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.
### Announcements
* Test on Wednesday (7-9pm)
* All Homework solutions posted on Piazza
* You may bring in one side of a piece of paper with your own notes
* Post your review problem by Tuesday at midnight for extra credit
- 10 bonus points on HW 5
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.
Consider a long coaxial with charge $+Q$ placed on the inside metal wire and $-Q$ outside metal sheath as shown.
<img src="./images/coax_abc.png" align="left" style="width: 300px";/>
Sketch the distribution of charge in this situtation using plus signs to represent positive chages and minus signs to represent negative charges.
Note:
* Ask them for answers, put up on board and turn into clicker question
* Answer should be plusses on outside of inner and minuses inside of outer (equal numbers)
If you were calculating the potential difference, $\Delta V$, between the center of the inner conductor ($s=0$) and infinitely far away ($s \rightarrow \infty$), what regions of space would have a (non-zero) contribution to your calculation?
<img src="./images/coax_abc.png" align="left" style="width: 300px";/>
1. $s<a$
2. $a<s<b$
3. $b<s<c$
4. $s>c$
5. More than one of these
Note:
* Correct answer: E
* Should be where the metal is
<img src="./images/coax_Qin.png" align="left" style="width: 300px";/>
Now, draw the charge distribution (little + and – signs) if the inner conductor has a total charge $+Q$ on it, and the outer conductor is electrically neutral.
Note:
* Ask them for answers, put up on board and turn into clicker question
* Answer should be plusses on outside of inner and minuses inside of outer and plusses on outside of outer (equal numbers)
<img src="./images/coax_offcenter.png" align="left" style="width: 300px";/>
Consider how the charge distribution would change if the inner conductor is shifted off-center, but still has $+Q$ on it, and the outer conductor remains electrically neutral. Draw the new charge distribution (little + and – signs) and be precise about how you know.
Note:
* Ask them for answers, put up on board and turn into clicker question
* Answer should be plusses on outside of inner and minuses inside of outer and plusses on outside of outer (equal numbers); shift only on outside of inner and inside of outer (no net field from them)
<img src="./images/coax_Qout.png" align="left" style="width: 300px";/>
Return the inner conductor to the center.
Instead of the total charge $+Q$ being on the inner conductor, sketch the charge distribution (little + and – signs) if the outer conductor has a total charge $+Q$ on it, and the inner conductor is electrically neutral. Be precise about exactly where the charge will be on these conductors, and how you know.
Note:
* Ask them for answers, put up on board and turn into clicker question
* Answer should be plusses on outside of outer; nothing else.