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. $V(r)$ doesnâ€™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
### 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";/>