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Test 1 Fall 2009

# Test 1 Fall 2009 - PHYS 2212 Test 1 September 16th 2009...

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Unformatted text preview: PHYS 2212, Test 1, September 16th, 2009 Name (print) __________________ __ _ _______________________ __ Instructions 0 Read all problems carefully before attempting to solve them. 0 Your work must be legible, and the organization must be clear. 0 You must show all work, including correct vector notation. 0 Correct answers without adequate explanation will be counted wrong. 0 Incorrect work or explanations mixed in with correct work will be counted wrong. Cross out anything you don’t want us to read! 0 Make explanations correct but brief. You do not need to write a lot of prose. 0 Include diagrams! ——3 6 0 Show what goes into a calculation, not just the ﬁnal number, e.g.: 953 = W = 0 5x104 0 Give standard SI units with your results. Unless speciﬁcally asked to derive a result, you may start from the formulas given on the formula sheet, including equations corresponding to the fundamental concepts. If a formula you need is not given, you must derive it. If you cannot do some portion of a problem, invent a symbol for the quantity you can’t calculate (explain that you are doing this), and use it to do the rest of the problem. Honor Pledge “In accordance with the Georgia Tech Honor Code, I have neither given nor received unauthorized aid on this test.” Sign your name on the line above Problem 1 (25 Points) A point charge q1 with charge 4.0 x 109 C is located at < 3,0,0 > meters, a point charge qg of 3.0 x 109 C is located at < 0,4, ——5 > In, and a point charge q3 of —l.2 X 109 C is located at the origin. When answering the following question be sure to express your answer as a vector. (a) (8pts) What is the vector electric ﬁeld at the origin due to the point charge ql? _/’7 i %‘p\ —5> Fiﬁ “'1” r : <0,°/°> —<3,°/°> : (4,0,0) ' "c. F‘ ‘ \ W: 3 7‘." <'M°»°V 1 ﬁC) l7 249/09?) = we (aw/C ' L 3m) {2: ring 776 C: (0)0/o>—<olql-§f : <0,v4,§‘7 L [61:64)Z+(S)1: m “r: (o, ’é‘,%> A MM), 3.IO?C/ '4 g EL‘7(O?)(WM)Z<OII,E> 1:7 : <Ol_q,u,/o"+/ 5’4"”? >M/C. (c) (4pts) What is the net vector electric ﬁeld at the origin due to point charges q1 and Q2? 2? ,7 2-) 5 I1 I? 5w+£ «*Ez : <‘4'lo‘10/-O\>+ <OI'4'H'(o I SILL/O ‘> 7— 1 : (—4wﬁ, elk/(«(0, ,SILMO' >AJ/C (d) (5pts) What is the force on the charge at the origin? Your answer must be a vector. Show all work. a _>) )3 1—7 I /J>M "‘ (—/,zﬁ/o¢'C)<~‘f-/O ,i4.//'/0 I 314 (a /C j 20 : mm“ +4~.e-/J‘i—a.n~w > N I Problem 2 (25 Points) Locations A, B, C, and D are each 3 x 10—7 m from the center of the dipole shown in the diagram below. The dipole consists of ions with charges +6 and —e, separated by a distance of 2 X 10‘10 111 (note that the diagram is not drawn to scale). 03 I’ “3/ I I ’ I I as \ \ \\ ‘9 \‘ 6‘) \‘ Q N x \ (a) (12pts) At each of these four locations, draw an arrow representing the electric ﬁeld due to the dipole. The relative magnitudes of the arrows should be correct (that is, a longer arrow represents a larger mag- nitude). Clearly label each of the four arrows E. (b) (3pts) At a particular instant an electron is at location D. Draw an arrow representing the force on the electron due to the dipole. Clearly label the arrow F. (c)(10pts) What is the magnitude of the force on the electron, due to the dipole? State what approxi- mations or assumptions you have made in your calculations. Show your work. 2 (lvk'ioeiﬁél(21/0'IOM> 5 EM :5” Z3 : (ﬁ’ﬂﬁﬂﬁ ) 3 ,i’v 491\$?) 1’ Ca {Ea/Quark?) : /0.[z& N/C V —i3/\/ fizg : (It-Iod’erUO‘H'J/c) " WW9 aka “(AWML \Cva M d A 85 u W slim m 36} l) g Willi Cm L lg riflUﬁ law? 6 V bll/UL (Show as Ell/mi“ (“waft/{w Problem 3 (25 Points) —} In a particular region of space there is an electric ﬁeld E 1 that is nearly uniform in magnitude and direction, _, due to charges that are not shown in the diagram. The magnitude and direction of the electric ﬁeld E 1 are indicated by arrows shown in the diagrams below. (a) (6pts) A plastic rod is placed in this region, resting on an insulating support not shown in the diagram. Show the polarization of a molecule inside the plastic rod at each of the three locations indicated by an 1:, using the diagrammatic conventions discussed in the textbook and in class. If a molecule at a given location would not be polarized, state this explicitly. (b)(6pts) Now the plastic rod is removed and replaced by a metal rod. On the diagram below, show the charge distribution in and/ or on the metal rod, using the diagrammatic conventions discussed in the textbook and in class. E1 llll (c) (6pts) In the center of the metal rod, at the location marked by an m, draw an arrow representing the electric ﬁeld at that location due only to the charges in and/or on the metal rod. Label the arrow E Tod. Or, if this ﬁeld has zero magnitude, state this explicitly. (d) (7pts) How does this magnitude of Brad compare to the magnitude of E1? Explain in detail how you know this. (Emmi, : We in W mtoxl. is<0,O,O§H/C MM a sax—ac gist;th Problem 4 (25 Points) A plastic ballpoint pen of length 14 cm acquires a charge of —3x10‘8 coulombs, distributed uniformly over the surface of the pen. A solid aluminum ball suspended from an insulated string acquires a charge of —2x10—9 C. The charged ball is brought near the pen, as shown in the diagram. The center metal ball of the ball is 3 cm from the pen. pen (a) (3pts) On the diagram, clearly show the distribution of charge in and/or on the pa aluminum ball. (b)(3pts) On the diagram draw an arrow labeled Eel showing the electric ﬁeld at the center of the ball due to charges on the wall. (c)(3pts)_)On the diagram draw an arrow labeled Fe; showing the electric force on the aluminum ball. __’_._ T I I l I I I | I I I I (d) (8pts) Calculate the magnitude of the electric force on the aluminum ball due to the charged rod. You can assume that the ball is small enough that it can be treated like a point charge. Furthermore, the ball is close enough to the pen that you can use the approximate value of the electric ﬁeld of the charged rod. Efci §'~l‘ E815 -’(7407Nm2) 2(54533/U4u63l ﬂ #________._ 417th F c1 (K {0}?) : imwo‘NQ _ —"l 7!; 2’: : (t/o’quU'Z‘WKOLV/C): 25.1” N 'ﬁmd ' (e) (8pts) Repeat the calculation from part (c) but this time use the exact value of the electric ﬁeld of a charged rod to ﬁnd the force on the ball. Was the approximation made in part (c) valid? I . [5‘(O—sc) If“ grad “’ 4774,?) I” (142)?» {7'10 I" )( )HLJLHO 'L 310—2541) \lla'ID M H a p.53? —4 Z-3éI % —; 3,70%; EW‘W" ...
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Test 1 Fall 2009 - PHYS 2212 Test 1 September 16th 2009...

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