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.
## Announcements * Exam 1 TONIGHT (7pm-9pm) - 101 BCH - Help session tonight: 5-6:30 (1300 BPS) * DC out of town next Wed night - Friday * Help session in limbo at the moment * Class on Friday - Dr. Rachel Henderson
A positive charge ($q$) is outside a metal conductor with a hole cut out of it at a distance $a$ from the center of the hole. What is the *net* electric field at center of the hole? 1. $\dfrac{1}{4 \pi \varepsilon_0}\dfrac{q}{a^2}$ 2. $\dfrac{-1}{4 \pi \varepsilon_0}\dfrac{q}{a^2}$ 3. $\dfrac{1}{4 \pi \varepsilon_0}\dfrac{2q}{a^2}$ 4. $\dfrac{-1}{4 \pi \varepsilon_0}\dfrac{2q}{a^2}$ 5. Zero Note: Correct Answer E
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 interior vacuum (i.e., both in and **inside the hole**), we know that the contribution to this integral in the metal vanishes. What can we say about the contribution in the hole? 1. It vanishes also 2. $\mathbf{E}$ must be zero in there 3. $\mathbf{E}$ must be perpendicular to d$\mathbf{l}$ everywhere 4. $\mathbf{E}$ is perpendicular to the metal surface 5. More than one of these Note: * Correct answer: E (A and B)
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 metal surface 5. More than one of these Note: * Correct answer: E (both A and D)
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; there's no field inside at all
<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