018/AABAC Version QTest #4 Antoniewicz (57030) This print-out should have 3 questions. Multiple-choice questions may continue on the next column or page find all choices before answering. 001 10.0 points Given a thick conducting shell with inner radius Ri and the outer radius Ro , centered at O, the origin. There is a point charge -Q located at O. The net charge on the thick conducting shell is -2Q. The potential at r in the region Ri < r < Ro , is given by 4kQ r kQ 2. - Ro 3kQ 3. - Ro 3kQ 4. - Ri kQ 5. - r 3kQ 6. - r 3kQ 7. - Ro kQ 8. - Ri 2kQ 9. - Ro 2kQ 10. - r 1. - + kQ Ri 3kQ Ro So, the resultant potential at r is Vc (r) = - V (r) = Va (r) + Vb (r) + Vc (r) V (r) = - 3kQ Ro
1
+
kQ kQ - Ri r
002 10.0 points Given three parallel conducting plates which are aligned perpendicular to the x-axis. They are labeled, from left to right as plate 1, 2 and 3 respectively. The corresponding plate charges are Q1 = -q, Q2 = 0 and Q3 = q. The width of the gap between 1 and 2 is d, and the width between plates 2 and 3 is d/2. Determine the magnitude of the potential difference across 1 and 3. 1. 6(q/A)d
0
9(q/A)d 2. 2 0 3. 0 4. correct 5. kQ kQ - Ri r kQ + Ri 6. 4(q/A)d
0
2(q/A)d
0
5(q/A)d
0
+
Explanation: The -2Q charge on the conducting shell will separate into +Q on the inner shell -3Q and on the outer shell, as can be seen from Gauss's Law. Thus, the three potentials from each shell of charge are Va (r) = - kQ r kQ r
Vb (r) = +
5(q/A)d 7. 2 0 3(q/A)d correct 8. 2 0 7(q/A)d 9. 2 0 Explanation: One may regard the 3-plate system as a composite system which involves two capacitor systems with the 12-capacitor followed by the 23-capacitor. The 12-capacitor has charges Q1 and Q2 + Q3 , i.e charges of -q and +q respectively. The 23-capacitor has charges Q1 + Q2 and Q3 , i.e charges of -q and +q respectively.
Version 018/AABAC QTest #4 Antoniewicz (57030) The potential difference is V3 - V1 = Egap,12 d + Egap,23 d V3 - V1 = (q/A)d
0
2
we can write V = 0 VAD = - (VBA + VCB + VDC ) = - [11 V + (-6 V) + (-16 V)] = 11 V .
+
(q/A)d 2 0
V3 - V1 =
3(q/A)d 2 0
003 10.0 points In the region of space depicted in the figure below, there are several stationary charged objects that are not shown in the diagram. B A
D
C
Along the path A B C D you measure the following potential differences: VB - VA = 11 V VC - VB = -6 V VD - VC = -16 V . What is the potential difference VA - VD ? 1. 8.0 2. 10.0 3. 12.0 4. 9.0 5. 3.0 6. 11.0 7. 5.0 8. 4.0 9. 7.0 10. 6.0 Correct answer: 11 V. Explanation: We know that around the entire loop, V = 0. Using the notation VBA = VB - VA ,