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.
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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! / itβ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 β 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 β 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 β 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.