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Test 1 Fall 2007 - <7 0 ° 7 Problem 1(23 pts Two...

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Unformatted text preview: <7. 0 » ° 7 Problem 1 (23 pts) Two small plastic balls with charges +2 nC and -2 nC form a dipole, oriented vertically as hown in the diagram The two plastic balls are separated by a distance of 6 mm, and the center of the dipole is located at H m. A small charged glass head has a net charge of- 8e—13 C and is located at <-4, 3, 0> 111. (You can safely treat the small bead as a point charge.) The observation location 15 the origin, marked with an “x ” (a) (3 pts) On the diagram, draw an arrow representing the electric field due to the dipole at the location marked “x” Label the arrow Edipole . (b) (3pts) On the diagram, draw an arrow representing the electric field due to the glass bead at the location marked “x”. Label the arrow Elm . (c) (10 pts) Calculate the net electric field vector at the location markedx “ ”. Show all your work! /€pmoutl : q”:— (31:5 : (apogee- ”Megs _ 3 ,5 €_ 7 4/ ———_.—§____ _. , ‘- (7) C E = O - Al DIFDLE <) 3 [SC- ‘7’ E )O> 1:; :<o,,—oo>—<43,o>m:<9 "30>w 540 To 0416/“ A e / Ce r =(‘7m)("”"” .<‘/fi3)0> (‘1‘ +31) Maw?) _—_ (—2.73541‘!)<i “—3. CD (—130.54) /.735—‘{,05_ff ‘ 15> E = o — ’V ”ye-r 011’0LL7+ arm —.,7. 3 E ‘l /. 7.22 E 4/ a): (d) (4 pt 5) A bromide 1on (Br, charge of —e) 15 placed at th origin. Calculate the vector force on the bromide 1011. i I ( / 6 y u > M [LBr gflr m7 ' 6- 7C)<’7-? 5 cl) LVQQE I < (am 523 IV 2.2 35-23 ’V) 0> ) (e) (3 pts) 011 the diagram, draw an arrow representing the vector force on the on bromide ion. Label the arrow FE, . Problem 2 (23 pts) Your friend shows you an unfinished program which is intended to calculate and display the electric field of a dipole at a single location. (a) (19 pts) In the blanks, write the VPython statements needed to complete the program Use the names already defined in the program. from visual import * from __future__ import division minus = sphere(pos=(—2e—10, O, 0), radius=.3e~lO, color=color.green) qm = —l.6e—l9 plus = sphere(pos=(2e—10, O, O), radius=.3e~10, color=color.magenta) qp = l 6e—l9 oofpez = 9e9 scalefactor = 7e—20 obs = vector(0, ~5e—10, O) rp = obs — plus.pos rpmag : 54ft (rF.X**2 +rF-7—‘Fal‘2. +rf),'-Z *x 1) rphat = r r m 4, Ep =(00'fl3ea x %g {FEW-a; +12} + rpm-e rm: Obs‘hinos. OS rmmag= 5 rt(rm. Kane 2 +‘rm. >t~x2 +rm.2**2) rmhat = VIM/rm maj/ Em: oo 22* m V'mma *lczlaxrmha-t Enet = Er +5144 Earrow = arrow(pos= 0‘75 , axis: 4:th *scalefactor) On the grid on the right, one small division represents 1e—10 m. (b) (1 pt) On the diagram to the right, draw the positive and negative point charges at the locations specified in the program above. Label each one clearly with u H a “+” ora - . (c) (3 pts) On the diagram, draw an arrow with its tail at the observation location specified in the program, pointing in the direction the electric field at that location should point. Problem 3 (14 pts) In a particular region of space there is an electric field E] that is nearly uniform in magnitude and direc- tion, due to charges that are not shown in the diagrami The magnitude and direction of the electric field E1 are indicated by arrows shown in the diagrams below. (a: 3 pts) 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 x, 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. E l m @@@ plastic rod E1 E1 (b: 3 pts) 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 tex— book and in class. " 65-“ .- (on metal rod (c) (4 pts) In the center of the metal rod, at the location marked by an x , draw an arrow representing the elec— tric field at that location due only to the charges in and/or on the metal rod. Label the arrow Erod- Or, if this field has zero magnitude, state this explicitly. (d) (4 pts) How does the magnitude of fired compare to the magnitude of E] P Explain in detail how you knowthis. -> ,5 l ER”) : [En ) ) —— BECAUSg gym, :0 “I pie-Tm. ,4: gm?" Elton +EI'O $71477 C €61 VIC/1347051 3A ProblemX(25 pts) A thin plastic rod, of length 4m, lies along the x—axis (only a portion of the rod is shown in the diagram). It has a charge of —300 nC uniformly distributed over its surface. A thin glass ring, or radius 6 cm, is centered on the y-axis, 10 cm above the rod. It has a uniform charge of +2 nC. 06'“ y K a ring radius 6 cm charge +2nC —————— i / 0/9/68 7: 2e, ~fi C‘ 1 Charged rod ength 4 In Charge ‘3OOHC x Z L (a: 23 pts) Calculate the force on a small ball with charge —5 nC placed at < 0, 0.05, 0> m. Your answer must be a vector. Clearly show all steps in your work. _. J.— Qz‘ : .2 * (-05-) V /EfllI/6/“‘ b/fléo (KZ+ZJ—33/1 & @eq ( Q Ci)2)3,L : I89? ‘7’)— (.o¢1+ 05' a _L EM: <0) ~127/7)o> % 2 cal/L) _ _ M /Ele°o/: 5/7750 4r 2 ‘76; (2))i:0)oe 61): “27°00m 05 .::> — .. V ' EMD— {0, 27000 ) 0774 15/57: €400+E3N6 ~ <Ol#‘2839?)0>% .A A V F: if: (”52—7)C<O)”2839?,0>74 E :<O)/.s’5‘e-_‘/,o>'\/ (b: 2 pts ) Draw the force vector you calculated on the diagram. ...
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