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Test 1 Spring 2009 - PHYS 2212 Test 1 January 29th 2009...

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Unformatted text preview: PHYS 2212, Test 1, January 29th, 2009 Name (print)_ ___________ k 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! o Show4what goes into a calculation, not just the final number, e.g.: 34’ = W = 5 x 10 ' 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 (20 Points) A negative point charge of unknown magnitude is at location A < 0,2,0 > m. At location B < 1,1,0 > m, the magnitude of E—field due to this charge is 3.5 N/ C. (a 8pts) Calculate magnitude of the E—field at location C < 0, —1,0 > m. #7 A A : <1,~\) 05M lfil15-Z A 73’ ’ fig/-3: (0,4,0).— 03,7705 .— z :<o,*3,0>m Will—.3 B _,t 7: EB—Llrrgb {$572, :: 475lfi'leB .. 2, _.L. 2 _, ”7‘ E 5c' 417651537" (at B (b 6pts) On the figure, draw the E—vectors at locations B and C. Take care with the relative lengths of the vectors, as well as the directions. (c 6pts) Calculate the direction of E—field at location B < l, 1,0 > m. Express your answer as a unit vector in component form. Put your answer in the box provided. A l \ E=<‘a, a, 0 > Problem 2 (20 Points) You have two strips of invisible tape, each about 15 cm long, with a mass of about 0.20 g. You smooth them down onto a table, one on top of the other, as was done in lecture and lab. You label the top tape “A” and the lower tape “B” The “sandwich” of two tapes is pulled slowly off the table. You rub your hand along the slick side of the upper tape, and observe that the tapes, still stuck together, do not interact with your hand. Now you quickly pull the tapes apart. You observe that both tape “A” and tape “B” are attracted to your hand, and the tapes are attracted to each other. Tape “B” is repelled by a negatively charged plastic pen. You attach the ends of tape “B” to the tops of two books, so it hangs loosely, in the position shown by the dotted line. You hold tape “A” above it, and slowly bring it down above tape “B”. When tape “A” is 2.3 cm above tape “B”, you see the middle of tape “B” begin to buckle upwards, as shown in the diagram. (a 15pts) Calculate approximately the amount of charge from a fundamental principle and clearly show all steps in 'l'aipe P.) Olocsmf’k MGM , A ~41 ’5 A .é ¥MYZQ+FC130 la original position of tape B on tape “B”, both magnitude and sign. Start your work. 9 .37 $=o or i=0 J. FM% :0 ici'éi .3. 3 (W3 '2) 4m (b 5pts) What approximation(s) or assumptions did you make in this calculation? Explain clearly. *4//o£ via/e (B ;5 ’e“ .AJcJ Problem 3 (20 Points) A small, very lightweight hollow aluminum ball carries an unknown amount of charge. The ball is suspended from a cotton thread. The events depicted in frames 1—6 then occur, in sequence. All diagrams show cross— sectional views of the objects. 1. The charged ball is 2. The ball is brought 3. The ball swings initially far away from close to an uncharged toward the block any objects. copper block (without touching) Diagram Diagram 4. The ball briefly 5. The ball swings away 6. A negatively charged touches the block. from the block and after plastic pen is brought a short while hangs at near the ball and the an angle of about 10 ball is repelled. degrees Diagram Diagram (a 12pts) For frames 1,3,5 and 6 write the 1etter(s) of the corresponding diagram(s) (A—P shown on the next page) that best depicts the distribution of charge in and/or on the aluminum ball, following the conventions for diagrams discussed in the textbook and class. Some letters may be used more than once; others may not be used at all. Diagrams showing cl,i,sti“il:mtin:m of chm‘gc in ancL-Fcrr 0n the aiumimm‘t ball. Only 3331— 1. + + i _ 4+ . i: terns are shnwn, flat magnitudes: bath riastrlb‘uncms at fight wmdd he represented by L‘, 1 131* O - ~ + f + a diagram A. *+ + +” (b 8pts) Suppose the final charges on the objects are measured, and found to have magnitudes |Qbaul, IleockI, and [QpenL In terms of these quantities, What was the initial charge on the aluminum ball? Chou/c”: CHLS'O/V’A'ia“ " lam; = \wai *- Mum Problem 4 (20 Points) A dipole is centered at the origin, as shown. Each charge has magnitude 4.0e—9 coulombs, and the distance between the two charges is 0.5 centimeters. The E—field at location C is indicated on the figure, directed toward the origin. (a 2pts) Indicate on the sketch which of the charges is positive, by drawing a plus—sign on that charge. (b 6pts) Draw the electric field vectors at locations A and B indicated by the crosses. Assume both A and B are the same distance from the origin as location C, and that this distance is much greater than the distance between the two charges. Pay attention to both the size and direction of the vectors you draw. If the E—field is zero at either location, write the word zero there. (c 12pts) Suppose we want to place a new charge at location C, so that the total electric field at the origin is zero. If the distance from the origin to location C is 20 centimeters, what value should this charge have? Clearly indicate both the magnitude of the charge (in Coulombs) and the sign (positive or negative). 6: Au i’b dipait at on'JM twink di’ / S‘a chm/ale ai’ C mats in be [Will/e“ _...L7 2 ,. ’— 4. f .— / 7—0 flu C O 5‘” Lime I” 4/143 {02 7776—0 ”(1 ’7 re 2 /' '1 0.1’2 2 ' Z .2 r‘ 2. $2 (1/012) (4v/0 7) H Problem 5 (20 Points) In a very thin spherical plastic shell of radius 15 cm carries a uniformly-distributed negative charge of —9 DC (—9e—9 C) on its outer surface. An uncharged solid metal block is placed nearby. The block is 10 cm thick, and the left surface of the block is 10 cm away from the surface of the sphere. l 10cm l 10cm I (a 4pts) Circle the diagram below that best represents the charge distribution on the block. y¥$¥¥¢¥44 fiffifffifi: +++++++£+ ++¢¢1¥++r (b 4pts) Draw the E-field vector due only to the charges on the plastic sphere at the point “x” on the above diagram. Label this vector Es (c 4pts) Draw the E—field vector at the point “x” on the above diagram due only to the charges on the metal block. Label this vector Eb - (d 4pts) Calculate the magnitude of Eb. Express your answer in newtons per coulomb. ( t V E : E *hhbto 1:5 Eb /c_ Mi’ , i=3, % . atag (e 4pts) Now consider the net electric field at the point labled “A” on the above diagram. If the metal block is removed, will the magnitude of this field increase, decrease, or stay the same? Explain your reasoning. Mksni'i'floqi (pl (A &CCM5LSC. ‘7/c_ “JP-A gs ‘lrEb 'Paiw-lr {a 43-44" 904M} Syrieérmw, ...
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