We usually choose $V(r\rightarrow\infty) \equiv 0$ when calculating the potential of a point charge to be $V(r) = +kq/r$. How does the potential $V(r)$ change if we choose our reference point to be $V(R) = 0$ where $R$ is close to $+q$. 1. $V(r)$ higher than it was before 2. $V(r)$ is lower than it was before 4. $V(r)$ doesn’t change ($V$ is independent of choice of reference) Note: * CORRECT ANSWER: B * Show redefinition.

### Electrostatic Potential Energy <img src="./images/cathode_ray_tube.png" align="center" style="width: 600px";/>

Consider slowly moving a positive charge from a location of low electric potential to one of high electric potential. What is the sign of the work done by you ($W_u$)? What is the sign of the work done by electric field ($W_f$)? 1. $W_u < 0$; $W_f > 0$ 2. $W_u < 0$; $W_f < 0$ 3. $W_u > 0$; $W_f > 0$ 4. $W_u > 0$; $W_f < 0$ Note: Correct Answer is D; Draw field

<img src="./images/three_charges.png" align="right" style="width: 300px";/> Three identical charges $+q$ sit on an equilateral triangle. What would be the final $KE$ of the top charge if you released it (keeping the other two fixed)? 1. $\frac{1}{4\pi\varepsilon_0}\frac{q^2}{a}$ 2. $\frac{1}{4\pi\varepsilon_0}\frac{2q^2}{3a}$ 3. $\frac{1}{4\pi\varepsilon_0}\frac{2q^2}{a}$ 4. $\frac{1}{4\pi\varepsilon_0}\frac{3q^2}{a}$ 5. Other Note: CORRECT ANSWER: C

<img src="./images/three_charges.png" align="right" style="width: 300px";/> Three identical charges $+q$ sit on an equilateral triangle. What would be the final $KE$ of the top charge if you released *all three*? 1. $\frac{1}{4\pi\varepsilon_0}\frac{q^2}{a}$ 2. $\frac{1}{4\pi\varepsilon_0}\frac{2q^2}{3a}$ 3. $\frac{1}{4\pi\varepsilon_0}\frac{2q^2}{a}$ 4. $\frac{1}{4\pi\varepsilon_0}\frac{3q^2}{a}$ 5. Other Note: CORRECT ANSWER: A

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.

<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