PHYS227N S13 COOK Test 1 - OLD DOMINION UNIVERSITY PHYSICS...

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Unformatted text preview: OLD DOMINION UNIVERSITY PHYSICS 227N/232N, University Physics Spring 2013 First Examination 8:30 am - 10:20 am Tuesday 05 February, 2013 Room 142, OCNPS PROFESSOR: Dr. D. C. Cook Answer all questions: All questions should be answered on the examination paper. If more space is required, attach sheets to paper. Text book may not be used. Candidate's -.-3‘ .11. ' mug N CONSTANTS AND EQUATIONS 80:8.8510'12(:2N_1m'2 1nC=10'9C 1pc=10‘6(: k = 47:80 = 9.00 109 N m2 (3'2 Electron charge 6 = -1.60 x 10'19 C k Fe = quzqz 1‘ Electron mass rne = 9.11 x 10'31 kg k E = fi 1‘ Proton mass m = 1.67 x 10'27 kg r2 p k k U = (’11le V = % F = Eq 1. ELECTROSTATICS I (Total 25 Marks) A charge of q1 = 30.00 uC is place at the origin 0 (position (0, 0)) as shown in Figure 1. A second charge of q2 = -50.00 uC is brought in from infinity and placed at the position P (2.00m, 0) along the x—axis. A point R is located at (0.50m, 0) along the x—axis. Figure 1. (i) Calculate the electric force on q; qum ; .. = 3.3%‘M 1' r (2.00m? w _ n. "a . __. ‘f‘f’ \/ A “ 7* M”; m... ‘ ANSWER-é. aaSN 4 (ii) Mum pomi‘gy‘fimspair of charges. Urlfij: =L(gO§’lDC 3 (—eroc— lac.) Y C 00m} M ANSWER '- (of-K 3' (iii) Calculate the electric field at the point R. E'- 5:; C Y2 ‘V 30240C. + (‘Sogfl'bc‘km , "10.7757- LWM‘ Ll. l“'- ANSWERi selmg‘ N/c, Continued on Page 3 (iv) Calculate the potential at the point R. \j: fl = k<30l§40€ _ {DE-MR A third charge of q3 = 15.00 uC is now brought from infinity and placed at position R. (v) Calculate the electric force on q3 Emmi ,» = L (gee-agora'E-MT + (gee—obtfie—‘oo E» V‘- (o.§m)7- (l-5N‘W /3 p ANSWER lcl .Z N 3‘ (vi) How much work was done to move q; to R? wr‘fl o5 = — ms: / v19? (WWW? t V—Gtfls 3r \4°\3¢(L ' _ .. - \Lse-M'X =\L w +G°Ezgéflc ANSWER — 3923) j ._ 7.0”; + ((—soewcwse— be) :0 If} bu : ~J-I‘r- (re-7;):3r Jar End of Problem 1 2. COULOMB’S LAW (Total 25 Marks) Two small spheres each of mass m = 15.0 grams are hung by silk threads of length L = 1.20 m from a common point as shown in Figure 2. When the spheres are both given the same negative charge of q1 = q; = -2.80 uC each thread hangs at the angle of 6 to the vertical and the two spheres hang in static . . . /_ t , ,2 equlllbrlum. 7’ P _’ O (a) On Figure 2 draw all the forces acting on each sphere. . Cc Flgure 2. l (b) Calculate the angle 6. ._ , , m I» - S N Z / aflovsvcgm an Is ~ LH‘H / L \ ' Q, Q 9n. / :g‘SmB Y7. 1 . Ce “7’ e R *ame :' Ol1t7>§qu (him) S\ne iflcvfiz 4 (ages (-zfie'bbl ‘ \ 2: “I - S\ne C036 00" ANSWER End of Problem 2. 3. ELECTROSTATICS II (Total 30 Mar s Three charged particles, q1 = -4.0 uC, q; t -4.0 uC and q3 = +4.0 uC are located at the corners of a right-angled isosceles triangle whose two equal sides are length a 2 0.10m, as shown in Figure 3. The point P is located at the position of charge ql at the bottom right corner of the triangle. ' C12 ,\ “o . ~ / ' L/\ M5“ x I \ \ \ \ \ \ \ \ \\\ D¢m a F \ . >0 ‘~ 0 \ xV‘DY Figure 3. P ’ “\‘D V Calculate the answers to the following 3 guestions. (i) Calculate the Electric field (magnitude and direction) at the point P in Fi ure 3. r~ g + C. qubC g\‘(\"\§vi\fl 5 Y. " “' \1— W4?“ ' t Y O‘D’Lm 0,01. '\ bf ’26?) D \ 263 = L (Ac—cc. musfi .. ’ 1 _ 1' k ' b 0-07. E ‘ ‘ vs a. +on\ M735 H: 5.3.5.; r '732”*\0k\1 -\ E sum A0“ = gov: ANSWER ’2. (95' c to N/C. Direction a 3 ° (12 Marks) [Continued on Page 6 (ii) Calculate the Electric Potential Energy of this system of 3 charges. 0’ \¢°\\°\'- L) =lc («145- (oQC’LlE'bq » {Kim Y' ANSWER — \fisto J. Marks) (iii) What is the electric potential at the point P? w M. \l¢ ‘t 35:23. + 14.5%) 7 _ \llozm °'\“" 6 ANSWER warms” M . ‘5 Marks) (iv) What is the electric force (magnitude and direction) on the charge q1? r. k.7_ ” Z '. [xx E Di”! r “r p: 6: @(HC (or) A' n) /] ' \1 _ E— ” \ _, - , 'r I“ , \L U V. [V ANSWER \H. N. Direction Q’ (+1) }5 Marks) End of Prob 3 4. CHARGE IN AN ELECTRIC FIELD. (Total 20 Marks) An electron is projected along the x-axis with an initial speed of v0 = 1.60 x 106 m/s into an electric field between two parallel plates as shown in Figure 4. The electric field is uniform in the vertically downward direction, and has a magnitude of E = 300.00 N/C. The electric field outside the plates is zero. The plates are separated by a distance D = 1.00 cm and the plates are of length L = 2.00 cm. The electron enters the field mid-way between the plates at x = 0 and y = 0, i.e. position (0, 0). The electron hits somewhere on the fluorescent screen located at the right end of the plates. Wew‘flu'flwmhhm I: raven-q um-Wam Figure 4. (i) On Figure 4 label the positively and negatively charged plates. (ii)What do you know about the magnitude of the charge n each plate? L 1+: Qmml H‘s (gawk? W €\~(o0x\o"°‘cv 4 (iii) Calculate the position on the screen (along the y axis) that the electron hits the green. Also mark the location on Figure 4 and label it “e”. h f/ m L. " <>< _ E W) 6L \0 ’ F ./ 61/? 7 ‘ C6 (V f‘ \1 a \3 -300“\Q ’ x»\' [q-“vJO—‘MU q QA “Vs-2B = gfi'S—ilvlb’w 44 _ A y _ OLQL/ Continued working on Page 8 V ' R— M.— U Fame“? (iv) If instead the projected particle was a proton, mark the approximate location “p” on Figure 4 where you expect it to hit the screen. End of Examination ...
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