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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
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EX: ELK ng :— lﬂlﬂéo [:3 W 635340 F :.__L.— [onm'ﬂic coy—S‘s?) BGXLO—ciCE .«x Lin6c) (6 MBa "’ + 63:0 my;
7" ' SMQ
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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. Qhé 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 ycomponent 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 ycomponent 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 7871 ﬁX{E} I it; 7; H E/_ Tic:
d)1:1>1:2=r3 Iii1" Elti—I 33119 5523* “Pam: ”ISME.” 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 0i 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— +hvgJeJl‘ 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 5015 (1% Mm, +lac+f3 m
PQFWQW‘ +0 E glﬁzkis 0. gluing“? ?C) W . (3‘0 l
133i: Cmstvml' 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° eXﬁlNCMQ ﬂo chem/1%, m digM}: POkn'le/g H/Q
dag: Must be. Moved FWQHJOJRF +0 the
ﬁledht 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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 Fall '08
 GIMMNACO
 Physics

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