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Unformatted text preview: (:31 / {2:7} 1? Name Oct. 27, 2009 ECE 311 Exam 2 Fall 2009 Closed Text and Notes 1) Be sure you have 18 pages. 2) Write only on the question sheets. Show all your work. If you need more room for a particular 1
problem, use the reverse side of the same page. E 3) No calculators are allowed.
4) Write neatly, if your writing is illegible then print. 5) The last 6 pages contain equations that may be of use to you. 6) This exam is worth 100 points. l
l
i
Signature l
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Problem 7 ABET Outcome Points Score 1 15 l 2 15 3 15 4 (ii) 15 5 5 6 101 J 7 15 8 1 10 100 F total 3
1. In a material having 8 = 280 , it is found that D : ZEOZIX + 28053}, —— 3080512 C/m2 . (5 pts) (a) Find electric ﬁeld intensity E. we Wt Mn. W: j; M W .3  «w :2 ~
W MW MW , H+ a / t 4* u > x
(Spts) (b) Find polarization vector P.
wt.ij ( l /”‘”" “mm i‘/%f /\ g; “:1 5% i W fl “a; (ll
2%,? “4:” M x W” 1 mm M TEA)
K / (QC L” “W” 5c 6/“ j w ﬁg \ 4 (15 pts) 2. A conducting solid sphere of radius 5 m is centered at the origin and embedded in a dielectric
‘material with 8 = 480 . If the sphere carries a surface charge of 4 nC/mz, ﬁnd E at (O, 3, 4). (The coordinates are rectangular coordinates). TA “ {I} (:w 3 ("ya/r“: ~»( 4 /‘Z9 Ag“, 14 (1: L:th «S if; (j. . Why / P5744 Cry. e91. lay; ((LJCZMrLrO/V/f distal?“ (“2 /‘:‘€ \ , f ' e W I ’ 4:;
m maxi/f" i '" if“; 7 WW“ I; } 2::7‘ :74
x \ gig“ ‘ ' I
If if! / {
K ” / [43"? 5
(15 pts) 3. The region for x < 0 is free space and for x > 0 a dielectric of relative dielectric constant 2. There
is a sheet of charge on the x = 0 plane of density —2 C/rnz. If the electric ﬁeld for x < 0 is E = 2 a 2 4 a V, ﬁnd the electric ﬁeld forx > 0. Z + a +
8.854x10‘12 x 8.854x10‘12 y 8.854x10“12 m 13/ X3 0 KW I] “: z¢ 2“ i,
‘ I f h w w 2 M i ‘ r 1/ u “ /
7 f (g, L //w
“Mam  k _ Mm new“... WWW a ,5}?
Z”; 5; ‘‘‘‘‘ ,m / '/
f/‘V x x
}\ W. . w ,, Mai
< Kr ~ ~ *
W 2, x; eeee ~> ‘  ._ é: ........ _V v “M; M. {9/1 % 2w 6 (15 pts) 4. A conducting hollow sphere of radius 1 m is enclosed by a larger hollow conducting sphere of radius 5 m. Determine the capacitance formed between two spheres. «MA m r“) K
5 er: ‘wWMA :2: ‘ uf‘] M»”L.I'<Zwo"/ Cay/v? (,S‘l/(«c t; “FDWIWK ~ 4'5 523 7
(5 pts) 5. Two perfect conductors are arranged to form a 600 angle as shown in the ﬁgure below. A point charge Q is placed in between the two perfect conductors. The number of images of the point
charge is
(a) 7
(b) 3
(92 4 \(65 6
(1) None of the above Perfect Conductor 8
(10 pts) 6. A loop of constant current I has the shape of two half circles connected by two short sections of line as shown in the ﬁgure below. The larger circle is of radius m, and the smaller circle is of radius r2.
(a) What is the direction of the magnetic ﬁeld intensity H at the origin point (0, 0, 0)? “W41. X“ f”: . I;
_ M. I “his ./
ll f’wfi Hit a ww ‘ v« I!“ Yﬁﬁh’ ‘ 3/ r f“ “w i l“ “mi... 6!)? 4/ Vi?» {m 41927 ;’ W1 :YQ ax my ,5 .. .enwuwmuwgm.w wwwmwwkww. ‘ > WW “WWW” “WWW “WW. (THIS PAGE IS INTENTIONALLY LEFT BLANK) E
y
E
E
E
§
2
,x
y 10 (15 pts) 7. For the currents and closed paths shown, calculate the value of the indicated integrals. L2
@—20 A L1 ®ZOA 6A L3 L4
20 A C1511 . d1: (j H 0 d1 = W. 2M) Email: (4;) (35mm: 3,6. 11
(10 pts) 8. Two circular cylinders, which are inﬁnitely long along 2 direction, overlap each other partially. The ﬁgure below shows a crosssectional view of the structure in xy plane. Along z direction, the
structure extrudes to inﬁnity. The two cylinders have the same radius: a = 2 m. The center points of the two cylinders are 01 and 02 respectively. The distance between 01 and 02 is c = 1.75 m. The
left cylinder carries a current of density Joﬁz A/mz, and the right cylinder carries a current of density —J0&z A/rnz. As a result, the current ﬂowing through the overlapped region is zero. Calculate the magnetic ﬁeld intensity H in the overlapped region, which is the shaded region in the ﬁgure. 1 2
(THIS PAGE IS INTENTIONALLY LEFT BLANK) \ r ‘ ,1 v» I j m. ‘+‘I~~c‘>"'"CFLbkwtﬂs2 ("
J /:/\ #1759 me gnaw =) H ‘ 0/5 2;; W. I; 77.“ //2_ «1
// (/ w / .2 ...
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