Does system energy "superpose"? That is, if you have one system of charges with total stored energy $W_1$, and a second charge distribution with $W_2$...if you superpose these charge distributions, is the total energy of the new system simply $W_1 + W_2$? 1. Yes 2. No Note: * CORRECT ANSWER: B * Draw 4 charges and show that it is not the sum of the 2 charges and the other 2.

### Exam 1 Information * Exam 1 on Wednesday, October 5th * Arrive on time! * We will provide Formula Sheets (posted on Piazza already) * You can bring one-side of a sheet of paper with your own notes. * 4 questions - True/False, Essay, Graphing, Calculations

### What's on Exam 1? * Identify whether conceptual statements about $\mathbf{E}$, $V$, and/or $\rho$ are true or false. * Sketch and discuss delta functions in relation to charge density, $\rho$ * Calculate the electric potential, $V$, for a specific charge distribution and discuss what happens in limiting cases * Calculate the electric field, $\mathbf{E}$, inside and outside a continuous distribution of charge and sketch the results

<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

<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

### 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 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.

We have a large copper plate with uniform surface charge density, $\sigma$. Imagine the Gaussian surface drawn below. Calculate the E-field a small distance $s$ above the conductor surface. <img src="./images/copper_plate.png" align="left" style="width: 300px";/> 1. $|E| = \frac{\sigma}{\varepsilon_0}$ 2. $|E| = \frac{\sigma}{2\varepsilon_0}$ 3. $|E| = \frac{\sigma}{4\varepsilon_0}$ 4. $|E| = \frac{1}{4\pi\varepsilon_0}\frac{\sigma}{s^2}$ 5. $|E| = 0$ Note: * CORRECT ANSWER: A * Might have to do derivation and go through details of infinitely thin line charge. Must be +sigma on other side, btw.