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PROBLEM [I] (25 points)
In the circuit MOW, the capacitor C is initially uncharged and the switch 3 is closed at time I = D. I 2:: 4:: 1::
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(:1) Find the currenlfjust aﬁerthe switchSis closed. \ m [an]: 31.4.. ﬁr ”nu, Igor 4:15:de
Aihule£=g Mmpagihritg unchanged. 1 qu+lij+aI—Ié=a
TWL I‘L bEhME‘I M a ghort’ Circuit .} 5'1; +LfI"=fE [email protected]
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_ I. Selma. ﬁrmG) Md®ﬁr1
a h C. lle. {Mkd
i n+1 :95
I" II I =l+ﬂ "Ml“; ﬁHQMIMF mtdfn I's
+5 + 1f1)+2(1‘}——i£=0 3I=10 ll clgJq =5r33ﬁ‘
..__.___—J {c} Find the potential difference ms the capacitor and detcnninn which plate, upper or lower, is
at higher potential at time I = I». Tim bop esp» ﬁrmw a594,; gnaw milk V£+H£¢3+2T~L=O 43May FmthJwtﬁké Nit1 1(1§)IL=0 Vc=vw_vm”=+ﬁ3v
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PROBLEM (2) (25 points) A reetangnlarloop of wire with dimensions It} em 5 cm. liea' In the 3} lane. It carries a current
of 200 A' In the direction ahewn' 1n the ﬁgure. A on orm magnetic ﬁeld, ={DJ} + 0. 2k) T exists intheapacearoundtheloop. . z WheatPM Weakw.
1:290 ﬁt
A: guanine4:90“;
M:I’ 5 em ‘9'
(a) ﬁnd the net magnetic force on the loop,‘ In vector fonn (in terms of unit vectors} RM Maumlﬁ’aei‘lH' a: at“?! we ”EM Fiﬁ" at
.5
MA Fb¢=_E:A ' maﬁa.  Low. I5» emawmmmw 1
LIZ'0 W3”? Mglrt‘ﬁhummiunﬂﬂk
fem. re mo {h} Find the torque on the loop, in vectorfonn (in terms of unit vectors) A worm 10410 In a. MW; dipole wilanataiacdipelemm
Uﬂcﬁ'Wﬂ 544mm ﬂ=lql= Mer‘l M4 (“#31 wildUta mint1m!
uedor hmfmﬂfmmtf Md wgmMr'ski WW5 "1‘3"" {Md—M‘ ﬁt: MM (—11) = (4}{290A){50K1e"fu th 1,) = ‘K 1‘“ Fe? e; =(E anthem; +n.zL)rj=—e'5 Exjwm Mfr—l
"5 _L
II E. 0*5315 ”IN (c) Find the magnetic potential energy,r of the loop.
MtjuB —(— 1a.») [(03J+enzh1'r3= 9'1“" E53 H Phys roe Seeom' Menu Page ere May 13. zone _ 0.7 ,. :
PROBLEM [3) (25 points) A thin, ini‘initteljir long wire C ing acurrent I. is bent as shown in the ﬁgure, with all sections
lying in the plane of th: 5:. 111d that magnitude and direction of the magnetic ﬁeld at the c'hhter of the circular arc of nus R. and of central angle of 135‘. (You may us: the derived formulas
direﬂiy.) . I .
Bi"! = E’h = L 3 "Li" NW3: r—mR
_ I . ,_ . 1.”
W &*——i’— WWW ; M «w a «r Suingliking ﬁrm magmatic Freed a: pom c, weﬁéd in
B. = f": I {MO I it?) pi = gun: 3 I
'1 'mR + Him. +41%? mm. + '42:? .. I .'
Br." 52?: (hi'i'r— 1'43?) III1+9 43:1?an .2. (if: F: 4’ HER
:3 1'? I
B;  ﬁ— 3 1149 m Page. Mﬁ.‘ Mam um. M Bigt_5amlr~t I” as: 1% Elm—.9, r1. “hike. 'hu. intgm! B 1de War4M; 5.4% wt}! M4 ‘Fl'ﬂd 5: ' Phys I06 Second Midterm Page 5m May M, 2m: PROBLEM (4} {25 points}
Two long cylindrical solid wires of radius R are in oonmet along their full length, as shown in
Figure I The wires eerryeq equal and uniformly distributed current: I III the +x direction (out of the page in Figure lIJ Using Ampere '5 law and superposition. ﬁnd the magnitude and direction of the
eldtaJ at point A and (h) at pointB (Give your results In terms of unit vectors. J magnetiei 08 AJPE'LAE lam“ : WM jimﬁqmasneﬂr. 15214 if POM‘tﬂ M WM B. 15 death "he. upper.31's @49le mm; éat'di :ﬂal ding“; Bllznf)=ﬁlﬂt MPHQSR We
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éb}. 45 mfg]: {Hg —" G {IMP} It MUM r“ 25£
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 Spring '12
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