Our next test will be on Tuesday, March 14

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Physics 2212G/H Test form Name Spring 2017 Test 2 Recitation Section (see back of test): 1) Print your name, test form number (above), an nine- igit stuent number in the section of the answer car

1 Physics 2212G/H Test form Name Spring 2017 Test 2 Recitation Section (see back of test): 1) Print your name, test form number (above), an nine- igit stuent number in the section of the answer car labele "STUDENT IDENTIFICATION". 2) Bubble your test form number (ABOVE) in columns 1-3, skip column 4, then bubble in your stuent number in columns A 3) For each free- response question, show all relevant work supporting your answer. Clearly box or unerline your final answer. Correct answers which are not supporte by aequate calculations an/or reasoning will be counte wrong. 4) For each multiple- choice question, select the answer most nearly correct, circle this answer on your test, an bubble it in on your answer car. Show all relevant work on your quiz. 5) Be prepare to present your Buzzcar as you turn in your test. Scores will be poste to WebAssign after they have been been grae. Quiz graes become final when the next quiz is given. 6) You may use a simple scientific calculator capable of logarithms, exponentials, an trigonometric functions. Programmable engineering calculators with text or graphical capabilities are not allowe. Wireless evices are prohibite. Numerical Constants: k = N m 2 /C 2 eo = C 2 /N m 2 e = C g = 9.81 m/s 2 me = kg mp = kg Your test form is: Our next test will be on Tuesay, March 14 page 1 of 8

2 The following problem will be han- grae. Show all your work for this problem. Make no marks an leave no space on your answer car for it. [I] (20 points) An insulating sphere of raius R carries a non-uniform volume charge ensity ρ(r) = C/r 2, where C is a positively-value constant The sphere is place in the exact center uncharge hollow conucting sphere of inner raius 2R an outer raius 3R. (i) Calculate the surface charge ensity on the inner an outer walls of the hollow sphere. (ii) (4 points EXTRA CREDIT) Apply Gauss s Law to fin an expression for the electric fiel within the insulating sphere, at a istance from the center of the sphere (i.e., for < R). Express your answer symbolically in terms of ε o, C, an/or R. Page 2 of 8

3 The following problem will be han- grae. Show all your work for this problem. Make no marks an leave no space on your answer car for it. [II] (20 points) A thin insulating ro is bent into a semicircle of raius R. It is place in the xy-plane as shown at right, with its center of curvature at the origin. Positive charge is istribute uniformly along the ro, with a linear ensity +λ o. (i) Use integration methos (i.e. not a memorize formula) to erive an expression for the electric potential at point P on the z-axis, a istance z = 2R from the origin. Express your answer in terms of λ o, R, an ε o. (ii) Suppose you trie to approximate the potential at z = 2R, by treating the entire ro as if it were a point particle (with the same total charge as the ro) locate at the origin. What percent error woul this approximation generate? [ Recall that %error = 100% (approx exact) / exact ] Page 3 of 8

4 The following problem will be han- grae. Show all your work for this problem. Make no marks an leave no space on your answer car for it. [III] (20 points) In the figure at right, a charge capacitor has plates separate by a istance. A particle of mass m an charge q is initially hel at a istance /3 from the right plate. (Note that the symbol q is inherently positive, so the particle itself has negative charge!) The particle is launche irectly towar the left plate with an initial spee v o. It is observe to slow own, stopping just as it reaches the left plate. Determine the electric potential ifference ΔV between the two capacitor plates. Express your answer symbolically in terms of the parameters given in this problem. Also, be sure to inicate which of the plates is at high potential an which is at low potential! Page 4 of 8

5 The next two questions both involve the following situation: In the figure at right, a positive source charge is hel fixe at the origin, an a negative test charge is initially at location i, moving vertically with spee v!. The test charge follows the otte trajectory, reaching position f at which point it is moving vertically ownwar. Question value 4 points (1) What can you say about the energy changes of the test charge, as it moves from i to f? (a) (b) (c) () (e) The charge has lost kinetic energy an lost potential energy. The charge has gaine kinetic energy an lost potential energy. The kinetic an potential energies of the charge have remaine unchange. The charge has gaine kinetic energy an gaine potential energy. The charge has lost kinetic energy an gaine potential energy. Question value 4 points (2) What can you say about the work one by the electric fiel of the (positive) source charge, an the electric potential ifference move through by the (negative) test charge, as the test charge moves from i to f? (a) (b) (c) () (e) The fiel has one positive work an the charge has move to higher electric potential. The fiel has one zero work an the charge has move to lower electric potential. The fiel has one negative work an the charge has move to higher electric potential. The fiel has one negative work an the charge has move to lower electric potential. The fiel has one positive work an the charge has move to lower electric potential. Page 5 of 8

6 Question value 8 points (3) A cylinrical conuctor of length L an raius R carries a total charge +Q. Which graph below best represents the magnitue of the electric fiel E(r) as a function of the istance r from the cyliner s axis. Hint: You may assume that L >> r, an that the conuctor has been allowe to reach electrostatic equilibrium. (a) (b) (c) () (e) Question value 8 points (4) Four very large, uniformly-charge sheets are arrange as shown at right. Rank the magnitue of the electric fiel in regions A to E, from the greatest to the least. (a) E! > E! = E! > E! = E! (b) E! = E! > E! > E! = E! (c) E! = E! > E! = E! = E! () E! > E! = E! > E! = E! (e) E! = E! = E! = E! = E! Page 6 of 8

7 Question value 8 points (5) What is the next flux through the torus of the figure at right, if Q! = 2.2 nc an Q! = +4.4 nc? (a) +750 N m 2 /C (b) 250 N m 2 /C (c) +250 N m 2 /C () 750 N m 2 /C (e) +500 N m 2 /C Question value 8 points (6) Three charges are initially place at the corners of a equilateral triangle having sies of length, as shown at right. How much work must be one by an external agent in orer to remove charge Q to a istant location? Assume all charges begin an en at rest. (a) (b) (c) () (e) 2kQ2 + kq2 + 3kQ2 + 2kQ2 kq2 Page 7 of 8

8 PHYS 2212 G/J Recitation TA an Room Assignments Tests will be returne in recitation, in the week after the test. In orer to ensure that you receive your test back as soon as possible, please enter your recitation section from the table above (G01 G10) on the front of this test. Page 8 of 8

Second Major Solution Q1. The three capacitors in the figure have an equivalent capacitance of 2.77 µf. What is C 2?

Second Major Solution Q1. The three capacitors in the figure have an equivalent capacitance of 2.77 µf. What is C 2? Secon Major Solution Q1. The three capacitors in the figure have an equivalent capacitance of.77 µf. What is C? C 4.0 µf.0 µf A) 7 µf B) µf C) 4 µf D) 3 µf E) 6 µf Q. When the potential ifference across