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PHYS 102 General Physics 2 – Final Exam
May 24, 2007 Thursday 15:00 – 16:30
Please read.
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Count to make sure that there are 5 pages in this question booklet
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Check your name, number, on front page, and student ID on each page..
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This examination is conducted with closed books and notes.
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Put all your personal belongings underneath your seat and make sure that pages of books or notebooks are not
open.
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Absolutely no talking or exchanging anything (like rulers, erasers) during the exam.
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You must show all your work to get credit; you will not be given any points unless you show the details of
your work (this applies even if your final answer is correct).
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Write neatly and clearly; unreadable answers will not be given any credit.
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If you need more writing space, use the backs of the question pages and put down the appropriate pointer
marks.
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Make sure that you include units in your results.
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Make sure that you label the axis and have units in your plots.
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You are not allowed to use calculators during this exam.
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Turn off your mobile phones, and put away.
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You are not allowed to leave the class during the first 15 minutes, and last 10 minutes.
1. (25 Points) A long straight wire is located next to a
rectangular loop as shown in figure below.
Answer the questions below considering the
different scenarios described in each part.
P102_Index:
a) Consider that the current in the long straight wire is increasing steadily at a constant rate, r=di/dt in the
direction shown below while the rectangular loop is kept stationary. What are the magnitude and direction
of the induced emf in the rectangular loop?
b) Consider that the loop is being pulled to the right at constant speed v while the current in the long straight
wire is kept constant. What are the magnitude and direction of the induced emf in the rectangular loop?
c) Consider that the loop is being pulled to the right at constant speed v while the current in the long straight wire is increasing
steadily at a constant rate, r=di/dt in the direction shown below. Find out a relationship between r and v such that there is no
induced emf in the rectangular loop.
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2. (25 Points) The parts (a), (b),(c),(d) of this problem are unconnected.
square-shaped wire circuit of side a is in a plane with surface vector at an angle θ to the axis of a
solenoid of radius b>a, number of loops Nb, and length h. The center of the wire circuit is on the axis of the
solenoid. What is the mutual inductance M of this system? Recall that the magnetic field due to a solenoid
has magnitude B=μoNI/h.
(a) A
(b) A square-shaped wire circuit of side a is in a plane with surface vector at an angle θ to the axis of a
solenoid of radius b<a/3, number of loops Nb, and length h. The center of the wire circuit is on the axis of the
solenoid and the wire circuit itself is outside the solenoid. What is the mutual inductance M of this system?
Recall that the magnetic field due to a solenoid has magnitude B=μoNI/h.
(c) Two coaxial solenoids of length h have radii a and b>a, number of loops Na = Nb that are equal to each
other. The wires of the solenoids, at one end, are connected as shown below. What is the self-inductance L of
this system? Recall that the magnetic field due to a solenoid has magnitude B=μoNI/h.
4. Repeat (c) for the end connection shown below.
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3. (25 Points) In the AC-circuit shown below, the voltages across the circuit elements are vS, vR, vC and vL.
The source voltage is vS = VS cos(ωt).
(a) What is the relation between vS and vL?
(b) What is the relation between vS, vR and vC?
(c) Draw the phasor diagram for vL and iL.
(d) Draw the phasor diagram for vR, vC and iRC.
(e) Let iRC = IRC cos(ωt +φ). Calculate IRC and φ.
(f) What is the average power dissipated over the resistor?
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4. (25 Points) Two coherent linearly polarized E&M waves with equal electric field amplitudes (Emax) and
magnetic field amplitudes (Bmax) travel along the x-axis. The polarization of the electric field (E) of the first
wave is parallel to y-axis and the polarization of the electric field (E) of the second wave is parallel to z-axis.
The second wave is in phase with the first wave.
(a) The equation describing the electric field (E) of the first wave is given below:
E=jEmax cos (kx-
(b) Write down the equation describing the electric field (E) of the second wave.
(c) Write down the equation describing the electric field (E) of the resultant wave.
(d) Write down the equation describing the magnetic field (B) of the first wave.
(e) Write down the equation describing the magnetic field (B) of the second wave.
(f) Write down the equation describing the magnetic field (B) of the resultant wave.
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