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Unformatted text preview: Name EE 311 Final Exam Fall 2010 December 16, 2010 Closed Text and Notes, No calculators 1) Be sure you have 13 pages and the additional pages of equations. 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. 5) This exam is worth 150 points. Name Score ABET Outcome Points Problem 0 19 v1
vi 12 l 3 14
total 3
(5 pts) 1. A point charge of 30 nC is located at (—l , O, 2), —20 nC at (0, 0, 0) and 10 nC at (l, 5, —l) The total electric flux leaving a cube of side 6 centered at the origin is A) — 20 nC D) 30 nC
B) 10 nC E) 60 nC
C) 20 HC (20 pts) 2. Circle true or false concerning the statements for a ferromagnetic material. The electric flux density on a spherical surface r = b is the same for a True False
point charge Q located at the origin and for charge Q uniformly
distributed on surface r = a where a < b. Energy cannot be stored in an inductor.
The inductance of a coil is independent of the current flowing through
the coil. Electric flux lines are never closed. Two thin parallel wires carry currents along the same direction. The True False
force experienced by one due to the other is perpendicular to the wires
and attractive.
Displacement current is caused by a changing electric field.
The integration of the Poynting vector over any closed surface gives True False A ferromagnetic material retains a considerable amount of its magnetization when removed from an externally applied field. the net power flowing out of that surface. A standing wave occurs when the electric and magnetic fields of a TEM wave are out~ofphase. The critical angle is where the angle of incidence equals the angle of reflectance. (5 pts) 3. A 5 LLC point charge is located at (1, 1c/4, 115/2) and experiences a force of F = 105,. — 5519 + 25% N. What is the electric field intensity at point (1 , 7t/4, 715/2)? (5 pts) 4. There is a 1 nC point charge at (—1, 1,0), a 2 nC charge at (0, O, 0), and a 1 nC point charge at
109 F . — in your calculations.
3611: m (1, 1,0). Choose V(I” = 00) = 0 and Use 80 in the form 80:
V(0, 1,0) is A)0V
B)c><>V
C)4V
D)1V
E) 36V
F)18V
G)9V H) none of the above 5
(8 pts) 5. For the currents and closed paths shown in the following four figures, evaluate (bH odl ‘ H) A ‘
10 A G
G) L ‘ ® 30 A
"Twirl ® A l\/\u “If, (c) (‘1) (ﬁHdl = dind1: (5 pts) 6. Which of the following statements is correct? a) The magnetic flux density is due to free and bound currents, the magnetic field intensity is
due to free currents, and the magnetization is due to bound currents. b) The magnetic flux density is due to free currents, the magnetic field intensity is due to free
and bound currents, and the magnetization is due to bound currents. c) The magnetic flux density is due to bound currents, the magnetic field intensity is due to free
currents, and the magnetization is due to free and bound currents. d) The magnetic flux density is due to free currents, the magnetic field intensity is due to bound currents, and the magnetization is due to free and bound currents. 6
(10 pts) 7. Two identical spherical conductors of radius a = 1m are brought into contact at a single point P. A total charge of Q = —1 nC is placed on the conductors such that the potentials for the two
conductors become V1 and V2. ,0..._w.m_..mmwm.m;5c Y2 (3 Pts) a) What is the relationship between V1 and V2 ? (2 Pts) b) Find the electric field intensity inside the two contacting spheres. (5 pts) c) Find the total electric ﬁeld at (s, y, z) = (0, 0, 10 km). Hint, take advantage of 10 km >>> I m
10‘9 F — in your calculations.
3611: m and Use 80 in the form 80 = 7 (15 pts) 8. A parallel plate capacitor has plate area 0.5 m2 , plate separation 0.02 m, and a dielectric
between the plates of relative permittivity 81. = 4. A battery is connected to charge the positive plate with 8.854x10‘gC and the negative plate with —8.854x10'9 C . The plates are
parallel to the yz plane and the positive plate is at x = 0 and the negative plate at x = 0.02 m. F
Ignore field fringing at the edges of the capacitor and 80 = 8.854x10‘12 — .
m (5 Pts) a) What is the electric flux density inside the capacitor? (5 Pts) b) What is the electric field intensity inside the capacitor? (5 Pts) 0) What is the voltage drop across the capacitor 8 A H
(12 pts) 9 The z = 1 plane contains a sheet current density of K = 10 — ay. The z = —1 plane contains a m
. A A . . . . .
sheet current den31ty of K = 10 ~— ay. Find the magnetic field mtensrty everywhere.
m 9
(10 pts) 10. A 1 kg sliding bar is on the rail system shown. The magnetic ﬂux density is everywhere
3:152 T , If the bar starts at rest at x = 0, what is the force on the sliding bar? Assume the resistances of the rails and the sliding bar are negligible. 10
(12 pts) 11. Consider the following conducting loops placed in the indicated magnetic fields. If current is ﬂowing in the direction of the arrow, clockwise, the current is considered positive. Indicate whether the actual current flowing is positive, negative, or zero for the indicated conditions. Note the positive y—axis is into the page. B:Boﬁy B=Botfl3
(>9 (9 (>9 ® (9 (>9
__ to
(>9 ( (>9 (9 (>9 ® 1) (>9
(9 (>9 ® (>9 (>9 (9
I is I IS
2
E
B28023), B:Bot33 so X
(>9 (>9 (>9 (9 ® (>9
Avg uo ﬁx ﬁx “0 ﬁx
(9 ( (>9 (>9 { (>9 ® (9 (>9 (>9 (>9 (>9 ll
1 19 pts) 12. The following is the equation of the electric ﬁeld intensity of an TEM wave. E: 35e‘5z sin(4TEX106t — 2nz)§x% Be sure to include units in the following (3 pts) What is attenuation constant of the wave? (4 pts) What is the skin depth? (4 pts) What is the wave number? (4 pts) What is the wavelength? (4 pts) What is the velocity of the wave? 12
(9 pts) 13. Shown are the amplitudes versus position for three TEM waves. What are the standing
wave ratios for each? \El g
I0m SW9? 13
(15 pts) 14. A TEM uniform plane wave is propagating in the +z—direction. The amplitude of the electric ID
field is E=Ian—, the wave velocity is 3X108?, and the radian frequency is
m m=3J§x1010 sl . (5 pts) a)Write the equation describing the electric field. (Not the phasor representation but the actual representation of the electric field.) (10 pts) b) Write the equation describing the electric field if the amplitude of the electric field is still
A V 1 1
E=103 ——,but the direction of ro a ation is in the direction —a +—?1 .
y m p p g \[2— x J5 z ...
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