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exam1solutions - Exam 1 Physics 2102 Fall 2009 Name...

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Unformatted text preview: Exam 1 Physics 2102 Fall 2009 September 24, 2009 Name: Solid; [gig ID # Answer all questions (7). Some questions are multiple choice. You should work these problems starting with the basic equation listed on the formula sheet and write down all the steps. Although the work will not be graded, this will help you make the correct choice and be able to determine if your thinking is correct. On problems that are not multiple choice, be sure to Show all of your work since no credit will be given for an answer without explanation or work. These will be graded in full, and you are expected to show all relevant steps that lead to your answer. Please use complete sentences where explanations are asked for. Please be sure that all numerical quantifies include appropriate units. The only electronic devices to be used during the exam are standard or graphing calculators. - All cell phones should be turned off and put away. Cell phones are not to be used as calculators. 1.) (20 points) Two point charges, of ~10 11C and +3.6 nC, respectively, are fixed in place on an xy coordinate plane as shown in the figure. At a point on the plane, P, no charge exists, but there is an electric field due to the presence of the two point charges. a) Calculate the electn'c potential at point P, taking the potential at an infinite distance to be zero. .._L-— ééi‘l Lit—+53. ' P'HTJZ r.- Wéalc e "”53”“ . (a V ”,L» donoqc ggxw'c"; _ V l’f‘llrLLo S‘om 30m 5 31101 b) At point P on the figure, sketch (and clearly label) three vectors the electric field contribution due to the -10 nC charge the electric field contribution due to the +3.6 :10 charge the net electric field c) Calculate the electric field vector at P in unit vector notation. —‘> _ A 4 , all 1c SVPWO- S'HTOV).-§> (lender EM — Elt EE) 1’2} 3m“ ‘07: 0 0:44:4ka . .- 19‘ ‘ ~ .4 walk me Cmfig [ #546089 + 13.}. 9.5%,; EX: ELK ng :— lfllfléo [:3 W 635-340 F :.__L.— [-onm'flic coy—S‘s?) BGXLO—ciCE .«x Lin-6c) (6- MBa "’ + 63:0 my; 7" ' SMQ 7 i l EX": luHL/ U/c Ea: Elaily'Z-g}: Til-141) gr}: 5 “L” “WOW-16’ $3340 :a.<3‘6% t l T3136 @.om)b 2.) {10 points) The electric potential in a region of space is given by the expression V I 150WZZ where x, y, and z are in meters, and Vis in volts. Obtain an expression for the electric field vector in this region of space. Qh-é -vaQAJL/lflavA E-‘VV- .ch AM :gK QV D Vm %§__, :5 303 $512 Vm 3.) (20 points) A uniformly charged rod is bent into a semicircle radius r and has a positive charge density, charge per unit length, 7‘... i’oint P lies at the center of the circular are formed by the charged rod. a.) Without calculation, write down the magnitude of the x—component of the electric field at point P due to the charged semicircle. Indicate the direction of the electric field at point P on the figure above. Ex :0 E38 Saimw—dEL b.) Write down an expression for the y-component of the differential field, (E, at point P due to a small charge dq from a segment of length 68 somewhere along the rod. Leave your answer in differential form, there is no need to integrate the expression for this part of the problem. [Hintz don” t even think about using Gauss law for this problem ] 1 &E:7I:’:;_3,SM9 [W[¢E:7lféag r3” PM a fi -1 MS 5 0‘53M23 ‘ne ebser—D c. ) integrate this expression 0 o s at? I e y-component of the electric field at point P. Be sure to relate the variables S and 6 as well as to explicitly write the limits of integration. T - f a “R . Ed , {gig}: [Lb— we, 5),; Je—- "frZ—r 5M} d9 : silent“ [—i ‘— i] n 4.) (10 points) The figure below shows three different orientations of an electric dipole (with dipole moment p) in a uniform electric field E, which points in the positive x- direction. (1) *——> ____, E p p (2) —l—> E p . (3) —‘-¥—+E (a) Rank the scenarios according to the potential energy of the dipole in the electric field, ' greatest first (circle the correct answer): __ .s. r" .r ”d-)'E iri/ Fl‘E/‘UZO a)U1>U2>U3 O " ? .2. #0 b U2>U1>U3 a} §>LE 1. U, U3>U2>U1 i d)U1>U2=U3 $2) U70 e) All tie (b) Rank the scenarios according to the magnitude of the torque on the dipole in the electric field, greatest first (circle the correct answer): a) TI >12>T3 ®2>T3i11 78-71 fiX-{E} I it; 7-; H E/_ Tic: d)1:1>1:2=r3 Iii-1"- Elti—I 33119 5523* “Pam: ”ISM-E.” s5 jam/a smeél "l. 5.) (10 points) Circle the correct statements about conductors. Note, there can be more than one true statement. @Electx‘ic field lines always point perpendicular to a conducting surface. b) Conductors make poor shields for electric fields. @The static electric field within the volume of a conductor is always zero. d) Lightning never strikes a good conductor. .Ionductors are equipotential volumes. f) Excess charge on a conductor is uniformly distributed throughout the volume of the conductor. 6.) ( 15 points.) The figure below shows a (nonconducting) spherical shell with uniform voiume charge density, p, inner radius, a, and outer radius, b. a) Using Gauss’ law find an expression for the electric field at positions where r < a. 3%: §€-4§=% Gauss Law), For ma smock jawssmh Swim; — Stlere. mazes <1, CeVVi'e/v'fiéj od- Cmier‘ Of 5%:ch Shell, as Shawn . Hoie gem :o. SW0. foe Ms: gqusSW/v Qwhce “€le 193W07I MW a may” ,1: mi 133:}: WWW saw/rd? E'Aeo; b) Using Gauss’ law find an expression for the electric field at positions Where a<r<b. r a -" W , . GCNSS Low 1; .2 {EM 2. 35/ We a gramsm 8‘ch — SEW TRANS. F; 6(2ka (1+ ii? Cewier 0-i- we, 3mm: mu. rm quwicm‘e He CW ewe/lake! 19} OW 96¢“me Swfitfice— my aim _‘ V I f/LL’T (r3 '0‘35 "VOi em?+;r gem—8‘ Oenclogec! 3‘? 3 :2 £1an 7.) (15 points) Short answers. Answer with one or two grammatically correct English sentences. a.) The potential is a constant throughout a region of space. Is the electric field zero or nonwzero in this region? Explain. It 1% ante/real {s COASJfi/vfil— +hvgJe-Jl‘ cr Vega ch“ $1? W elCCdfi‘c tie/(d WSVL be Eero M +14: read". The (Basses was; to 36: Saw: 1% “medal; the flitotthm E':V V) LON/ice +{Ae ifldlend’ at a (MW {5 i Mean; Eem. b.) In a region of space where the electric field is constant everywhere, but not zero, is the potential constant everywhere? “0 3W- W: " f 5-015 (1% Mm, +lac+f3 m PQFWQW‘ +0 E glfizkis 0. gluing“? ?C) W . (3‘0 l 133i: Cmstvm-l' 1M W3 ‘tjlkm. c.) A positive test charge is placed in an electric field. In What direction should the charge be moved relative to the field, such that the charge experiences no change in the electric potential? / 1° eXfil-NCMQ flo chem/1%, m dig-M}: POkn'le/g H/Q dag: Must be. Moved FWQHJOJRF +0 the filed-ht field. ”3am, Smce AVl'fgéf/ «2 ML .L to 7;:ng a gem 49+ mw/ 0mg Was 20m Okanflg m 'Pci‘lewhal. ...
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