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Unformatted text preview: ECE 329 Introduction to Electromagnetic Fields Spring 08 University of Illinois Goddard, Peck, Waldrop, Kudeki Exam 1 Thursday, Feb 14, 2008 — 7:008:15 PM warmer «ach 7 Section: 9 AM 12 Noon 1 PM 2 PM \ Please clearly PRINT your name in CAPITAL LETTERS and circle your section in the above boxes. This is a closed book exam and calculators are not allowed. You are allowed one formula sheet of 8.5 by
11 inch dimensions — both sides of the sheet may be used. Please show all your work and make sure to
include your reasoning for each answer. All answers should include units wherever appropriate. Problem 1 (25 points) Problem 2 (25 points) Problem 3 (25 points) Problem 4 (25 points) ETAL (100 points) H :) M( in 1. Consider the static charge distribuition shown in the following diagram:
y (In) a) (6 pts) What is the electric ﬁeld E at the origin? Explain. «€30 out M OvCS/{w lei/i.3 leliqi/ lawmA
.::.===‘=="’—’ ﬂwwewdﬂ 'TLVL ﬂirt/x ClALVfﬁ d/{f'lviwd‘m b) (6 pts) What is the electric ﬂux fsl E  dS computed over a spherical surface 8'1 of radius 3 m
located about the origin? gg'eazzéyisic‘
 £0 0% c) (6 pts) What is the electric ﬂux 9952 E ' dS computed over a spherical surface 8'2 of radius 5 m
located about the origin? 9% 2 1:?le : QV'L : ‘Qcml ('44:) :
30 P $3
ﬂz d) (7 pts) If a positive test charge q > 0 were placed at position P1 (indicated in the diagram) in
which unit vector direction would the charge be accelerated? Explain. ' 2C
‘39 A [MS—{Him imokwSe i will lrm AHYM/fed +0 m ,Z.c at“:ch M 73qw‘ may; gWSLLU WW.
h w éme WW‘i‘Jﬁl Cl/kL—zyt «71 7="~iw~' Mcfw) accx/(Lrwlw‘xm duhr uh'm.‘ 01 a! Wad/(J be “P; I F " zetxm“ M / 2 // H2 /\ 2. A current I : 5 A ﬂows from 2 z —00 to +00 along the z axis. a) (5 pts) Consider a square path in the my plane deﬁned by the vertices, in order, (1,—1,0), (1,1,0),
(~1,1,0), and (—1,—1,0). Find the numerical value of the line integral fCH  (11 along this path of
the magnetic ﬁeld H produced by current I. C ‘ ’
.QAAc/CaC/ecl) W? C an “lZ'oLueOh’an, ‘
‘“ M = ‘3 A
b) (5 pts) NOW consider a simple circular path with a radius of r = 1 In. Find the numerical value of the line integral along this path (taken in the same direction as in part (a)) of the magnetic
ﬁeld H produced by current I. gait“, Mosh/Lt wlik root“; k;( 5‘ “give—4., '0‘)!» c,
Ca.) 61051 (A) ext/~ch €/(ku( ~2— acid—cg Marl} $‘A/ (Mr #044 / mace, AW“ 30C H011 zﬂ/ c) (5 pts) What is the magnitude of H at (1,0,0)? (Hint: use the circular path of part an. w (M g3 m]: 2m UH = 6% a (HP; 7:
C M d) (4 pts) What is the direction of H at (1,0,0)? (121404 ~ WM 1W M we“ 01/! 0M ’AAMJ 4::(1
“(7AM {bumr/ momma, "ii/mil 1w;qu WM :24 H
W b1 1'}: M ( 1/0, 0) . e) (3 pts) What is the force per unit charge of a charge movihg‘isvit a velocity 158 m/s at (1,0,0)? E
l
g l l l ‘f We (1;; ’29 E...— ” ,_C")X(A)log J,“ W a " 1X g
0‘ Q/“ﬁ w/i/As M ’ ‘2. ____ 2 , g l l l l l l i f) (3 pts) What is the force per unit charge of a charge moving with a velocity 13} m/s at (1,0,0)? 3:“ 1m“; (M £20 111Lch C—ﬂfgs/u.§
‘l A’lﬂ/OV’Z) : “~51 3. (25 pts) An important identity in vector calculus is that the divergence of the curl of any vector ﬁeld
F = Fay/2+ FyQ—I— Fzé with differentiable Cartesian components Fm, Fy, and Fz is equal to zero. Prove
this identity by ﬁrst expanding the curl of F. (Pi/WK Va VXE'W? A A /\ ﬂo {ad/Secure; Maw/c with Poi/\Vréd M01423 Tot/lag iwf
(MM m Mom to VLmoLL/ M Via/1A3 JacoszfiM /ﬂm/ v.9»? :0 Lama! / (d) (e) (f) In free space (where 12,, = c = 3 X 108 m/s) there is a surface current density in the z = 0 plane of the
form J s = £13003), where Jso(t) = ~Kt for O < t < 1 us and 0 otherwise, as shown in the diagram above on the left; constant K = 106 A —— and the horizontal and vertical axes of the diagram are
labeled in ,us and A/m units, respectively. HIS Consider the graphs a—h shown above on the right and answer the following questions —— in each
part explain brieﬂy your reasoning for your answer: a) (8 pts) Which waveform shape (a—h) describes the y—component, Hy, of magnetic ﬁeld H produced
by J S as a function of position 2 at time t = 2 as? Hint: Where will parts A, B, C of the source
waveform end up at t = 2 us? ' H WMb‘eoVk» IE ((1) l’LLCGtMLL EL WVFaﬂm
7W9 rig/A] I’M/(L b) (7 pts) Which waveform shape describes the (Ia—component, Em, of electric ﬁeld E as a function
of position 2 at time t = 2 as? E, vaw—M— }S (h) %€Mlaﬁ%&m]¢»cﬂ"fhmj a
and i=3?» Mat 1% Janka {a orpm’te Amer/Hm. with
1—30 WWQFoll—MA MWV(/ 9K WWW/FM U c) (5 pts) At time t = 4 ,us, what is the width of the triangular region of the wave disturbance (i.e., pulse Width) for z > 0?
g ’9
_ 4x10 3*) = 260 «4
(gm) imam = C 4’6
rl’va—L 1;: d) (5 pts) At time t = 4/13, what is the maximum distance of the wave disturbance from the z = 0 We H m a}
plane? is‘ @xlmol (24x5)< H7 Nov/463ml ’ﬁﬁ‘fk' 2: ...
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This note was uploaded on 04/14/2009 for the course ECE 329 taught by Professor Franke during the Spring '08 term at University of Illinois at Urbana–Champaign.
 Spring '08
 FRANKE

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