240 Physics Fall 2003: Final Exam
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Form #1
Instructions 1. 2. 3. 4. Fill in your name above This will be a 2 hour, closed book exam. The exam includes 25 questions. You may use a calculator, please do not share calculators You may use four 3"x5" note cards (three from the earlier exams, plus one new one) with notes and equations you think may be useful. You can write on both sides of the card if you like. 5. You may be asked to show your University student ID card when you turn in your exam.
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Table of constants: 0 = 8.85 x 10-12 C2/Nm2 k = 1/(40) qelectron=-1.6 x 10-19 C qproton=1.6 x 10-19 C melectron=9.1 x 10-31 kg mproton=1.67 x 10-27 kg 0 = 4 x 10-7 Tm/A G = 6.67 x 10-11 Nm2/kg2
1: A scuba diver looks up through the calm surface of a lake and notes that the Sun seems to be 40 away from straight overhead. The diver's friend sits in a boat above him. At what angle from the straight overhead does the friend see the Sun? The index of refraction of water is 1.3. A) 57 B) 33 C) 40 D) 48 E) 52
2: Which of the following statements is true? A) Constant magnetic fields are produced only by permanent magnets B) Constant electric fields can be produced by changing magnetic fields C) Electric fields are only produced by electric charges D) Electric fields must be zero inside all materials E) Changing electric fields can be produced by constant magnetic fields
3: A `coaxial' cable is made by surrounding a solid cylindrical conductor of radius `a' by a cylindrical conducting shell with inner radius b and outer radius c (see the figure). If the inner conductor holds a charge per unit length 2, and the outer conductor holds a charge per unit length -, what is the magnitude of the electric field between the conductors, at a radius r from the center of the inner conductor?
A)
4 0 r 2 B) 0 r 2 C) 0 r
b a c r
D)
2 2 0 r E) 2 0 r
4: One of the experiments placed on the Moon during the Apollo missions was a `retroreflector'; a reflector which reflects any light which strikes it directly back along the direction in which it came. By firing a laser beam at this device and carefully measuring the time it takes the beam to return, the distance between the Earth and Moon can be measured precisely. If the total travel time of the beam can be measured to 0.03 nanoseconds, what is the implied uncertainty in the distance to the Moon? A) 24 cm B) 3.9 cm C) 6.2 m D) 4.5 mm E) 6.2 m
Retroreflector on the Moon
5: Sunlight reaches the surface of the Earth with a total intensity of about 1200 W/m2. This sunlight shines at an angle of 30 from the vertical onto a flat black 15m by 45m rectangular roof. What is the total force this sunlight applies? A) 2.3x10-3 N B) 6.1x10-8 N C) 4.0x10-6 N D) 0.33 N E) 1.7x10-4 N
30
6: At a particular instant in time an electromagnetic wave has an electric field which can be written:
r ^ ^ E = (6.22 N/C)x + (2.87 N/C) y
What is the magnitude of the magnetic field at this moment? A) 6.5x10-3 T B) 0.69 T C) 2.3x10-8 T D) 1.9x10-5 T E) 6.9 T
7: A series RLC circuit is constructed from a 12 resistor, an 0.15 mH inductor, and a 180 nF capacitor. This circuit is then driven by an AC voltage source. At what frequency, in Hertz, should we drive this circuit to produce the largest possible oscillating current in the resistor? A) 3.7 kHz B) 8.2 MHz C) 1.4 kHz D) 970 Hz E) 30.6 kHz
8: Imagine four point objects, three with charge Q and one with charge +Q. They are held together evenly spaced on a circle of radius R. The top negative charge is released and allowed to escape. What is its final kinetic energy when it is far away from the other charges? A)
kQ 2 +2 2R 3kQ 2 B) 4R 3kQ 2
2
(
)
-Q
-Q
R -Q
2R kQ 2 D) 2 2 -1 2R 3kQ 2 E) 2R 2
C)
(
)
+Q
9: An RC circuit constructed of a 100 resistor and a 50 F capacitor is driven by a 60 Hz AC generator. What is the relationship between voltage and the current in this circuit? A) Current lag voltage by a phase angle of 24.2 B) Current leads voltage by a phase angle of 73.3 C) Current lags voltage by a phase angle of 54.9 D) Current leads voltage by a phase angle of 28.0 E) Current leads voltage by a phase angle of 47.8
AC
10: Consider a flat rectangular conductor connected to a battery as shown. The conductor is embedded in a magnetic field going into the page. When current flows through the conductor, the electric potential on it is larger on the left than on the right. Which of the following statements is true? A) The charges which flow feel a magnetic force into the page B) The electric field in this conductor points into the page C) The charges which flow in this conductor must be negative D) The electric field in the conductor points to the left E) The charges which flow in this conductor must be positive
V
11: A metal loop is suspended by a string above the gap between the poles of magnet. When it is held still, the tension in the string is equal to the weight of the ring. If the ring is lowered at constant velocity towards the magnet, which of the following statements is true? A) Tension in the string is greater than the weight B) Tension in the string is less than the weight C) ring The feels a net upward force D) The ring feels a net downward force E) The ring is deflected to the right
V
N
S
12: A rectangular loop of area A sits next to a long straight wire as shown in the figure. The current in this long straight wire flows to the left and is gradually increasing. Which of the following statements correctly describes what happens? A) The loop feels a torque pulling side A into the page and pushing side B out of the page. B) The loop feels a torque pushing side A out of the page and pulling side B into the page C) The loop feels no net force or torque D) The loop feels a net force pulling it toward the wire E) The loop feels a net force pushing it away from the wire
Side B
Side A Iwire is increasing
13: Inductance in a circuit helps to smooth out changes in current. It prevents currents from starting instantly when the circuits are connected. Imagine a circuit which contains a 60V battery, a switch, a 150 resistor, and an inductor. If, when the circuit is closed, the current rises from zero to 0.3 A in 1.5 s, what is the value of the inductor L? A) 6.3 mH B) 2.4 mH C) 4.7 mH D) 2.3 mH E) 0.16 mH
150 60 V L
14: Four different ions enter a mass spectrometer which contains a region of constant magnetic field. Each ion has the same charge, and their masses are m1=m, m2=2m, m3=3m and m4=4m. The ions enter the chamber with velocities v1=v, v2=2v, v3=3v, and v4=4v. All velocities are perpendicular to the magnetic field. Which of the four ions travels through a semicircle and strikes the detector in the shortest time? A) m1 B) m2 C) m3 D) m4 E) All four strike at the same time
Example path
Detector
15: An insulating rod carrying unknown charge is brought near a ball suspended from a thin insulating thread. If the suspended ball is repelled from the rod, which statement must be true: A) The ball is made of an insulating material B) The ball is positively charged C) The ball is negatively charged D) The ball has some non-zero net charge E) The ball is made of a conducting material
16: Given the circuit shown, what is the current through the 3R resistor shown circled in the center of this network? A) 4V/5R B) 3V/8R C) V/3R D) V/12R E) Zero
2R V R 3R
4R
2R
17: The switch in this circuit is closed for a long time. Describe what happens to the bulb labeled A after the switch is suddenly opened. A) The bulb suddenly becomes bright, then fades out. B) The bulb suddenly becomes bright, and remains constant C) The bulb never lights D) The bulb starts out off, then begins to flash E) The bulb starts out off, then becomes continuously bright
R
A
V
R C Switch
18: A parallel plate capacitor is constructed of two round plates with a 5.6 cm radius and a separation of 0.9 mm. The space between the plates is filled with a dielectric with dielectric constant . When the charge on the capacitor is 1.3 C, the voltage between the plates is 750 V. What is the dielectric constant ? A) 1.8 B) 3.7 C) 4.4 D) 2.2 E) 0.6
19: The electric field in some region of space which can be expressed:
r ^ E = (2.0 x )x
What is the change in electric potential when an object moves along the x axis from the point x = -3 to the point x = 10? A) -125 V B) -91 V C) 100 V D) 73 V E) 109 V
20: What is the equivalent capacitance of the set of identical capacitors shown in this figure? A) 4C/3 B) C/3 C) 3C D) 3C/4 E) C
C C C C
C
C
21: Consider the circuit shown in the figure. What is the total charge on the 20 nanoFarad capacitor long after (like a minute after) the switch is closed? A) 6.0x10-7 C B) 4.5x10-8 C C) 2.6x10-7 C D) 1.5x10-8 C E) 8.1x10-8 C
20 nF 30 V 75
200
50 mH
22: Maxwell's equations suggest a strong symmetry between electric and magnetic fields. Why is this symmetry not more obvious in the electric and magnetic phenomena we usually see? A) Electric fields are typically stronger than magnetic fields B) Magnetic fields are typically stronger than electric fields C) Positive and negative charges are usually found together D) There are no magnetic monopoles E) Natural magnets are rare
23: Linearly polarized light of intensity I0 passes through three sheets of polarizing material. The three sheets are oriented at angles 30, 45, and 70 from the initial polarization axis of the light. You are trying to minimize the light transmitted. To do this you may place these three sheets in any order, but may not rotate them. What is the minimum light intensity you can have emerge from the third filter? A) 0.21 I0 B) 0.11 I0 C) 0.76 I0 D) 0.25 I0 E) 0.18 I0
24: Note the different types of electromagnetic radiation: (1) X-rays (4) visible light (2) radio waves (5) infrared radiation (3) gamma rays (6) ultraviolet radiation Which list correctly ranks the electromagnetic waves in order of increasing wavelength (from smallest to largest)? A) 2, 5, 4, 6, 1, 3 B) 3, 1, 6, 4, 5, 2 C) 3, 6, 1, 4, 5, 2 D) 2, 3, 4, 5, 6, 1 E) 2, 5, 4, 1, 6, 3
25: Because charge can flow freely in them, conductors exhibit a variety of special properties. Which of the following statements about conductors is false? A) The electric potential inside a conductor must be zero B) The total electric charge on a conductor may be positive or negative C) The electric field inside a conductor is everywhere zero D) Any charge inside a conductor must be distributed on its surface E) The electric field just outside the conductor is directed perpendicular to its surface