlap, field goes to zero, must be E gets smaller as they get closer. same volume

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### Conductors <img src="./images/electron_sea.gif" align="center" style="width: 700px";/>

### The conductor problem <img src="./images/metal.png" align="center" style="width: 500px";/>

A typical metal has one free election per atom. These electrons are free to move in response to external electric fields. There are $\sim 10^{22}$ free electrons in a cubic centimeter of copper. Roughly what size of electric field could a single 1cm cube of copper "respond" to by polarizing? 1. 1 N/C 2. 10 N/C 3. 100 N/C 4. 1000 N/C 5. Something more than these Note: Correct answer is E. It's closer to 10e17 N/C

A point charge $+q$ sits outside a **solid neutral conducting copper sphere** of radius $A$. The charge q is a distance $r > A$ from the center, on the right side. What is the E-field at the center of the sphere? (Assume equilibrium situation). <img src="./images/copper_1.png" align="left" style="width: 300px";/> 1. $|E| = kq/r^2$, to left 2. $kq/r^2 > |E| > 0$, to left 3. $|E| > 0$, to right 4. $E = 0$ 5. None of these Note: * CORRECT ANSWER: D * Net electric field inside of a metal in static equilibrium is zero * Talk about the net field versus the field due to the charges on the metal.

In the previous question, suppose **the copper sphere is charged**, total charge $+Q$. (We are still in static equilibrium.) What is now the magnitude of the E-field at the center of the sphere? <img src="./images/copper_2.png" align="left" style="width: 300px";/> 1. $|E| = kq/r^2$ 2. $|E| = kQ/A^2$ 3. $|E| = k(q-Q)/r^2$ 4. $|E| = 0$ 5. None of these! / it’s hard to compute Note: * CORRECT ANSWER: D * Talk about the net field versus the field due to the charges on the metal.

Consider a long coaxial with charge $+Q$ placed on the inside metal wire and $-Q$ outside metal sheath as shown. <img src="./images/coax_abc.png" align="left" style="width: 300px";/> Sketch the distribution of charge in this situtation using plus signs to represent positive chages and minus signs to represent negative charges. Note: * Ask them for answers, put up on board and turn into clicker question * Answer should be plusses on outside of inner and minuses inside of outer (equal numbers)

If you were calculating the potential difference, $\Delta V$, between the center of the inner conductor ($s=0$) and infinitely far away ($s \rightarrow \infty$), what regions of space would have a (non-zero) contribution to your calculation? <img src="./images/coax_abc.png" align="left" style="width: 300px";/> 1. $s<a$ 2. $a<s<b$ 3. $b<s<c$ 4. $s>c$ 5. More than one of these Note: * Correct answer: E * Should be where the metal is

<img src="./images/coax_Qin.png" align="left" style="width: 300px";/> Now, draw the charge distribution (little + and – signs) if the inner conductor has a total charge $+Q$ on it, and the outer conductor is electrically neutral. Note: * Ask them for answers, put up on board and turn into clicker question * Answer should be plusses on outside of inner and minuses inside of outer and plusses on outside of outer (equal numbers)

<img src="./images/coax_offcenter.png" align="left" style="width: 300px";/> Consider how the charge distribution would change if the inner conductor is shifted off-center, but still has $+Q$ on it, and the outer conductor remains electrically neutral. Draw the new charge distribution (little + and – signs) and be precise about how you know. Note: * Ask them for answers, put up on board and turn into clicker question * Answer should be plusses on outside of inner and minuses inside of outer and plusses on outside of outer (equal numbers); shift only on outside of inner and inside of outer (no net field from them)

<img src="./images/coax_Qout.png" align="left" style="width: 300px";/> Return the inner conductor to the center. Instead of the total charge $+Q$ being on the inner conductor, sketch the charge distribution (little + and – signs) if the outer conductor has a total charge $+Q$ on it, and the inner conductor is electrically neutral. Be precise about exactly where the charge will be on these conductors, and how you know. Note: * Ask them for answers, put up on board and turn into clicker question * Answer should be plusses on outside of outer; nothing else.