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Unformatted text preview: EEL 3472  Electromagnetic Fields and Applications I Moore
Spring 2011 Midterm Exam #2 15 April 2011, 10:40 — 11:30 AM, Larsen 330 Open book. Open notes.
Absolutely NO communications. 3 problems.
100 total points. Name: é’gLL/T? M g A
Honor Code Observed:
Signature
Student to My Left:
Student to My Right: Handout 15 April 2011
VERSION A Instructions: Solve 3 problems. Please take your time to think about solutions before start
ing to write them down. Clearly demonstrate the methodology you employ, and be sure to ' attempt each problem. Useful Taylor expansions for small x: (1+x)”m 1+nx
exm l—l—x
axre l+xlna
ln(1+x)mx Table of useful integrals: / dx
dx
/ x2 + b2 / xdx
x2 + b2 dx
fW II x
———————— + const.
WW
1 tan“1 (x) + const
1) b '
1
5 In (x2 —— b2) + const
In W + b b 72 1. Coaxial capacitor. A coaxial capacitor consists of two concentric, conducting, cylindrical sur
faces, one of radius a and another of radius 19, as shown below. The insulating layer separating
the two conducting surfaces is divided into two sections, one ﬁlled with dielectric 81 and the
other ﬁlled with dielectric 82. Dielectric '82 ﬁlls 0L radians of the coaxial cable, as shown, and
dielectric 81 ﬁlls 2n: —— 0t radians. Develop and expression for the total capacitance, C, in terms
of the length I and the given quantities. (33 points). 1. Coaxial capacitor. A coaxial capacitor consists of two concentric, conducting, cylindrical sur
faces, onc of radius a and another of radius b, as shown below. The insulating layer separating
the two conducting surfaces is divided into two sections, one ﬁlled with dielectric 81 and the
other ﬁlled with dielectric 82. Dielectric 82 ﬁlls 0t radians of the coaxial cable, as shown, and
dielectric 81 ﬁlls 2n — or. radians. Develop and expression for the total capacitance, C, in terms
of the length l and the given quantities. (33 points). ' 2. Inhomogeneous semicircular resistor. The ends of a semicircular conducting ring of rectan
gular cross section are connected to a DC battery, as shown below. The electrical contacts are
perfect. In cylindrical coordinates, the conductivity of the bar varies radially and is given by 0(r) :— 01 + [(62 — 0'1)/(b — 51)] (r u a) for a g r S 19. Find an expression for the total resistance,
R, of the bar. (34 points). 3. Mutual inductance. A star—shaped wire loop consisting of 1 turn encloses an area of 257E cm2 and is located at the origin. A circular 100p of radius 1 cm with N = 10 turns is oriented in
the same plane as the star and is centered. a distance of 100 cm from the center of the star, as
shown. What is a good approximation for the mutual inductance? Provide sufﬁcient reasoning. (33 points). Jr: 100 cm +X 71: cm2
N= 10 turns ﬂﬁwma m 5221“?va zﬂAé’JMR/‘LES a... m? up}; CLPQla 7437/
agiw am i... m dike/6Q W I“; MIA»: ...
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