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Instructor: P. Avery, Z. Qiu
PHYSICS DEPARTMENT
PHY 2054
Final exam
April 27, 2013
Signature:
Name (PRINT, last, first):
On my honor, I have neither given nor received unauthorized aid on this examination.
YOUR TEST NUMBER IS THE 5-DIGIT NUMBER AT THE TOP OF EACH PAGE.
DIRECTIONS
(1) Code your test number on your answer sheet (use 76–80 for the 5-digit number). Code your name on your
answer sheet. DARKEN CIRCLES COMPLETELY. Code your student number on your answer sheet.
(2) Print your name on this sheet and sign it also.
(3) Do all scratch work anywhere on this exam that you like. At the end of the test, this exam printout is to be turned in.
No credit will be given without both answer sheet and printout with scratch work most questions demand.
(4) Blacken the circle of your intended answer completely, using a #2 pencil or blue or black ink. Do not
make any stray marks or the answer sheet may not read properly.
(5) The answers are rounded off. Choose the closest to exact. There is no penalty for guessing.
>>>>>>>>WHEN YOU FINISH <<<<<<<<
Hand in the answer sheet separately.
Constants
−12
−31
ǫ0 = 8.85 × 10
F/m me = 9.11 × 10
kg
mp = mn = 1.67 × 10−27 kg e = 1.6 × 10−19 C
k = 9 × 109 N m2 /C2 µ0 = 12.56 × 10−7 H/m NA = 6.02 × 1023 atoms/mole c = 3 × 108 m/s
g = 9.8 m/s2
micro = 10−6
nano = 10−9
pico = 10−12
1. An electron and a proton, located far apart and initially at rest, accelerate toward each other in a location undisturbed
by any other fields or particles. Just before they collide, the ratio of their kinetic energies, Ke /Kp is approximately
(1) 1830
(3) 3.4 × 106
(2) 1.0
(4) 5.5 × 10−4
(5) 43
2. Four particles of charge Q are fixed at the corners of a square with sides of
length L, as shown in the figure. One particle is moved from its original
position to the center of the square by an external force. The work performed
by the external force is:
Q
Q
1
2
×
3
4
Q
Q
√
(1) (5/ 2 − 2)kQ2 /L
(2) kQ2 /L
√
(3) 3 2kQ2 /L
√
(5) 2kQ2 /L
(4) 0
3. A resistor in the form of a solid cylinder of material is connected across the terminals of an ideal battery and the current
is measured to be 6.0 A. A second resistor made of the same material and having the same volume but two times the
length is put in parallel with the first resistor. What is the total current in the new circuit?
(1) 7.5 A
(2) 9.0 A
(3) 0.60 A
(4) 4.8 A
(5) 30.0 A
4. What is the charge on the 20 µF capacitor if the battery has an emf of 30 V?
12µF
24µF
12µF
6µF
20µF
+
(1) 225 µC
(2) 240 µC
(3) 640 µC
(4) 120 µC
(5) 180 µC
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5. A 12.0-V truck battery is rated at 239.0 ampere-hours and has an internal resistance of 0.9 Ω. Approximately how long
can it supply current to a 3.0 Ω load?
(1) None of these
(2) 95 hours
(3) 115 hours
(4) 60 hours
6. A conducting rod slides at 4.0 m/s on metal rails separated by 2.0 m. If a
current of 40 mA is generated in the circuit with resistance R = 0.36 Ω, what
is the magnetic field between the rails (in mT)?
(1) 1.8
(2) 0.028
(3) 110
(5) 239 hours
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(5) 3.6
7. A series LR circuit includes a 9.0 V battery, a resistance of 0.50 Ω, and an inductance of 0.80 H. The elements are in
series with an open switch. What is the voltage across the inductor 2.0 s after the switch is closed?
(1) 2.6 V
(2) 0.0 V
(3) 9.0 V
(4) 6.4 V
(5) 4.0 V
8. A proton cyclotron has protons circulating in a magnetic field of 0.20 T that extends out to a radius of 0.40 m. What
is the maximum energy of protons in this machine?
(1) 4.9 × 10−14 J
(2) 1.6 × 10−13 J
(3) 3.2 × 10−13 J
(4) 3.2 × 10−14 J
9. Two long parallel wires are aligned vertically 30 cm apart as shown in the figure. The left
wire carries a 6.0 A current upwards while the right wire carries a 15.0 A current downwards.
What is the magnetic field (in µT) at a point between the wires at point P, a distance of
10 cm from the left wire?
(1) 27
(2) 3.0
(3) 6.0
(4) 15
(5) 4.9 × 10−13 J
P
(5) 90
10. A circular loop of wire with radius 10.0 cm and resistance 0.50 Ω lies in the plane of the page within a magnetic field
directed into the page. The magnetic field strength changes at a rate of 10.0 T/sec. Which of the following answers
describes the induced current? (cw = clockwise, ccw = counterclockwise)
(1) 0.63 A, ccw
(2) 0.63 A, cw
(3) 20 A, cw
(4) 0.2 A, cw
(5) 20 A, ccw
11. Light polarized along the vertical direction is incident on four polarizing sheets with their transmission axes oriented at
20◦ , 30◦ , 50◦ and 60◦ relative to the vertical. What fraction of the initial light intensity is transmitted through this set
of polarizers?
(1) 0.73
(2) 0.86
(3) 0.26
(4) 0.068
(5) 0.46
12. A light ray in the core (n = 1.37) of a cylindrical optical fiber travels at an angle θ1 = 47.9◦ with respect to the axis of
the fiber. A ray is transmitted through the cladding (n = 1.25) and into the air. What angle θ2 does the exiting ray
make with the outside surface of the cladding?
(1) 23.3◦
(2) 66.7◦
(3) 42.7◦
(4) 47.3◦
(5) 38.7◦
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13. As shown in the figure, a light ray is incident normal to one face of a triangular
block of material with index of refraction n2 = 1.65 that is immersed in water
(n1 = 1.333). What is the maximum angle α for which total internal reflection
occurs at P?
(1) 36.1◦
(2) 53.9◦
(3) 52.7◦
(4) 41.4◦
P
n1
n2
α
(5) 37.3◦
14. A dental hygienist uses a concave mirror to see the back of her patient’s teeth. When the mirror is 1.5 cm from a tooth,
the image is upright and 3.0 times as large as the tooth. What is the focal length of the mirror?
(1) 2.25 cm
(2) 1.50 cm
(3) 2.4 cm
(4) 1.13 cm
(5) 0.75 cm
15. A laser beam of wavelength 632.8 nm has intensity 13.3 W/m2 . The amplitudes of the associated electric and magnetic
fields, in V/m and µT, respectively are:
(1) 100, 0.33
(2) 70.7, 0.24
(3) 10,000, 33.4
(4) 56.5, 0.19
(5) None of these
16. Two converging lenses, the first with focal length 25 cm and the second with focal length 20 cm, are separated by 30 cm.
A 4.0 cm tall object is placed 50 cm in front of the first lens. Where is the final image?
(1)
(2)
(3)
(4)
(5)
10
20
20
10
50
cm
cm
cm
cm
cm
after the second lens
after the second lens
before the second lens
before the second lens
after the second lens
17. A person has his nearsightedness corrected by lenses of −5.00 diopter. Without his glasses, his near point was 12.5 cm.
With his glasses on, what is his near point? Assume the lenses are next to his eyes.
(1) 33.0 cm
(2) 13.0 cm
(3) 20.0 cm
(4) 17.5 cm
(5) 7.50 cm
18. A thin film of soapy water, n = 1.37, is held vertically. Light of wavelength 600 nm is reflected from the film and
horizontal dark lines appear. What is the difference in thickness of the soap film from one band to the next?
(1) 219 nm
(2) 300 nm
(3) 438 nm
(4) 600 nm
(5) 900 nm
19. A grating with 8,000 slits space over 2.54 cm is illuminated by light of a wavelength of 546 nm. What is the angle
corresponding to the third order maximum?
(1) 31.1◦
(2) 15.1◦
(3) 26.3◦
(4) 10.5◦
(5) 21.3◦
20. A binary star in the constellation Orion has an angular separation between the stars of 10−5 radians. Assuming a
wavelength of 500 nm, what is the smallest aperture (diameter) telescope that will just resolve the two stars?
(1) 6.1 cm
(2) 3.0 cm
(3) 4.2 cm
(4) 12.6 cm
(5) 2.2 cm