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@i {1.1. Three charges are placed as shown in Ihe ﬁgure. The magnitude 0qu is. 15.40 mi, but Sign of charge q. and sign
and vein: of the charge q; are not known. Charge q; is +4.11!) “C.
and the net Farce F on q; is entirely in the negative xdireeliun. at 5hour. q‘l. —"
:1} Considering the dilTeqent pessible signs :3qu and 11;, there are four possible force diagrams
representing the ﬂames F. and F; that q. and q; exert on +43. Skew]: these tbur possible force
ennﬁgu ration5 on the ﬁgure: below. ,7
6 7 &
F1 Ft "7 ,._
F' r in] 1.3ng the sketches From part It” and the direction [if F. determine :11: sign af'mc e argeg q, and q: (1.49
ﬁe?‘ c: Calculate the magnimde ofehaage cu. wilymLL %%¢W¢ELGV&z
Iii1L tyre. ;' ‘argEL .15: m; We. CM)
2') C 1‘.   i w i the. M .1 we {a}
iiifl  dﬁ‘ét. J??? :ﬁn; 3 LEE;— : we. 5 "H iii1i mitt: Elam“ 33' FM: 7"Wm” iﬁzi293 fr; Gr} {Eh {Elie15+[ﬁi dg : J. [on its 1, 5.6, $1M?) : QJ. Point charges (9':  4D x1 Ell"cl C and Q; = H.0xlﬂ" C are separated by 3.0 mm. forming an
electric dipole. 69 3} Find the magnitude nfd‘ne electric dipole mmnent. ii= ‘ii ={txrt'3clé3xm‘ f...
."‘. '1“; hi Thit‘r diwit iii in il UHiTGI'I'I'I nilWill: iiEId when: direction makes an angle el‘ji" with the line
2L: ' connecting the charges. 1Iii"Ital is the magnitude oi‘thr electric ﬁeld il‘the torque exerted an the dipole ltaedmagnitude 7.1 a:  lil'a N.rn'.“ t=P55m3 a» £=._ai __
FEM5"
Jl'n '3
F'__*.L}it'ﬂ‘t'iu'lt '.'.' E=lr13tdfc ' 5:11: L2] What Wﬁri'i is rtquired to change the erienlatien of the dipole in the eleeuic titId gladly From 3?’
"r" to W“? 111,3. .J. nanumtdueting sphere af‘radius R has a mental charge 2Q,wi.th spherically Symmetric distribution of Valium: charge density p = A r, when: A is 1 ennslam.
it is. concentric with a unnductingsphea'ical sheIi uni—inner radius 2R. ﬂuter radius JR and tutu] eharge Q as shown in the ﬁgure. : 05] :1] Calculate the canmmt A in mm: cr‘ GI and R. ,1 r [2. 1. i _+
2.01 = l; feii'J = “a {Ina} Lh’iiriueir‘] : {139' r_'__ I = ”4 :1
G a Ir'l a ; 1M.“ : Pi: "——. A 
11 " 1} Iii" #:2'Qfﬂ.{'r in“ b] 33. using Gauss's Lattr. calculate the electric ﬁeld . in terms 01'5“ .0 and R. within the man eundueting aphere as :1 Function et‘r'where r“6 R. .1 G . r . 5*
.3_.*.q..t.‘’r
v' E, 1 ..'
Jr b * “Mr"
the nﬁr' " "ﬂa
t 
.u 1;._F__é‘:_' _..__..——..
'='' "' . " . ; 
x. 1;. .._. 5.:
raw
1‘ 4H1
'3='—":.
.’ Ina
J.‘, {9115' e: Find the charges on the inner surface and outer surface ct'the conducting spherical shell. lﬁﬁzi ﬁat"$13.1 . ?.G I A
’1' .. 5._.~ “IL.73“, [D 5} d} B} using Gauss's Law. calculate the electric ﬁeld. in lite conducting spherical shell as :1 Function of
: uhetc 2R< r 4 3R. \ E ,_ O i .wymigm 1. Li".‘t~..L.I‘":r m
n
U QA. Tim thin rings with equal radii Inf F'I have total :icctrII:
charges +0 and 20 dislribuled unifamly. The}: an: placed
parallel to each other along their common axis as Shawn in the ﬁgure. The distance hemcan their centers A and E is (JIMR. a} Find the potential at the ecmcrot'the first ring. paint .I'II
I'in terms of END and R]. HM... r" ft'EE. {luff—p.“
L xt III
Warm ‘ " "Lg
EITHER.
IIIII : i
emit. e  i RV
= __ 29 
“ft = ‘4 sat3'? '.2IIIII: E
@213 b] Findthepalenlialalthecenmrat‘lh: secondring, pointBtintemsmEo. (Jami R}.
\IQ = A _i__ MS
1
LMJL IE + L; F1")
“Ida: 3e
Jewel
841.3: “ﬂ
HIEEJL
\I'g __ UR 4.1” “i =ﬂL
2mm. —1L I
24: 1 .rI FiIIIi [I'IL' errL inquired 10 name a charge «:1 Frnm paint B to poi!“ .11.. w “in = LEA—mg F'F'l
'~.
: ‘31 {\‘dﬁ— U2 ,1}
L—i— + .11
24mm. new} mw=.é@t w
ﬂatware '" J . “Jan. — {1.5. A spherical capacitor is Famed ﬁom two mnmntriﬁ.‘ Spherical.
conducting sheiis separated by air. The inner sphere has radius a = 4.5 cm and the cuter sphere has radius [1 = 9.1} cm. A potential
difference of?! = 3} V is applied to the capacitor as shown in. the ﬁgure. ® 3.} Find the capacitance pfthe capacitor. @ in Find the charge on the inner sphcrc.
9 = C “at.
_...1
= {Lesc Mtgepi —_o —__‘E..::I..CJ C
Q Ii Li ; i‘J Find 1hr: magnitude ef the electric ﬁeld. at r = M cm. them :he center pf'lhe inner sphere. I ..— . reg
E: 6' JI ‘55 \éﬂi‘a 4: anti}? “KER'1 (when)z '5
E = 1.0 {.13 guy
if.
3 .
2.3 1 H} 'N/
@ :1} Find the energy stored in the capacitor. L
Chi Li: 3.1..5‘j ...
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 Spring '11
 NoProfessor
 Physics

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