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Unformatted text preview: Physics 2212 G/H I rpTe'sitform E} 3 _ ,Namg Selems
~Spi'iug2008 . ’ MQuizS ' ' ' ' ' ' Instructions: seat:
1) Print your name, test form number (above) , and ninedigit student number in the
section of the answer card labeled "STUDENT IDENTIFICATION". 2) Bubble your test form number in columns 13, skip column 4, then bubble in your student
number in columns 5513. _' 3) For each multiplechoice question, select the answer'most nearly correct, circle this answer on
your test, and bubble it in on your answer card. Show all relevant work on your quiz. 4) For each freeresponse question, be sure to show all relevant work supporting your ﬁnal answer.
“Correct” answers without adequate justification will receive a reduced score. 5) Turn in your test and answer card and leave. Be prepared to show valid photo ID. Scores will be
posted under "Course Standing" as soon as'possible. Quiz grades‘become final when the next
quiz is given. ' ' ‘  ’    n . 6) You may use a calculator that cannot store letters, but no other aids. k = 8.99x109 Nm2/C2 e = 1.60x10'" C m. = 9.11x1o3‘ kg
5, = 8.85x10‘” C2/Nm2 g = 9.81 m/s’ m, a 1.67x10‘27 kg
Bldnk space  Feel free to use thisspace for stretch I I Standardlntegralr:
work »  “n+1
/u"du= +C (nsé—l) n + 1
fu"du = lnlul + C (n = 1)
/ sin(u) du = —c03(u) + C
/ cos(u) du == sin(u) + C
/e“ du 2: e“ + C ' ~/ue"du=l(u—1»)‘e“+C pagelof7 331 The following problem will be handgraded. Make no marks and
leave no space on your answer card for it. new M i h ‘5 with“: . 4+1 [I] A capacitor consists of two plates separated by a vertical distance H. The top plate is . V = 0
_ held at an. electric potential V'== 0, while the E POE/Wis gram 5%
bottom plate is held at potential V= —V°. 1° ‘0”
(a) (8 points) Find an expression for the electric. V = —V ﬁeld between the capacitor plates. Sketch in . . the ﬁeld lines inside the capacitor. <———— W = 2H ————> A\l= S:E8‘$.—~%r awe {2th 40 tall» (image: ‘.'V;V;='4'€=.‘A'3'(w&wﬁeil)' ~ ' ‘ eve—(or ~EH ~t> E= KW
.VézﬁH (hwswﬂkansgcl) (b) (12 points) An electron is ﬁred with an initial speed v9 from the bottom plate of the capacitor,
moving at an angle 9 = 45° above the horizontal, as shown. Will the electron reach the other plate
of the capacitor? If so, what will be its speed when it hits? If not, where will the electron end up?
(That is, will it leave the capacitor to the right, or return to the bottom plate?) Ste: oaié: 6 will tandem]; EQ’GWikg
~, ' ~45: CW 3‘ “am " ’ can M v; we — on deedrm 9:;ng > Page 2 of7 331 The following problem will be handgraded. Show all your work ﬁzr L121: problem. Make no marks and leave no space on your answer card for it. [II] A solid, insulating sphere of radius R has a charge Q Q
distributed uniformly throughout its volume. Gauss’sv Law tells us that the ﬁeld strength of this sphere is given by: 71:37:54” forrSR
E(r)= ’ * row.212; (a) (8 points) Use this information to derive an expression for
the electric potential Vaxr) at points outside the sphere,
relative to V 0 at r = as. What is the electric potential at the V(R)
surface of the sphere, V(R)? (Warning: W u . w . . . . .0 (b) (12 points) Use the ﬁeld information above, and the results of part (a) to derive an expression for
the electric potential Vm(r) at points inside the sphere. What is the electric potential at the exact
center of the sphere, V(0)? Hint: start at the surface of the sphere, assuming that V(R) is a known quantity, from part (a). I. ‘ >
(£5 4 2 ﬂ 4+ Pt": EMMA ﬁf<k
“ Q A .
=5 W») — vaa) =  SR has] 0
V again— WT;ch 4° imiﬁnzi‘m Wk _\/(I~) :VOE) i , 331
The following problem will be handgrqded. Make no marks and leave no space on your answer cerde it. [11]] Consider the network of capacitors at right, with a switch S
that can be either open or closed. _ i
(a) (12 points) Compute the equivalent capacitance for the 3C S C network(intermsofthepamneter0),bothwith the we»: _ ' c. 54. T 3 open, with it closed. Which of the is greater? fmllel/TCQLBSCtc =th (b) (8 points) Suppose that with the switch open, the network is hooked up to a battery with emf a
and is allowed to reach “full charge”. The network is then carefully removed from the emf, and
held with the two terminals isolated from any other electrical contact. The switch is then closed.
Will the total stored energy of the capacitors increase, decrease, or remain the same? Justify your
answer with supporting calculations. [Hint the results of part (a) will be very useﬁd, here! ] .—bdws_e 'l" ‘W.®e=§m'€)9¢[% ﬁ
' '53!) W ChiIa: en remain Q01 mailed" Islam do“; >Cqu‘ UM < Uapm \, 7 u 5149K am '3lequ L,“ N W40f7 a“ _ "new! “id; " ‘J '“H " 5““ C‘P“iéalsﬂ, Dan «L, .L \ 331 Question value 5 points (I) Consider the plot of equipotentials shown at right. Rank the electric ﬁeld magnitude at points A, B i. _ ' EC
and C, from greatest to least. ' A A 5,4“?! I , gas, ‘
(b) 5.4 > E: > EC  Q, =. (c) EA > E6) E8 FtJA is ﬂy: MIN + .5 g x
‘ (d) ’ E‘ > EC  shes «99 f’mﬁHw“ . i" *im'v (a? 409v (e)"E.4>Ec'>E§ ' is sTseeesT (he. More m Mﬂ~"' JON—tr Speed: di‘ 5’ leach cinsg‘yspecd ai‘ A =45 Es > Ec > EA
I' éPaM cham E3 I I Question value 5 points V .
(2) Consider the equipotentiol map inthe prior, problem. Suppose that echatge q 3 l.0 Inc is
' _ observed to pass through position i with a kinetic energy K, it 50’ m}. ‘Whatwould be itskineﬁc ' energyatpointC?
(a) Kc==+150mJ kt ’ 2‘ Kw“ “M U‘ZV
*(b) Kc—50mJX 1%: «W K; ._._._ K14); .  . .>(d> Kc=+somJ.. . _ . , I I ' ; 00 M
(C) It is impossible to say, becausethe " 59": i 3
charge can never reach position C. = __ 50 m: Pa¢¢50f7 331 Question value 1 0 points (3) A volume V of copper wire is run through an “extruder”———a machine that
shapes the .copper into a cylindrical wire'of some length L; and diameter Dl‘. '
Another equal volume V of wire is run through a second extruder to form a
wire with twice the diameter of the first wire (i.e. D2 =‘2Dl). The two wires
are spliced together, and a current I is driven through them. How do the
potential differences across the two wires compare with each other? (Do NOT assume “ideal” wires, here!) mm W iva WW I
(a) AV2_=2AV, _ V :V
(b) “’2 AV! A, L, = A.L1
AV =AV (C) 2 I «Am Asmssmlml are: =
(d) AV2=4AVl ml Tc 2
(e) AV2=(1/16)AV1 A? 1," A: $93., = M. .L‘ I L1 z ’4 LI s. o ' l
he“ “was Eff—3, ALL)“ = =5 Q,=r59, :$ Sawe (Gr/WV!» v‘nencla MM! I :3; ——> eyL : 9y: :‘eyk" =0 6 Pat'th («A3 Q» stingdlrﬁv}, W‘l‘ COW“ Lg) 1 Question value IOpoints + _ kg. 0.
a (4) In the diagramat right, three point charges: are placed at the , » , .L ’ ________ "k _ _ ‘ Q5  comers of a rectangle. The shaded charge is then moved to , A i; “‘4 Alro the open corner of the rectangle, as shown. Assume all .
’ charges Sbegin an§ en§ at rest] Which of the following 4a statements best describes the potential energy change (AU)
that occurs and the external work (Wm) that was done . I a) l
during this process. _ C0“ the)”; M39 ‘g’:\ @c
'(a) 'AUisnegative andW.,,iSnegative. ‘ .  ' . . .' .._Q 3a ~ +Q “am 3‘ (b) and W,,, is negative. CRAF+ (c) AU is positive and Wm is positive.
4‘ (d) AU is negative and Em lS posrtxve. (e) AU is negative and W“’ is zero (because the wOr
‘ ’ was done by the ﬁeld; not by an external force); 7 " UM lad}! MM) so 331 Question value 1 0 points (5) A conducting sphere of radius R has a charge Q placed on it.
Consider point C at the center of the sphere, point R at the
surface of the sphere, and point r, somewhere outside the
sphere. Rank the electric potentials at these three locations,
from greatest to least. ’ . ‘ “(21) [14> VRS> Vc : Q (b) VR>Vr>Vc ' h: VMM¢ = map [at Qmﬂ e.» Vmws “an?
*(e) @> Vrv Tag—i1; 5.50 ’90 whee mm « thtég Pug: 7 of 7 ...
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 Spring '08
 N/A
 Physics, Electric Potential, Energy, Kinetic Energy, Potential Energy, Wm, Namg Selems

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