04 April2013
EXAMINATION
United States Naval Academy
Electrical and Computer Engineering Department
EE 372
Exam 2
4 April 2013
1. You must present your work completely and legibly to receive partial credit. You must show
sufficient steps to justify intermediate results as well as final answers.
2. Put all your work on the exam. If you need more space than that provided, ask your instructor
for paper. Write your answer clearly and use appropriate units. You have one hour and 50
minutes to work this examination.
Problem
1
2
3
4
Questions
Total
Value
25
25
30
25
25
130
Score
I have neither given nor received assistance while completing this exam.
Signed and date
1
EXAMINATION
04 Apri12013
(1) ((25 points) A 5mC point charge is located in free space at (4m,O,O) using the
Cartesian(x,y,z) coordinate system. What should be the magnitude of a point charge
located at (6m, 0, 0) such that the magnitude of the electric field intensity at (2m,O,O) is
0?
,£--~
I
---
{):::£
2
04 April 2013
EXAMINATION
(2)
(25 points) Use Gauss's law to find the electric field intensity due to an infinitely long
line with uniform charge density 6 !JC/m that resides along the z-axis in free space.
h
((6
--?
Y/o- 6)
12-
.tt~o
/£/~;zJTr
==
/z5/==
])
,£
-
6 X/ o- (:,
::::;
?-//
-
r
,/\
r
-l,
"'J:)
~v
bJ/o
-:::
;2/T r
kv
/o P
r
h--t
3
(r, rs- fi/0--/:;.)
EXAMINATION
04 April 20 13
-
~
(3) (25 points) For the vector field H = 5rrp, that represents the magnetic field intensity in a
certain conducting region, verify Stoke's theorem by evaluating
(a) H · dl over the circular contour shown in the figure below.
f
(b)
J(v x H). dS over the surface of the circle in the figure shown below.
(c) What is the current density,
J?
y
( o' -3./
(b)
Vxi:f
~
o"I
)
+[-fo(rAI)]+ 1-o
" 5 ~ {fr r(s-r)] ~ i ~-tor~
0
-2"
_ 2"""' _L
)(;
/
)
(/o ~
=/o 2~
J
J ('?hi) .c/S =1J'?!T/o 1· f nfl cfr: /o (27r} f rclr
r~D
-= I o
(l~c::>
f~ n )
r;::;o
r
2-
~
J
D
-
......-
J
4
3
2
=
I o /T ( ; ) =
7 o 7T
EXAMINATION
04 April2013
(4) (25 points) Suppose a time-varying magnetic flux density,
cylindrical coordinate system as
B = 4r sin(l 0 9 t) z
for
B , is defined in space in the
r ~ 1Ocm
B= 0 z
for r > 1Ocm
Determine the resulting induced electric field intensity where r > 1Ocm. (Hint: The
induced electric field intensity will be in the ¢ direction)
~
1
rj£ .j£
==-
J~ ..1.5
~~____,_·_··~_,.,_~--~---"'~t,,rh [/fo/i ·r/~* = j~r/O~o:;i/of))I·¥</Pfr
0
)f
¢~u
(:::- o ¢~v
()I
I""
-f'(Jo~<-os(/z,>/)..,77 (rzdr
3 01
/fo /;t.7Tr ~- 'f tcf J-·o5tor.f}rJTJ{ ] ' "
,/;,d77Tr"'
r:::o
r~D
J£1/ r
:
-
'i
(;o~} Cos {ort) yi'_(o.J)J
-...3
/£/~ -~{/o~')cosf?_o7/} (oi;).l
3r
g - -¢
j, J
CoJ ( /0
I
Y
5
J
04 April 2013
EXAMINATION
Questions:
(1) (5 points) Explain the difference between a perfect and imperfect dielectric in terms of
free charges.
(2) (5 points) The x-y plane is the boundary between two slabs of different dielectrics.
Dielectric 1, located at z>O has a dielectric constant of 4 and Dielectric 2 located at z< 0
has a dielectric constant of 3. If E1 = 5x + 7 y VIm, find E2
G)
~ ....
.,_
"/
CD
-
£2
ry
....,
:::;
5"
X+-7:i'
~,...=--2
(3) (5 points) What does Lenz' law describe?
:1)/,-cc. /~...,.. o /
cu,/~,/- //ccJ "f'vc:i ~~~~ #e
c~rr.c,ju! /n;J"'"J,-<. /,,_!/ o//"'<J. lie.
c.L;;J''})' ""//"''},·
/e-U 1--L/ /~/.u/ ./k
(4) (5 points) Explam in s1mple terms the physical phenomena modeled by the equation
V·B=O.
/?--D
.f'p(__,;-C"-e
s
/elc/
(5) (5 points) After removing the copper from your circuit in the clean room last week, you
did a final solvent rinse. Why was the solvent residue collected in the glass beaker pink?( Be
specific for full credit.)
C'vr,_,j
04 April2013
EXAMINATION
7