Examen de fisik c mit
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This document is an exam for a course on electrostatics. It contains 4 questions covering various topics: 1) A charge distribution problem involving a spherical charge distribution with constant charge density inside one radius and a point charge outside another radius. 2) A parallel plate capacitor problem where a third uncharged plate is inserted between the other two plates. 3) A multiple choice question about electric field lines around a uniformly polarized sphere. 4) A question asking about stable mechanical equilibrium configurations of point charges.
Examen de fisik c mit
- 1. ESG 8.022 Fall 2006 Exam 1 Instructor: Michael Shaw Wednesday, October 11th, 2006 @ 1:00PM 1 Spherical Charge Distribution (35 points) Consider the following charge distribution in 3-dimensional Euclidean space. ｧ ｨ c1 揃 r r r1 r1 鐃 鐃2 = (r) = ｩ c2 揃 隆(r r2 ) 揃 r r > r1 r2 where r is the usual spherical polar coordinate and r1 < r2 . a. What are the units of c1 and c2 ? b. Find the electric 鍖eld for r < r1 c. Find the electric 鍖eld for r1 < r < r2 d. Find the electric 鍖eld for r > r2 e. Graph the electric 鍖eld as a function of r. Is the electric 鍖eld continuous everywhere? Is this ok? f. Find the electric potential in all space. Graph the electric potential as a function of r. g. Is the electric potential continuous everywhere? Is this ok? h. Find 0 so that the total charge is Q. 1
- 2. 8.022 Fall 2006 Exam 1 Wednesday, October 11th, 2006 @ 1:00PM 2 A Parallel Plate Capacitor (35 points) Two 鍖at, square metal plates have sides of length L, and thickness s/2, are arranged parallel to each other with a separation of s, where s << l so you may ignore fringing 鍖elds. A charge Q is moved from the upper plate to the lower plate. Now a force is applied to a third uncharged conducting plate of the same thickness so that it lies between the other two plates to a depth x, maintaining the same spacing s/4 between its surface and the surfaces of the other two. a. Find the electric 鍖eld Ew in the wide region. b. Find the electric 鍖eld En in the narrow region. c. Find the surface charge in the wide region, w and in the narrow region, n . d. What is the potential di鍖erence between the upper and lower plates? e. Find the capacitance of the system. f. What is the energy stored in the electric 鍖eld? g. What force (magnitude and direction) must be exerted on the middle plate to keep it from moving? h. If the force is no longer applied, in which direction does the middle plate move? 2
- 3. 8.022 Fall 2006 Exam 1 Wednesday, October 11th, 2006 @ 1:00PM 3 Multiple Choice Question (10 points) 3. A sphere is uniformly polarized as shown in the diagram above. Circle the case below that shows the correct electric 鍖eld lines. 4 Electrostatic Equilibrium (20 points) When can a point charge be in stable mechanical equilibrium in the electric 鍖eld of other charges? That is, is there some arrangement of point charges so that if we 鍖x all but one of them, the other one is in a stable equilibrium? If so, what con鍖gurations are possible? Please show su鍖cient reasoning for your answer. Note 1: A mathematical proof is su鍖cient reasoning. So is a good proof by example. So is a sound physical argument. So is any other technique that shows you have a good grasp of the concept at hand. Note 2: A stable equilibrium is one where if we move the charge in any direction, there is a restoring force directed opposite to the displacement. Hint: Use Gausss Law. 3