True or False: The electric field, $\mathbf{E(\mathbf{r})}$, in some region of space is zero, thus the electric potential, $V(\mathbf{r})$, in that same region of space is zero. 1. True 2. False Note: * CORRECT ANSWER: B * The electric potential is a constant in the region; it might be zero, but doesn't have to be.

True or False: The electric potential, $V(\mathbf{r})$, in some region of space is zero, thus the electric field, $\mathbf{E(\mathbf{r})}$, in that same region of space is zero. 1. True 2. False Note: * CORRECT ANSWER: A * If the potential is zero in that space is zero, then it's gradient is zero in that space, so E must be zero also.

### Announcements * Exam 1 is October 5th (next Wednesday) * Coverage: Griffiths Ch 1, Ch 2.1-2.4 * Mathematics (including $\delta$ functions), Coulomb and Gauss, Potential and Energy * Specific topic/questions on Wednesday * No homework due next week * Homework 5 will be a touch longer

Should we post Homework 5 on Friday or wait to post it until after Exam 1? 1. Post it on Friday. 2. Post it after Exam 1. 3. I don't care either way, but I won't work on it until after Exam 1.

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";/>

<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