2212_Test1_Key

# 2212_Test1_Key - PHYS 2212 Test 1 Sept 15th 2010...

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Unformatted text preview: PHYS 2212 Test 1 Sept 15th 2010 Name (print)__________-_~____lé£:3 ____________________________________________________________________ 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! 0 Show what goes into a calculation, not just the ﬁnal number, e.g.: ":75 = W = 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 PHYS 2212 Do not write on this page! Problem 1 (25 Points) At a particular moment, three small charged balls are located as shown in the ﬁgure Where: Q1=2><10“QC Q22—4x10‘90 Q3=1x10-90 The charges are located at positions: FQI = (0,0.08,0) m Fm = (009,0,0) m F423 = {—0.08, ~0.04, 0) m (b 8pts) Determine the electric ﬁeld at the location of Q3 due to Q2. 3 “‘5 ——3 F2 = res ran. 1: IOJ? ~0.0'4 o>m :<-0.08,—o.a'+,o7—(0.0ﬁlolo7 < I I €22 AWE-b 2’ 'L 7’ \r l __ “ ‘ «0,04,059'14 I (—440 ’0) {LL—ﬂ.“- M... 27 m ) 2 W E: “(4190.3 nl/C, ){mcrwh‘l ~‘2z‘10, 0> -)) M E; : (Memo, was”) /c 7.. £2 : (Ll-103, 2.3740 , ojd/é (c 4pts) Determine the electric ﬁeld at the location Of Q3 due to Q1 and Q2. .2; .a —=-'> Elai— = E rEZ M 3 2 IA a”: <-l.5‘103,—2.3'(03,0>E+<"l"°I 2.7.10 ,0); .2 gm : <“5‘0"°2; 4.0403, 0) ”/c (d 5pts) Determine the net electric force on Q3 due to Q1 and Q2. .27 ,9; I: ‘7’ Q3 EM+ '23) Problem 2 (20 Points) The following program is intended to calculate and display the electric ﬁeld at several locations due to an electron. Complete the program by ﬁlling in the blanks with the necessary VPython code. You may ﬁnd it helpful to write out the algebra, then translate it to VPython. Use the names already deﬁned in the prograrn. - ‘ from __future__ import division from visual import * ## Constants oofpez = 9e9 qelectron = —1.6e-19 scalefactor = 1e—20 ## Objects particle = sphere(pos=vector(1e-10,0,0), radius=2e-11, color=color.red) ## Observation Locations first_obs = vector(4e—10,0,0) second_obs = vector(1e-10,3e~10,0) ## (a 8pts) Calculate the electric field E_1 at the first observation location, first_obs r = «Firshobs - arh‘c . as tin/Mg = mag ((1) rihn+ : ViZWAWug -lma. = vol: 22“ eke-ham rim “L Evl a I«rill/tort 1 u eal = arrow(pos=vector(first_obs), axis=scalefactor*E_1, color=color.orange) ## (b 8pts) Calculate the electric field E_2 at the second observation location, second_obs r2 : ((jn,‘ __o v “r41‘&‘ .92; {‘Zmugi‘: Ma%lv‘l) TZl/tnl' ': r21 (‘Zvvma E-2 a, 1'? a 24 la ‘l'h {'2 “fl Eel '7— Ea'lmga 4’ V'Zl’hxl" ea2 = arrow(pos=vector(second_obs), axis=scalefactor*E_2, color=color.green) (c 4pts) On the ﬁgure below draw arrows that indicate the direction of the electric ﬁeld at each observation location (firsLobs and second_obs). ’ Problem 3 (25 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. t. 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. copger block (without I touching) Diagram B Diagram C'l 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 H Diagram H (a 20pts) For frames 1,3,5 and 6 write the letter(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 ball7 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. Diagrmm showiug (Eistribu {Lion of charge: in ancifqr on flat: almnﬁrunn baii. ()1'1‘iy'33at— ' x x ¢ I x - ‘7 f , ternx 31?? si*)mwn, mm m 23.31;!“ hides: bath chﬁh‘ihnftxom; at. right wank? be represen EECI 13}: f0.” or O . t. - + + 6,» dmgrmu A. ‘ (b 5pts) Suppose the ﬁnal Charges on the objects are measured, and found to have magnitudes IQbaul, lleockh and lQpen]. In terms of these quantities, What was the initial Charge (magnitude and Sign) on the aluminum ball? Gm); 2'- - 162M! - mum Problem 4 (30 Points) Fig. 1: A permanent dipole in a uniform electric ﬁeld. (a 2pts) On the diagram in Fig. 1, draw an arrow that indicates the direction of the net electric force on the dipole due to the uniform electric ﬁeld. Label the arrow Fnet. If the net electric force is zero, state this explicitly. Ml' ﬁrm, is gen: (b Zpts) For the situation shown in Fig. 1, state whether the direction of the net electric torque on the dipole due to the uniform electric ﬁeld is clockwise or counter-clockwise. If the net electric torque is zero, state this explicitly. ’ijbv‘77ukc, is clockwi se Fig. 2: ’5 a A neutral atom in a uniform F; F electric ﬁeld; the uniform elec- (—— 7 g ”’3 tric ﬁeld polarizes the atom, that ‘3 E is, the ﬁeld induces an electric dipole on the atom. The atom is ,1? shown just before it is polarized. Fact—7' (C Zpts) On the diagram in Fig. 2, indicate the direction of the atom’s polarization by either showing the locations of both the positive and negative charges in the dipole or by drawing an arrow, labeled 13’. (d 2pts ) On the diagram in Fig. 2, draw an arrow that indicates the direction of the net electric force on the induced dipole due to the uniform electric ﬁeld. Label the arrow Fnet. If the net electric force is zero, state this explicitly. . Ml three *5 Eco (e 2pts) For the situation shown in Fig. 2, state whether the direction of the net electric torque on the dipole due to the uniform electric ﬁeld is clockwise or counter—clockwise. If the net electric torque is zero, state this explicitly. {30¢ng CS Z'CVD Fig. 3: A permanent dipole placed near a negative point charge —Q. .- \- (f 2pts) On the diagram in Fig. 3, draw an arrow that indicates the direction of the net electric force on the dipole due to the point charge. Label the arrow Fnet. If the net electric force is zero, state this explicitly. mi ’QDFLQ. is wowu‘etm quit (mag lexHr (g 2pts) For the situation shown in Fig. 3, state whether the direction of the net electric torque on the dipole due to the point charge is clockwise or c0unter~clockwise If the net electric torque is zero, state this explicitly. 'iibrqw, 1': CGVW‘l’tV— ciockvuisc Fig. 4: A neutral atom located near a negative point charge —Q; the electric ﬁeld of the point charge polarizes the atom, that is, the ﬁeld induces an electric dipole on the atom. The atom is shown just before it is polarized. .3 —-—'-'? .3 g3. .. (h 2pts) On the diagram in Fig. 4, indicate the direction of the atom’s polarization by either showing the locations of both the positive and negative charges in the dipole or by drawing an arrow, labeled 13’. M} two; F: mauve—era and} (mud: (e34— (i 2pts ) On the diagram in Fig. 4, draw an arrow that indicates the direction of the net electric force on the induced dipole due to the point charge. Label the arrow Fnet. If the net electric force is zero, state this explicitly. (j 2pts) For the situation shown in Fig. 4, state whether the direction of the net electric torque on the dipole due to the point charge is clockwise or counter—clockwise. If the net electric torque is zero, state this explicitly. ‘ifO (Tl—e. ‘5 9‘4") Fig. 5: A metal block located near a neg- ative point charge (with charge —q); the electric ﬁeld of the point charge polarizes the block. (k 2pts) On the diagram in Fig. 5, illustrate the polarization of the block by showing the locations of both the positive and negative charges. (1 2pts ) On the diagram in Fig. 5, draw an arrow that indicates the direction of the net electric force on the block due to the point charge. Label the arrow ﬁnd- If the net electric force is zero, state this explicitly. (m Zpts) For the situation shown in Fig. 5, state whether the direction of the net electric torque on the block due to the point charge is clockwise or counter—clockwise. If the net electric torque is zero, state this explicitly. ”51‘in i3 a<rz>5 SiMilax rl-a «slam (\o‘er) (n 4pts) Determine the magnitude of the electric ﬁeld due to the block (and ONLY the block) at the observation location 0 marked by an ’X’ in Fig. 5. Draw an arrow at that location that indicates the - direction of this ﬁeld. Label the arrow Eblock' If the electric ﬁeld at 0 due to the block is zero, state this explicitly. ...
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