<img src="./images/conducting_cap_plates_simple.png" align="right" style="width: 300px";/> Given a pair of very large, flat, conducting capacitor plates with total charges $+Q$ and $-Q$. Ignoring edges, what is the equilibrium distribution of the charge? 1. Throughout each plate 2. Uniformly on both side of each plate 3. Uniformly on top of $+Q$ plate and bottom of $–Q$ plate 4. Uniformly on bottom of $+Q$ plate and top of $–Q$ plate 5. Something else Note: * CORRECT ANSWER: D

### Announcements * Test on Wednesday * All Homework solutions posted on Piazza * You may bring in one side of a piece of paper with your own notes (formula sheets provided) * No homework due Friday; Homework 5 posted on Wednesday

<img src="./images/conducting_cap_plates.png" align="right" style="width: 400px";/> Given a pair of very large, flat, conducting capacitor plates with surface charge densities $+/-\sigma$, what is the E field in the region between the plates? 1. $\sigma/2\varepsilon_0$ 2. $\sigma/\varepsilon_0$ 3. $2\sigma/\varepsilon_0$ 4. $4\sigma/\varepsilon_0$ 5. Something else Note: * CORRECT ANSWER: B

<img src="./images/capacitor_gap_bigger.png" align="right" style="width: 300px";/> You have two very large parallel plate capacitors, both with the same area and the same charge $Q$. Capacitor \#1 has twice the gap of Capacitor \#2. Which has more stored potential energy? 1. \#1 has twice the stored energy 2. \#1 has more than twice 3. They both have the same 4. \#2 has twice the stored energy 5. \#2 has more than twice. Note: * CORRECT ANSWER: A * E same; twice volume

<img src="./images/capacitor_gap_connected.png" align="center" style="width: 500px";/> A parallel plate capacitor is attached to a battery which maintains a constant voltage difference V between the capacitor plates. While the battery is attached, the plates are pulled apart. The electrostatic energy stored in the capacitor 1. increases. 2. decreases. 3. stays constant. Note: * CORRECT ANSWER: B * Potential same; field is reduced; but shows up squared while d is increased, overall goes down

### Laplace's Equation <img src="./images/laplace.png" align="center" style="width: 900px";/>

<img src="./images/region_w_no_charge.png" align="right" style="width: 200px";/> A region of space contains no charges. What can I say about V in the interior? 1. Not much, there are lots of possibilities for V(r) in there 2. V(r)=0 everywhere in the interior. 3. V(r)=constant everywhere in the interior Note: * CORRECT ANSWER: A

<img src="./images/region_with_no_charge_Vset.png" align="right" style="width: 200px";/> A region of space contains no charges. The boundary has V=0 everywhere. What can I say about V in the interior? 1. Not much, there are lots of possibilities for V(r) in there 2. V(r)=0 everywhere in the interior. 3. V(r)=constant everywhere in the interior Note: * CORRECT ANSWER: B