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Unformatted text preview: Name Section: (check one) Chappell Jiao
April 23, 2009
ECE 311 Exam 3 Spring 2009 Closed Text and Notes 1) Be sure you have 17 pages. 2) Write only on the question sheets. Show all your work. If you need more room for a particular
problem, use the reverse side of the same page. 3) No calculators.
4) Write neatly. If your writing is illegible, then print. 5) The last 6 pages contain equations that may be of use to you. Feel free to separate these pages from
the rest of the exam booklet. 6) This exam is worth 100 points. (Signature) Problem ABET Outcome Points I Score —._l
1 1o ‘ ‘
2 10
3 10 ﬂ—————.
4 5
*_—“ 5 iv 10
6 V 10
7 V _
_—
—
—_
—_— 3
(10 pts) 1. A current of 1 A is ﬂowing in a loop shown below. ‘ 0 = 2 m ' (a) If the loop is placed in a uniform magnetic ﬁeld of
1—5” = 10051} T, what is the maximum torque received by the loop?
y
l = 1 A V 4 I
WWW ,ng M”;
l + x 7” :r: m Ki“ t?
+————————>
b = 1 m a WE —» (b) If the loop is subject to a vector magnetic potential of A = x52 , in which plane the loop rests after it
has rotated? w y I
f got 7 L{J€w,/ :6, v f
' a g "A ‘2‘ x“ ('7 f n “NAM “M37 M) [61:] a; I, ‘‘‘‘‘ v Q \ 4
(10 pts) 2. A 1 C charge of mass 2 kg is moving in a uniform magnetic ﬁeld E = 1031z T. The velocity of the
charge is known to be 2? = 2 ><105 5x m/s at time t: 0. What is the kinetic energy of the charge at t= 4 s?
1’
m i mi» ; [ff/V? i5
(W s
2* V :3 *5 € 2. K / a: g
f «~\ f! {1,}! j!
MA f,
{f
f
' «e ~ i
"“ t w 2r"; 5
(10 pts) 3. A solid dielectric sphere of relative permeability 4 is placed in free space. The radius of the sphere is l m. The H ﬁeld is known to be H = 251’]. + 453 A/m inside the sphere. No current ﬂows on the surface of the dielectric sphere. The H ﬁeld outside of the sphere is A) H = 0.52;, i
m
B) F1 = 0.521,. + 250 141
m
A a a A
C) H=0.5ar +406 +4a¢—
m
C) H = 43g 5
m
K». R .7
f D) = 852, + 4% i g" H EM"
Roof m
a, , a. a. VJ 5? w z” .A
E)H=2&r+2ag£ {’1’ H” be H 2
m
.55.; 9‘; r .
F) None of the above 1! H ‘2' )1 A Whit“ k
. L (é / k ‘ (L If. :3: [ZN/arr. (5 pts) 4. a] E 0 d1 = 5 V, which one ofthe following is true? A) TE 0 (11 is independent of the path
y A (:B) is due to time—varying sources.
C) E is due to static charges. D) <1 E 0 dl cannot be nonzero. E) None of the above. 6
(10 pts) 5. Derive the inductance per unit length for two parallel plates partially ﬁlled with a material having relative permeability of 100. The crosssectional View of the structure is shown in the (xx/~13 following ﬁgure. The length direction (current ﬂowing direction) is into the paper. kaiser; i? g) (:1 ks}; cgﬁmrxii éiF‘SE/“r‘éém / 4‘74“ "i" ":5" //~/;,’ 5) V W V, jam"; i 7
(10 pts) 6. Shown is a circuit consisting of two resistors. A magnetic ﬁeld exists inside the circuit loop.
The magnetic ﬂux out of the page is known to be l// = (101 + 5) Wb . What is the reading V on the voltmeter shown? 8
(lSpts) 7. The sliding rod in the following ﬁgure is located on two rails that are separated by 1m. At time t = 0, the rod is atx = 1 m. After 1‘ = 0, the rod is pulled in the +x direction as shown at velocity
of 1 m/s. In the shaded region from x = 2 m to x = 4 m, there exists a magnetic ﬂux density of 10672 T . Plot the current versus time in the 10 £2 resistor from 1‘: 0 to t= 6 s. The reference direction of the current i is given in the ﬁgure below. 9
(30 pts) 8. The region of space for z < 0 is ﬁlled with a dielectric of relative permittivity 4; the region for z > 0 is free space. The electric ﬁeld for z < 0 is given by E = (26—jﬂz " ejﬂz)ax V/m. The frequency of the wave is 1 GHz. (5 pts) The velocity of the wave in z < 0 region is m .
A) 3x108 — f
S (if? i. “WM W W“ f; m ,2’ £5
if B)f1.5 x108 — a n ("V
C) 6 x 10 8 —
S
D) None of the above
(5 pts) The wavelength of the wave in z < 0 region is
A) m N ting” B)j:0.15 m ' a]
C) 0.2 m L???
D) 0.3 m
E) None of the above (5 pts) The wave number (propagation constant) of the wave in z < 0 region is mm” rad/s 3 I“; f «wka 3 rad / s
ism!” 3 D) None of the above 10
(5 pts) In region 2 < 0, wave is propagating in A) y direction
B) —y direction
C) 2 direction
D) —z direction
E) x diection
F) ~x direction ,a v wng G) None of the above (5 pts) In region 2 > 0 which is free space, E ﬁeld has x—component only
MNB) y—component only
C) z—component only D) x— and y— components E) x and zcornponents F) y and z—cornponents G) None of the above (5 pts) Derive the instantaneous form of H for z < 0 region ...
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