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# test1_solution - Problem 1(30 pts(ﬁgure not to scale A...

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Unformatted text preview: Problem 1 (30 pts) (ﬁgure not to scale) A glass rod, 2 m in length, with a uniformly distributed charge of Q = +5.3e —9 C, lies on the x-axis, its center at the origin. A hollow plastic ball, with a charge of q = —l.4e —9 C uniformly distributed on its surface, is above the rod, and its center at < 0.08, 0.06, 0> m. (a, 20 pts) Calculate the net electric ﬁeld at the observation location < 0, 0.04, 0> In, marked with an “X” on the diagram. A Show all your work. Express your answer as a vector. ’ ,2 , .27 5.3 ea) i‘ER00i:LTnneo (GE/L.) —(7&‘i) ( ( e :_ //‘7'2.5' é! ._\ r‘ (02 )(0.043 —— —— M "Ma. (UN/72.5 E' I 0)’ AngLL : 9716—61.: (1:77.? ) F: <0)0'0L/)0>m~<0.08)0.OG)O>H: ‘ r <~0.08}‘0.02)f0>m [F]: V*o.0069m1 : 0.033% m ,0: i: (-0.9701—0M2L/310v ——- __ (”(#4) <— .Civo)-0.:zq3,0>= —/85‘2.7('-970;‘.373.0> EBRLL— (ﬁfe C?) .0098 ‘9 ~—‘ «.4 M t : 7 _ :1 (I747) 4579,0753; ) Eun' EMLL+ERM <17? ) /6 43 t 07c (b, 4 pts) List any assumptions or approximations you made in your calculation. 0 LEA/67H 0F Ron >7 ptsnucg F120”! R00 7‘0 085. LOC‘ 42 PLASTIC BALL IS NOT POLARIZED MUCH {57’ ERG/J (BALL BEHAVFS L//<e' A Pom/7' CHAKG€> (c, 2 pts) On the diagram, draw an arrow representing the net electric ﬁeld at the observation location. ((1, 4 pts) An alpha particle (charge = +28) is at the observation location. Calculate the net electric force on it, and express it as a vector. .5 F3? E:(¥)(ﬂée~lé)</7?7) /é‘/3)O> N :<5.7{€«/¢) {owe-m, 0 >A/ Problem 2 (25 pts) (a, 9 pts) Locations A, B, and C are all the same distance from the center of the dipole. At each of the locations, draw an arrow representing the net electric ﬁeld at that location. A longer arrow should represent a ﬁeld with larger magnitude. (b, 6 pts) Location C is a distance r = 6e-10 m from the center of the dipole. The magnitude of the charge of one end of the dipole is q — 1. 6e-19 C and the separation between the two charges 15 s I 1. 8e— 14 m. Calculate the magnitude of the electric ﬁeld at location C. L/ﬂéo i. /§/= 4-— T: (1e?) (Me ”Mme-1‘01 (QC-(0)3 /.;285 E c Now, a second dipole, identical to the ﬁrst (same q, same s) is placed at location D, a distance y directly below (vertically) location C. The second dipole is placed in such a way that the net electric ﬁeld at C is now zero. (c, 4 pts) On the diagram at the right, draw the dipole at location D, clearly indicating the orientation of its positive and negative charges. (d, 6 pts) Calculate the distance y from the second dipole at D to observation location C. ) (Ema/=0 157/: Ml Problem 3 (20 pts) The VPython program below, when completed, will calculate and display as arrows the electric ﬁeld of a -3 nC charged particle at two different observation locations, called obs l and osz in the program. In the blank spaces below, ﬁll in any missing lines of code needed to complete the program. Your code should be written in terms of symbols and deﬁned variables, and should not use numeric values. from __future__ import division from visual import * #constants oofpez = 9e9 q = —3e—9 scalefactor = 5e—7 #objects particle = sphere(pos=( 0.03, 0.02, O), radius = 5e—3, color=color.red) obsl = vector( 0.01, 0.04, O) osz = vector(—0.02, —0.0l, 0) # Write the lines of code needed to calculate the electric field at obsl I“? 1' obsl -' Particle./aos .x >992 +017“sz + ripple.) [419‘447/3 53,“:(1‘1 rims: r1 /V‘j_m¢;, E1'=(oofre2 >4< 3 /P{Lm4;,>l<9€l> * Fit/.44: # Write the lines of code needed to Calculate the electric field at osz f2 = 0bs.2——/9artfc (e -,oos era = Sﬁrt (r2.xx*2 +V‘2.7’a<*2+r‘2.z>t<x2) fthEZF‘J/V‘QW“? E.) = (009‘ch *f/ VJWM}*:F2) >t< (‘2 hq-t # Fill in the blanks below E_arrow_l = arrow(pos = OLSi , axis = E l. *scalefactor) E_arrow_2 = arrow(pos = 01352- , axis = 6—2 *scalefactor) Problem 4 (25 pts) A small glass ball is rubbed all over with a small silk cloth (both initially neutral). The ball acquires a charge of +5 nC. The silk cloth and the glass ball are placed 30 cm apart. If any of the electric ﬁelds you are asked to draw is zero, state this explicitly. (a, 4 pts) At the location marked “x” draw two arrows, representing the electric ﬁeld due to the silk cloth, and the electric ﬁeld due to the glass ball. Label them E clo ECLOTH E glass ball L silk cloth '3" L Now a positively charged metal block is placed between the two objects. (b, 6 pts) On the diagram below, draw the approximate charge distribution in and/or on the positively charged metal block, using the diagram convention of this course. At the location marked “x” draw and label four arrows, using the same scale as in part (a): (c, 3 pts) The electric ﬁeld due to the silk cloth cloth, E (d, 3 pts) The electric ﬁeld due to the glass ball, E (e, 3 pts) The electric ﬁeld due to the charges in and/or on the metal block, E (f, 3 pts) The net electric ﬁeld, Em cloth ball metal T .1. + + +- silk cloth +- .l. glass ball + metal block‘l' Now the metal block is removed, and replaced by a neutral plastic block. (g, 3 pts) Show the polarization of a molecule at each location marked “x” below, using the diagram convention of this course. ‘ @@@——© glass ball silk cloth plastic block m and EM“ respectively. The relative lengths of these arrows should be correct. ...
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