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Unformatted text preview: Georgia Institute of Technology School of Electrical and Computer Engineering Midterm Exam #1 Date: September 29, 2009 Course: ECE 3025
Section: RPY, RPK
RCC Time: 8:05 AM — 9:25 AM (80 minutes)
Name: SOLUT/OMS Guidelines for Midterm Exam #1: 1. Closed book, closed notes, no calculators. 2. The work you show on the exam paper itself is the only work which will be graded. You may use the backs of the quiz pages, if you find you need
additional space. 3. Plots, sketches and diagrams must be labeled in detail. 4. Answers must include proper units, whenever applicable, and vector quantities must be clearly indicated using the convention
adepted for this course. 5. It is required to show all work in order to receive full credit for your
answers, regardless of whether or not the answers are correct. Incorrect
answers may be awarded partial credit when apprOpriate. 6. There are 6 pages to this exam (including the cover sheet), plus a vector
operator page at the end. Be sure you have not overlooked any problems! _ 1 _ Name: Problem 1: Simple Electrostatics (30 points) a) 10 pts. Censider two point charges in a material with dielectric permittivity e = 10'11 F/m: 41: M]
at the point (x=1 m, y=o, 2:0) and 4Tt' nC at the point (x=1 In, y=o, 2:0]. Derive an expression for
the electric ﬁeld strength as ﬁnnction of position along the zaxis. ":3 Qt Q“ "‘3’ .a  : ————.r—":"“‘ A 5 WE“; .. ,': Ck m E LliTélV"rd? Oman it“! it'—F:.1a " "‘5' r" it “F *' CM: 4 %0\z once (if; :. (xxr» 240.; Tnf i‘ glen? EmoS‘
“5“ 1... {ﬂ + A x _S. 4 m2: Oqﬁff 1 ....,_;..;?‘_'_iﬂa_ a w ,t) a. 4.. ~ as: + 2 0t ‘ We)": .. " “‘2' “i__ LiiTxtS'q  'D‘W ﬁ 7: EEOC: ax V
b) 10 pts. Find an expression for the force due to these two point charges acting on a third point
clgrg: of lng at tﬁmsmon (i=0,y=f:ﬂ,z=0); : _ 2 96 V/JIM Symmesﬁry‘
—1‘‘ A ~r2 — "LOO 4"
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F ‘— Q L— " l é) x O 2 )4 —__::_.> E:“L'\XlO—l06fo c) 10 pts. A ﬁlamentary line of uniform charge density Q; C / In lies along the zaxis. Find an
expression for the differential contributiou to the total electric ﬁeld at an arbitrary observation point F
due to an inﬁnitesimally short section of ﬁlamentary charge at point (x=0, y=0, 2:20) with length all.
Assume that 20 and all are given in meters. Note: you do not need to ﬁnd the total electric ﬁeld. A; a QQMA 3?; _\t 2 E033
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' ' NaInC: Problem 2: Maxwell’s 1st Equation (30 total points) 2a) 10 pts. An unknown charge distribution yields an electric ﬁeld proﬁle given by the following 7
2 10 Sin(% J05; V/In. Use Gauss’s Law to ﬁnd the total charge contained in the
it 50 right rectangular prism depicted below, which lies entirely in the first octant and has one vertex at the
origin. equation: H?) = mil A 5“? Ky
(1,2,3) 6‘ a 093'. D «3) .J r W
Z ’ “‘5‘ .3 .3 s; l I”? ’ l) T 6:} l; S I OWL9,1,? am “gr”; " U; u. as. , J “a
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QM 5' » é: : Ti, a: M) C 2b) 5 pts. Use Maxwell’s 11"t equation in point form to determine the charge density as a function of Position. J l? H: :3 ‘ i “In? \i I;
.— __ _. ' :57 it" E m" Fr \7 Q” v1. “Mix? ._.I _!? ‘, \ "°' z “3 C 056‘? xx} 5/9”“;
w 3 _ Name: Problem 2: Maxwell’s 1st Equation (continued) 2c) 5 pts Using your regult from part 2b), perform a volume integration to obtain the total charge
contained in the right rectangular prism depicted above. ' h «33“ m: If'x— I
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7 as 1 cw‘wbs r 2d) 10 pts. Find the electrostatic potential at the point (1,2,3) with respect to the electrostatic potential
at the origin. f [9* 0w {O,o,o\ﬂf L3.— 01,73"). ,2
T‘ﬂ rh A be.» . \ér\
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The £5: 11’ 6.0.  4  Name: Problem 3: Energy and Potential [20 points) 33] 10 pts. If the electric ﬁeld strength is given by E" (p, (11.2) = pdqg, V/m in cylindrical coordinates, ﬁnd the work required to move a charge of Q Coulombs through the ﬁeld along the unit circle from
(2 In, 0, 0) to (2 in, 2n, 0) in the clOckwise direction. Is this a conservative ﬁeld? Justify your answer. we «933$ Aerwer
New; W: '— x} ' 5955) fr? W: are 6‘2 {5? sou
For W, _ ‘—__ _. . —.—...___’;l :32; j \ v_,..——————— _. ...—.. _—._ . ..  3b) 10 pts. Consider instead a single point charge of Q1 Coulombs at (31:0, y=1 In, 2:0). Assuming E = so, write down the expression for the electrostatic potential at every point in space due to this
point charge. What is the work required to bring a second charge of “Q2” Coulombs to the point (x=o,
y=2 m, 2:0)? V M riffiZ/mﬂ? Problem 4: Electrical Current (20 points) A conducting wire of length 6 cm lies along the xaxis from x=o to X=6 cm, and has a radius of 1mm in
its cross section. The electrostatic potential along the wire is known to be (x / 1r) uV, and the electrica] conductivity of the wire 60  1 0‘5 S / In. Find the current density within the conducting wire, and then
ﬁnd the total current. Does the current ﬂow towards or away from the origin? A 40' : \f A ._ ﬂ 3.. A P... w ﬂi‘x 1r“ J “ T? m7"
ms, t, J i A A“
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