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Unformatted text preview: Name EE 311 Final Exam Fall 2007 May 4, 2007 Closed Text and Notes 1) Be sure you have 20 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 T_._ Problem ABET Outcome Points Score
1 5
2 6
3 5
4 5
5 5 _J
6 1' 15
7 8
8 T 5
9 6 10 V“ 5 1 1 ii 10
12 V 4— 10
13 V 10
14 Vi 15
15 vi 1 20
16 vii 5 17 Vi L— 5 18 15
19 45 total 200 3 (5 pts) 1. The component of 10ax + 5ay —10az in the direction of 3ax + 4ay is
A) 50 B) 30aX +2021y
C) 30aX + 20ay —10aZ
D) 10 (6 pts) 2) Convert the point (10, 300, —5) from cylindrical to Cartesian coordinates. (5 pts) 3. Which one of the following statements best describes the equipotential surfaces surrounding
a point charge?
A) The equipotential surfaces are planes extending radially outward from the charge. B) The equipotential surfaces are curved planes surrounding the charge, but only one passes through the charge. C) The equipotential surfaces are concentric cubes with the charge at the center. D) The equipotential surfaces are concentric spheres with the charge at the center.
E) The equipotential surfaces are concentric cylinders with the charge on the axis at the center. (5 pts) 4.Which one of the following statements concerning the magnetic force on a charged particle in
a magnetic field is true? A) It is a maximum if the particle is stationary. B) It is zero if the particle moves perpendicular to the field. C) It is a maximum if the particle moves parallel to the field. D) It acts in the direction of motion for a positively charged particle. E) It depends on the component of the particle's velocity that is perpendicular to the field. 4 (5 pts) 5. A parallel plate capacitor with plates of area A and plate separation d is charged so that the
potential difference between its plates is V. If the capacitor is then isolated and its plate
separation is decreased to d/2, what happens to the potential difference between the plates? A) The potential difference is increased by a factor of four.
B) The potential difference is twice it original value. C) The potential difference is one half of its original value.
D) The potential difference is one fourth of its original value. E) The potential difference is unchanged. (15 pts) 6. Determine f cTS) over the closed surfaces represented by the dashed lines. Note charges within a dashed line are completely contained within the closed su1face
represented by that dashed line. / surface 1
_"'_"'_— surface2
l I y/ I I l— — — — — — — — — — — ——
._____._I I 0 I
I 4\ “a I
I /\\ 0/0, I
 / \ 3m I
I, \ I
\
If \ '
I L _ _ _ _ surface3 / p =3 C/m \
L \
/ l4—2mPl \
L \ 5 (8 pts) 7. For the vector field shown, indicate whether the divergence of this vector field will be positive, negative, or zero at the points indicated by open circles. _ 2
3
4 (5 pts) 8. Two loops carry equal currents I in the same direction. The loops are held in the positions shown
in the figure and are then released. Which one of the following statements correctly describes
the subsequent behavior of the loops? A) The loops attract each other. B) The loops remain in the positions shown. C) The top loop moves to the right; the bottom loop moves to the right.
D) The loops repel each other. E) Both loops move to the left. 6 (6 pts) 9. A solid metal sphere is situated inside a hollow sphere as shown. The region between is filled with an insulator of relative dielectric constant Srl = 2. If this configuration is placed in a region of space that has an electric field of E = EOY—ax, where E0 is a constant, sketch the charges m
that will form on the spheres and the shape of the electric field lines.
conducting
hollow sphere O 4 conducting
solid sphere (5 pts) 10. At a time of t = 10 s, an inductor in a circuit of inductance 1 H has a current flowing through it of 2 A and a voltage across it of 4 V. The energy stored in the inductor at this time is, A)8J
B)2J
C)8J D) energy cannot be stored in an inductor 7 (10 pts). 11. Derive an expression for the capacitance of the shown parallel plate capacitor using field concepts. Assume an infinite plate approximation, where the fringing fields are neglected. In each case, the conducting plates have dimension J5: by JE meters, giving an area of S ml. The plate separation is d m. The top half of the capacitor is filled with a dielectric of relative permittivity 81.1 and the bottom half with a dielectric of relative permittivity BIZ 8 (10 pts) 12. A conducting rod moves with a velocity of ZaZ—nl parallel to a long straight wire carrying a
s current of 10 A as shown. Calculate the emf induced in the rod and state which end is at the higher potential. 10A u=2m/s
+ a <——>l<————> 0.1 m 0.2m b 9 (10 pts) 13. A perfect conducting square loop of width 1m in the xy—plane contains a 100 resistor as shown. The magnetic flux density is B = 0.5t2 all]; What is the current flowing in the loop? m
Indicate with an arrow on the figure the direction of the current. ‘I m 10
(15 pts) 14. The region of space for z < O is filled with a dielectric of dielectric constant 82. The region for z > 0 is free space. The electric field for Z < O is given by E = (206—ij —1Oe+j”)z)—V—ax
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. ' (20 pts) 15. Answer E(x,t) = 3OCos[(8nxlOl4s’1)t+ (1 107m'1)x]az —— 2.5 The electric field is a wave propagating in the
A) +ax direction
B) ax direction
C) +aZ direction
D) aZ direction E) it is not propagating, it is a standing wave The wavelength of the wave is A) 2.5 x10"7m B) l x107m
2.5 C) 81: x1014m D) 5 x10'7m The frequency of the wave in radians per second is,
A) 2 x lOgs‘l B) 3 ><1085‘l C) 8% x 1014 s"1 D) 1‘— X107S_1
2.5 The magnitude of the velocity of the wave is A)2x108—”1
S B)3x108ﬂ
S C) 1x107ﬂ
2.5 s The maximum value the electric field can obtain is, A) 30K
m B) 15K
m C) 6O—V—
m 11 the following question for an electric field that
V m is described by 12 (5 pts) 16. The forward propagating voltage wave on a ZO = 50 9 transmission line is given by, V; = 3Oe'jﬂZV. If the load impedance is 150 Q, the reflected wave on the transmission line is A) V; = 306"”sz
B) V; =15e‘WV
C) V; = 60e'WV
D) V; = 30e+fﬁzv
E) V; =156+WV
F) V; = 60e+fﬂzv (5 pts) 17. In a certain material the electric field is given by E(z,t)=106’0'lz cos[(2><108s'1)t— (2m'1)z]ax X. What is the skin depth?
m 1 3
(15 pts) 18. A light is placed in a decorative pond 1 m below the surface. What is the area of the surface of the pond that will be illuminated? The refractive index of water is 1.33. 14 (45 pts) 19. Indicate whether the following statements are true or false. I At every point in space, ap ° 21,, = 0 True False
In a coordinate system, the unit vector for a coordinate always points in the True ‘I False
direction of increasing value for that coordinate. Lines of electric flux never terminate on themselves True False
'Lines of magnetic flux always terminate on themselves True False
Flux linkage is the number of times a wire is coiled onto itself. rTrue False
The Poynting vector physically denotes the power density leaving or True False entering a given volume in a time—varying field. The speed of light is the same in all materials True False
There can be an electric field plane wave without a magnetic field wave. True False
The higher the capacitance per unit length of a transmission line, the slowerI True False the phase velocity of the wave on the transmission line. I The input impedance to a transmission line depends on the length of the True False transmission line. ['In a changing magnetic field there is an induced voltage that acts to oppose True j False
the time rate of change of the magnetic flux In order for a charged particle to experience a force from a magnetic field, True False
it’s velocity must be parallel to the magnetic field. The electric flux density on a spherical surface r = b is the same for a point True False
charge Q located at the origin and for charge Q uniformly distributed on
surface r =a where a < b. When a steady potential difference is applied across the ends of a True False
conducting wire, all the electrons move with a constant velocity. The characteristic impedance of a transmission line does not depend on the True False
length of the transmission line. ...
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This note was uploaded on 02/05/2012 for the course ECE 311 taught by Professor Peroulis during the Fall '08 term at Purdue UniversityWest Lafayette.
 Fall '08
 peroulis
 Electromagnet

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