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Unformatted text preview: Name ____— Section: (check one) Jiao Melloch EE 311 Final Exam Fall 2008 December 19, 2008 Closed Text and Notes 1) Be sure you have 18 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) Write neatly, if your writing is illegible then print.
4) The last 6 pages contain equations that may be of use to you. 5) This exam is worth 200 points. Name ABET Outcome 3 (5 pts) 1. In spherical coordinates, a unit normal vector to the plane (,1) = 45” is
A) ar B) a9 C) a¢ D) none of the above (6 pts) 2. Convert the point (2, 450, 450) in spherical coordinates to rectangular coordinates. (6 pts) 3. The intersection of the surfaces defined by p = 10 and q) = 75/ 4 is a
a) a point
b) a straight line
c) a circle
(1) a plane
e) a cone (1) a cylinder (6 pts) 4. In free space a plane of charge 17.708x10‘12 C/m2 is located at z = 1 m. The electric field
intensity at the origin is, a) 8.854x10‘1231Z K
m
b) ~8.854x10‘12&zy—
m
c) 1&2 Y—
m
d) .125 Y—
m e) none of the above 4 (8 pts) 5. The sliding rod in the following figure is being pulled in the +x direction as shown at 1 m/s on
two rails that are separated by 1m. Everywhere is a magnetic flux density of lszzT y 100 1m/s 1m (5 pts) What is the current ﬂowing through the resistor? (3 pts) With an arrow on the figure indicate the direction the current is ﬂowing. 5 (12 pts) 6. For the currents and closed paths shown, calculate the value of the indicated integrals. L2 L1 20 A 10A ® L3 L4
20 A Q) 10A gﬁHdl= gind]:
1 gﬁHdl= gSHd1=
3 4 (6 pts) 7. Suppose a uniform electric field exists in the room in which you are taking this exam such that the
electric field lines are horizontal and at right angles to one wall. As you walk toward the wall
from which the electric field lines emerge into the room, (so if you were a positive charge you would be pushing against the force due to the electric field) are you walking toward a) points of the same potential (along an equipotential line).
b) points of lower potential. 0) points of higher potential. (6 pts) 8. A parallel—plate capacitor connected to a battery stores twice as much charge with a given
dielectric as it does with air as dielectric. The susceptibility of the dielectric is
A) 0
B) l
C) 2
D) 3
E) 4 6 (10 pts) 9. The region for z < 0 is free space and for z > 0 a dielectric of relative dielectric constant 2. There is a sheet of charge on the xy plane of 1—9;. If the electric field for z < O is,
m 2 1 7 a K , then the electric field for z > 0 is, E=—————a +—~—~a +—————
8.854x10‘12 " 8.854x10‘” y 8.854x10‘12 2m 2 1 4 V a) E=————_12—ax +—~33a +—————ﬁaz——
8.854x10 8.854x10 y 8.854x10 m
b)E=———————2 12aX+——————1 12a +—————5 _12azK
8.854x10‘ 8.854x10' y 8.854x10 m
C)E=—2——:2~ax+—~1———_ﬁa +—————3—_12azy—
8.854x10 8.854x10 y 8.854x10 m d) E=———3 12ax+—————2 _12a +—————5 _12azK
8.854x10" 8.854x10 y 8.854x10 m
8.854x10 8.854x10 y 8.854x10 m f) none of the above (10 pts) 10. Flowing in the xy plane is a sheet current density of 6€zx Derive the magnetic field intensity
m everywhere. (Hint use Ampere’s circuit law.) 7 (10 pts) 11. How much energy is stored in a collection of three +1C charges that are all in a line and with 1 In between them as shown? 1m 1m (10 pts) 12. The region for z < O is free space and for z > 0 a non—magnetic material with relative dielectric
A constant 2. There is a sheet current density of —1&X —— ﬂowing on the xy plane. If the
m
magnetic field intensity for z < O is,
A . . . . .
H = 23K + 1ay + 4aZ —, the magnetic field 1ntens1ty for z > 0 1s,
m
a)H=2ax+1ay+4azé A
m d)H=Zax+0ay+2az——
m
A
b) H=2ax +1ay +532—
m A
e) H=1ax +1ay +5az—
m
A
c) H=2aX + lay + 332—
m f) none of the above 8 (15 pts) 13. The region of space for z < 0 is filled with a dielectric of dielectric constant 31 = 230 and
permeability Ho. The region for z > 0 is filled with a dielectric of dielectric constant 92 and permeability M0. The electric field for z < 0 is given by E(x,t) = 3OCos[(2.51x1015)t (1.26x107)z]ax —lOcos[(2.51x1015)t + (1.26><107)zjax K
m (5 pts) What is the standing wave ratio? (5 pts) What is the reflection coefficient? (5 pts) Give an expression for the magnetic field for z < 0. 9 (20 pts) 14. Answer the following question for an electromagnetic field that has the following magnetic field intensity that is described by H(x,t) = 30cos[(l.26 x1015)t + (1.26 x107)xjaz K m (5 pts) The frequency of the wave is A) 2x1014Hz
B) 1.26 x 107Hz
C) 2 X106HZ
D) 1.26x1015Hz (5 pts) The wave number of the wave is A) 1.26x 101551
B) 1.26x 107ml
C) 1x108 D) none of the above (5 pts) The velocity of the wave is A) 1x 108$}z
S B) 1x108—"Zaz
S C)1x108ﬂ&x
S D) —lx108ﬂ&x
S D) —3x108i"—&x
S (5 pts) The wavelength of the wave is A) 4.99x10’15m
B) 4.99x 107m1
C) l.26x107m
D) 1.26x10‘5m 10
(10 pts) 15. Two point chare of —2 nC and 1 nC are placed, respectively, at (0, 0, 1m) and (O, 0, 2m) while an infinite conducting plane is at z = O.
(2 pts) How much charge is induced on the plane? (8 pts) What is the force on the l nC charge? 11 (15 pts) 16. Consider a structure consisting of two plates of width w and separation d. Assuming W >> d,
determine the inductance per unit length. Hint the condition W >> d allows you to determine the
magnetic field between the plates as if the plates were infinite in extend. Also, if the current in the top plate is I as shown, the current ﬂowing in the bottom plate is —I. W
<————> / 12 (45 pts) 17. Indicate whether the following statements are true or false. .n an orthogonal coordinate system, the coordinates are mutually True False
perpendicular. The magnetic flux density is a scalar False
Electromagnetic waves travel faster in dielectrics than in free space False The frequency of an electromagnetic wave remains the same as it travels True False
from free space into a dielectric. In a linear dielectric the polarization field varies linearly with the electric
field intensity. The electric field intensity for an equipotential object is always tangential to
the surface. The dielectric strength is the maximum electric field that a dielectric can
tolerate or withstand without electric breakdown. In a lossy dielectric the electromagnetic wave loses power because of False reflection of the wave. The displacement current density is the time rate of change of the electric True False
flux density. The magnetic ﬂux density is measured in T or Wb/m2 True False If the current is doubled flowing through a wire coil, the inductance of the True False coil is doubled. Two waves of equal magnitude, but propagating in opposite directions, will True False result in a standing wave. A polarization field cannot result from an applied electric field in a material True False made up of non—polar atoms or molecules. True False In a ferromagnetic material like iron, the individual atoms have large
permanent magnetic dipole moments. The skin depth is independent of the frequency of the electromagnetic wave. True False ...
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