With $\nabla \times \mathbf{E} = 0$, we know that,
$$\oint \mathbf{E} \cdot d\mathbf{l} = 0$$
If we choose a loop that includes a metal and vacuum (i.e., both in and just outside of the metal), we know that the contribution to this integral in the metal vanishes. What can we say about the contribution just outside the metal?
1. It vanishes also
2. $\mathbf{E}$ must be zero out there
3. $\mathbf{E}$ must be perpendicular to d$\mathbf{l}$ everywhere
4. $\mathbf{E}$ is perpendicular to the metail surface
5. More than one of these
Note:
* Correct answer: E (both A and D)
## Announcements
* Exam 1 TONIGHT (7pm-9pm)
- A149 PSS; Across from FRIB (Wilson side)
* Homework 6 is posted (Due next Wed.)
## Physics Colloquium
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#### The Real Story About Employment for Physics Graduates
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American Physical Society
**In this room, tomorrow 4:10pm-5pm**
A neutral copper sphere has a spherical hollow in the center. A charge $+q$ is placed in the center of the hollow. What is the total charge on the outside surface of the copper sphere? (Assume Electrostatic equilibrium.)
<img src="./images/coppersphere_hole_and_charge.png" align="left" style="width: 350px";/>
1. Zero
2. $-q$
3. $+q$
4. $0 < q_{outer} < +q$
5. $-q < q_{outer} < 0$
Note:
* Correct answer: C
<img src="./images/cylinder_charge_outside.png" align="right" style="width: 250px";/>
A long coax has total charge $+Q$ on the OUTER conductor. The INNER conductor is neutral.
What is the sign of the potential difference, $\Delta V = V(c)-V(0)$, between the center of the inner conductor ($s = 0$)
and the outside of the outer conductor?
1. Positive
2. Negative
3. Zero
Note:
* CORRECT ANSWER: C
<img src="./images/conducting_cap_plates_simple.png" align="right" style="width: 300px";/>
Given a pair of very large, flat, conducting capacitor plates with total charges $+Q$ and $-Q$. Ignoring edges, what is the equilibrium distribution of the charge?
1. Throughout each plate
2. Uniformly on both side of each plate
3. Uniformly on top of $+Q$ plate and bottom of $–Q$ plate
4. Uniformly on bottom of $+Q$ plate and top of $–Q$ plate
5. Something else
Note:
* CORRECT ANSWER: D
<img src="./images/conducting_cap_plates.png" align="right" style="width: 400px";/>
Given a pair of very large, flat, conducting capacitor plates with surface charge densities $+/-\sigma$, what is the E field in the region between the plates?
1. $\sigma/2\varepsilon_0$
2. $\sigma/\varepsilon_0$
3. $2\sigma/\varepsilon_0$
4. $4\sigma/\varepsilon_0$
5. Something else
Note:
* CORRECT ANSWER: B
<img src="./images/capacitor_gap_bigger.png" align="right" style="width: 300px";/>
You have two very large parallel plate capacitors, both with the same area and the same charge $Q$.
Capacitor \#1 has twice the gap of Capacitor \#2. Which has more stored potential energy?
1. \#1 has twice the stored energy
2. \#1 has more than twice
3. They both have the same
4. \#2 has twice the stored energy
5. \#2 has more than twice.
Note:
* CORRECT ANSWER: A
* E same; twice volume