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Unformatted text preview: Physics 2220,
Spring 2008
Examination 1, Name: Key A Student ID: Instructor (circle one): Littler Matteson ' ' Weathers _ This test consists of 7 multiplechoice questions and 5 freeresponse problems for a tetal of 110 ’ points (so that 10 points of extra credit are possible). To receive credit for the freeresponse
problems, you must Show all of your work on the pages provided. Don t hand 1n any extra sheets or other paper. You may also earn partial credit for the some of the multiple choice problems if
you show your work. Suggested procedure for solving the problems: 1. 95":“9’!” Read each problem carefully and make sure you know what is being asked before ,
starting the problem. Draw a ﬁgure for the problem. List the parameters given. _ . Write down the equations to be used. Solve for the answer symbolically. ' , Substitute numbers into you final equation and circle your answer. , : WORK THE EASY PROBLEMS FIRST” 1; (4 points) Consider two tennis balls sitting side by side on a table, separated by about 0.1 m.
Given that each ball contains approximately 3 >.<1025 protons and electrons, each of which
corresponds to a charge of magnitude 5 ><106 C, why is the force between the two balls so
small? ‘ a. The elementary unit of charge e is very small. b. The halls are not conducting. c. The halls are too far apart. (1. The gravitational force cancels the electrical force.
63) Each hall is neutral or nearly so. 'Wmdhévm; between like. adumlilw. 9044394 Wang. 2. (4 points) Two charged conducting spheres of different radii are connected by a long, straight
conducting wire. When the system is in equilibrium, the greater charge density resideseon’ a. the sphere with the greater charge.
@ the sphere with the smaller radius. 0. the sphere with the greater radius. This TWWM W TTWJ ‘M We fat/Feud
d. the sphere at the higher electric potential. ‘m d4“ ', Ouéwﬂ‘wllaeeﬂupwblw: '
e. neither; the chargeis evenly distributed. , ' ' , " Each splm is at it» Saw. palatial: ‘R'. , E; Q,  Ti: Q’s i 3. (4 points) You can remain safe inside a car
(essentially a metal box) during a lightning strike
because a. the electric potential is zero inside the car.
® the eleCtric ﬁeld is zero inside the car. c. the tires insulate the car from the ground. (1. the eliectricwﬂiiitw near the caris zer6;V V ' ' V' V
e. the car remains electrically neutral. 112‘!"le «(AW ls studded 4. (5 points) A point charge q is located at the, center of a cubic Gaussiansurface of side a. If
the electric ﬂux outward through one face of the cube, dueto the charge is +5.0 ><105 N'mZ/C, whatisq? , , I, _ . ,
_ a. 4.4uC ' ' It mwdmﬁq‘f'wgkmlmlstlmﬁﬁlﬂw d.:;~4,..4 MC , : l Ml‘i e? ‘V “’4’ c. q‘cannot be deterrnined’Without’k’knowing a. 5. (6 points) The electric potential in some'region
of space is represented by the equipotential
contour plot shown at right. The contours are , ,
drawn at intervals of 10 V potential difference. In the folloWing statements, the subscripts A L
and B refer to the corresponding points in the
ﬁgure. Identify all correct statements: _ a. EA = EB
(13) lEAl > IE3!
(3 WA! < lEBI ., d. EA and EB aredirected to theright '
EA and EB are directed to the left a my. a MmldtﬂWmc/UWW) . E ls'direchélé’ you/aid": he, lit/WWW
‘Iniw‘ticla V0104? 2 in Was Cw to 1%,,
Mt a! 4M . ' A and BM mmsw WWIMW 6. (5 points) How much electrical charge q would a dust particle of mass of m = l ><10‘13 kg
have to carry in order for it to levitate in Earth’s gravitational ﬁeld (g = 9.8 m/sz) if it is in an
electric ﬁeld E = 1 ><105 V/m directed downward? a. 1 ><1o18 C W ~17 ‘ '
lg. i :137 CC_ " ' ‘Lmﬂ 2E, : ”'ij sOLE : ma: 0 ‘FW [eviMm (Why)
d. ~~1><10"18 c “‘5 ' _ W}
@ ~1x10"”c _ » 3, or a. f. —1 x107 0 E 7. (4 points) The ﬁgure shows a paired set of charges on the left, and either a single charge or O—® Q paired set of Charges on the right. In which cases will the objects
(i) +q ~q W on the left and right be attracted to each Fother? ,
(ii) % 3%, b (ii) only , I... In;{i)f,8Nmsitec4a/[email protected] 90 WWW +3 ’3‘ _ . “1, c, (iii) only 1‘ tsW ’ " L ' 37d " (iV)0n1Y n is b: lb cine/win
(iii) 53? 8—3; (i) and (iii) , E“ ( )Y‘WW «gnu W cm I an
' ' f. (iii) and (iv)
(1 ('71)) [Mia [ﬂu o. (ml'ﬁa‘iahajﬁi, Midi!“
 0% a0 g 0) (iii) an (iv) WWW. {Le W333... am...
(1V) +4 ~61 q +q
({w} IS Mae (ml bvlrwr‘ll» lint Maw CW claw 5? 8. (13 points) In a certain region of space, the electric potential is given by the function V(x, y, z)= axy2 + bxz/z + cy3, where a= 4.0 V/m3, b —— —2. O V/m, and c — 5.0 V/m3. Find the
electric ﬁeld at (x, y, z)= (2.0 m, 2.0 m, 2.0 m). _ L ’2Vm m. J I
lax“3i ‘43“? = —4%s<23)‘3‘2~M{.2* ~ 32% .,E?.,f,‘5‘.' Wt 393 = ~24 .0332“) 333.42..) .423 9V 2: "ZV/m (2M)  V
E? 9?, Z . p (231)” 17‘ . (15 points) A point charge q1 = +4.00 ”C is located at (x, y) = (0.00 m, 2.00 m), a second
point charge q; = ~2.00 “C is located at (x, y) = (—1.00 m, 0.00 m), and a third point charge
q3 = +2.00 “C is located at (x, y) = (1.00 m, 0.00 m). Find the force on 413 due to q] and q2. é a: I.., L.
> as “'3 9 J. x
Pu:
'5 d g Ea A "e IQ "
F:F23TE3 : _y...i§fz+ $130,531
. T25 43
, Le A
f Wcl'jﬂs‘mg‘]
m
X “X:
when. Gos6= 3 ~
9'03 , J
L smB; Yévy'
T13?" (2....)2 (my
= "2.56, “0““ N3  l. 2? «IO'ZNJ ’ J , ~ '9 '6 . ~c . .
=> F: 3"9V‘°°'N*%Z2x'0'°cg 2110 c + 4on c M); + Wk] 10. (14 points) Find the total electrostatic potential energy for the same system of charges
described 1n the previous problem. » _ c
2 (I141: Y Axis
O w rm 1&2 Wm? ‘
=f(l~o)‘+(o2)z p. v' Em $113619 «109 Ant/ca “WW“ ““40 i ‘WLZ“’°““C)‘2"°"9 + (efﬂ“ﬂ um] 11. (18) A charge q = 20 11C is uniformly
distributed throughout an insulating sphere of radius
a= 5 cm. This sphere 1s located at the center of a
hollowspherical conductor of inner radius [1— — 10
cm and outer radius c—— = 20 cm; this conductor
carries a net charge of Q = —30 71C. Use Gauss s
law to ﬁnd the electric ﬁeld a. forr=7cm ." : 'ke—i L x8%!b9N 7E; . Zono‘iiéc _ _ 4N
E—i HF (71104141 M) 3.641140 k. b. for r=15cm 57‘" (Mid: W) o. forr = 25 cm s’ l: gm)‘ 899110‘3Nmé (20 v3ozx/o‘ 96. 1
E= ‘ rt r .— (gs‘xm m)” = l 441% ”/c 12. (18) For the same system described in the previous
problem (i. e. q _=_20 nC, a = 5 cm, b = 10 cm,
6 #720 cm5 and Q,= ~30 nC), , ‘ 7 Find the eleeﬁ'ie potential a. tow: 7cm b L ”Ax/=4 £2149» Vebisi‘vzez§gd,zg gal , :. ice?( I,
~=’> VG). V(b)+ head.) 9 _ 2. w o—go)xlo"’c _ zom'qc 2ozzo"’c
:kQ/m) keq’ fa — 8'99)!” I’m/é I 02M. OJ». 4' 007m c. for r=15cm k, ta) 8.99xl09N'M%=(20‘~3o)m't
V: "'%—’ z =  f0
quﬂm 4 V c. forr = 25 cm 9 a. '95
v'iéﬂ) = Weeﬁwl/ _ r'  v tawdm ...
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 Spring '00
 Littler
 Magnetism

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