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Unformatted text preview: Physics 222, Summer 2009
FINAL EXAM Friday, August 7, 2009 Name (Printed):
Section Number: Recitation Instructor: INSTRUCTIONS: 1. This is a two hour exam consisting of 30 multiple—choice questions. Questions 101
through 120 are each worth 1 point. Questions 121 through 130 are worth a half point (1/2
point) each. I will count all your correct answers for a total of up to 25 points. Use your
previous bubble sheet answering questions # 101 through # 130 on the back of your
bubble sheet from the first three exams.. 2. Use a number 2 pencil when marking your bubble sheet. Do not use ink. Ask for a pencil
if you did not bring one. Fill in the appropriate bubble completely. It you need to change any entry, you must completely erase your previous entry. Also, circle your answer on the
exam. 3. Carefully read each problem and its five possible answers before beginning to work on
the problem. Select only one answer for each problem. Choose the answer that is closest
to the correct one. 4. Before handing in your exam, be sure that your answers on your bubble sheet are what
you intend them to be. You should copy down your answers on a piece of a scratch paper
for comparison with the answer key to be posted later. 5. When you are finished with the exam, place all exams materials, including the bubble
sheet, the exam itself, and scratch paper that you used for the exam, in your folder and
return the folder. Enjoyed working with you this summer and wish you all the best in your future
endeavors. Good Luck!  Art Meyers A resistzneclcss LC circuﬁ consists of a capacitor and an inductor, as drawn in ﬁgurc 101. Whom the
extent flowing through an incluomr changes. a voltage (emf) gets created in the inclucwr that Opposes
the cling: in the current 30. inductors have an “inertia” with mm to changes in cmjust like masses have inertia with respect [0 changes in velocity. In an LC circuit, charge oscillates back and foul) between the two mpaeitor plates. just like a penéuium’s
position oscillates back and forth between the two endpoints of its For Woe. in ﬁgure 1 l3,
suppose the bottom plate initialfy carries negative charge. Excess elemans ﬂow off the bottom plate. the inductor, and onto the top plate. So. the top plate new carries the negative charge. But then.
the negative charge "slashes" back onto the bottom plate. In this manner, the charge oscillates. At given mommt, the energy stored in the capacitors U: = g %, where Q denotes the net charge
on the top plate. and C denotes the capacitance. The energy Stored in Lb: inductcx is UL = % 1.12, where I
denotes the currem wrong}: the circuit, and L is a constant called me inductance. Since the circuit is
essentially resistanoeless, no has! clissiparcs as amen! oscillalcs back and forth. in this circuit C =‘ $3.16 Ends and L =10 henna. (Farads and hem”; are both 51 units) initially. at
time 1‘: 0. the bottom plate has charge — 1.0 mulombs. and no current is flowing, 101. Vsﬁtich graph best represents the charge on the top plate of the capacitor as a function oftime? ,ptm A. L 2 pins: ' + —{
l ,
Ea G g G
. E i :3 ' .
Figure 101 g g a; amt
C. D.
+ r
u o
=5 e:
E 0 . E D
.1: mm; ,“
J J
E
i
‘A I E) None of the above graphs represent the charge in the top plate of the capacitor as a function
of time. t 102. An ion of mass m and of charge +e is in circular orbit aromd a ﬁxed
pomt charge Q. with charge 8.0 uC. The radius of the orbit is 0.20 m. and
the speed of the ion in the orbit is 1.2x10‘ m/s. A uniform external magnetic
ﬁeld, perpendicular to the plane of the orbit, is present. The magnetic force
on the ion is equal to the electric force in magnitude and in direction at all
points of the orbit. In the ﬁgure. the mass m of the ion is closest to: A) 6x10 ’2‘ kg ~
B) 5x10 ‘2‘ kg
C) 4x10 '2‘ kg
D) 8x10 '2‘ kg
E) 7x10 '2‘ kg IV=1.2xlﬂsm/s a, If an electron is accelerated through a potential of 300 V and then enters, from the left, a region with an
electric ﬁeld of 12.00 x 106 N/C pointing down [see figure below]: 103. 104. 105. 106. : '1.
X‘ X X X [for/v Mam). What is the election speed leaving the accelerating potential? [in m/s] A) 1.05 X 10 1‘ B) 5.25 x 1013 C) 10.27 x 106 D) 1.05 x 107 E) Need more information to solve the problem. What magnetic ﬁeld pointing into the paper will allow the electron to travel to the right without
being deﬂected up or down? [See ﬁgure above.] A) 0.987 T B) 1.05T C) 1.168 T D) Not enough information given in Problem #103. E) Impossible since ﬁelds are in the wrong direction for there to be no deﬂection. You have a long solenoid which has 1500 turns in 20 cm with an AC current of 3.5 amps flowing
through the coil. This coil has a diameter of4 cm and a resistance of 25 ohms. What is the
magnetic field inside the center of the solenoid? [ in Tesla] A) 6.60 x 10'3
B) 0.3299 C) 3.299 x 10'2
0) 4.67 x 10'2
E) 1.649 If a coil of 300 turns with a diameter of 1.00 inch was placed in the above solenoid (assume
Brms = 10 x 10" T) what will be the Ems voltage reading on an AC voltmeter or on a digital scope
(in volts) if the frequency = 5000 Hz? [in Volts] A) 45
B) 2.5
C) 21
0) 23.5
E) 30 inﬁll)! 107. Consider a genus RI. circuit cumming ofa battery. 2 Switch. an inductor and a resistor all
connected in series. The Switch is closed and the current and the voltage change with time are
measurch noted and plotted in graph #1 and graph 5:12. The graphing persons forget to label the.
axes. As a physicist, you wilt do this far them. These are graphs of current and voltage versus
time. The W axes labels are as follows: ' r g #52
A GE}; all C Gm h .
GRAPH #1 B GRAPH #2 o
A L3. ' Q Q A) time _ current time voltage
3) current time voltage time
C) time mistage rim: current
D) voltage time current time E) None of the above combinetions‘ 108 1n the ﬁgure, an insulated wire is bent into a circular loop of radius 6.0 cm
and has two long suaight sections. The loop is in the xy plane, with the center
at the origin. The straight sections an: parallel to the pans. The wire can'ies a
current of 8 A. The magnitude of the magnetic ﬁeld at the origin. in 1.1T, is
closest to:
A) 90
B) 80
C) 110
D) 100
E) 70 109. 110. 111. 112. An electron has the same de Broglie wavelength as an 800 nm photon. The speed of the
electron is closest to: [in m/s] A) 600
B) 700
C) 800
0) 900
E) 1000 An object 8 m high is located 125 m in front ofa concave mirror which has a focal length of
200 m. Which of the following set of positions, size, and character of the image is correct? Image Position 3:; Character of Image
A) 500 m +32 m erect virtual
B) 333 m +213 m erect virtual
C) +333 m 21.3 m inverted real
D) +500 m 32 m inverted real
E) None of the above. Determine the focal length of a converging lens which will project the image of a lamp magniﬁed
4 diameters, upon a screen 10 m from the lamp (in m). A) 125 B) 10 C) 2.0 D) 2.5 E) Not enough information. A narrow beam of light strikes a glass plate (n = 1.60) at an angle of 53° to the normal. If the
plate is 20 mm thick, what will be the lateral displacement of the beam after it emerges from
the platelin mm)? A) 265
B) 150
C) 115
o) 90 E) Not enough information. 113. 114. 115. 116. Two identical beakers are filled to the same level, one filled with water (n = 1.361) and the other
with mineral oil, (n = 1.47) they are both viewed from directly above. Which beaker appears to
contain the greater depth of liquid? A) same depth B) water depth greater
C) mineral oil depth greater ’
D) Not enough information. An amateur lens grinder wants to grind a converging lens of crown glass (n = 1.52) with the
same curvature on both sides and a focal length of 25 cm. What radius of curvature must he
grind on each face? [in cm] A) 13
B) 25
C) 26
D) 50
E) Not enough information. The interference pattern of two identical slits separated by a distance d = 0.25 mm is observed
on a screen at a distance of 1 m from the plane of the slits. The slits are illuminated by
monochromatic light of wavelength 589.3 nm (sodium D) traveling perpendicular to the plane of
the slits. Bright bands are observed on each side of the central maximum. Calculate the
separation between adjacent bright bands (in mm). A) 1.08
B) 236
C) 4J2
D) 5.80
E) None ofthe above. The headlights of a distant automobile are 1.4 m apart. If the diameter of the pupil of the eye is
3 mm, what is the maximum distance at which two headlights can be resolved? [in m] Consider
the headlights as point sources of wavelength 500 #144. A) 2030
B) 5700
C) 6100
D) 6900 E) No enough information. 117. A grating having 15,000 lines per inch produces spectra of a mercury arc. The green line of the
mercury spectrum has a wavelength of 546.1 nm. What is the angular separation between the
1St order green line and the 2"" order green line? A) 18.8°
B) 21.40
C) 40.2°
D) 590°
E) None of the above. 118. In an important experiment in 1927, a beam of electerons was scattered off a crystal of nickel.
The intensity of the scattered beam varied with the angle of scattering, and the analysis of
these results lead to the conﬁrmation of A) the particle nature of light. B) the Bohr model of the atom. C) the wave nature of light. D) the Rutherford model of the nucleus.
E) the quantization of energy levels. 119. You have a blackbody radiator with a maximum intensity at a wavelength 0f414.3 nm, what is
the Temperature of the blackbody radiator? [in Kelvin] A) 6000
B) 6500
C) 7000
D) 7500
E) Not enough information. 120. The work functions for potassium and cesium are 2.25 and 2.14 eV, respectively. Will the
photoelectric effect occur for either or both of these elements with an incident light of
wavelength 565 nm? A) neither cesium nor potassium
B) cesium only C) potassium only 0) both E) Not Enough information. PHYSICS 222  Summer, 2009
Laboratory Final
NOTE: Each of these questions are worth 1/2 a point. 121. In the electron beam experiment, the electron d
tube contained two electrodes: _ r ano e a. a straight, glowing ﬁlament
(perpendicular to the page in the ﬁgure narrow slit on the right);
b. a cylindrical anode that surrounded the k electron beam
ﬁlament. filament On the side of the anode was slit through which a
beam of electrons emerged. What was the primary cause of the kinetic energy of the emerging electrons? A) The magnetic ﬁeld generated by the currents in the two large Helmholtz coils;
B) The high temperature of the glowing ﬁlament; C) The potential difference between the two ends of the glowing ﬁlament; D) The potential difference between the ﬁlament and the cylindrical anode; E) None of the above. ' 122. Consider two conducting spheres mounted on insulating rods and #1 #2
located (with the relative positions shown) in a region of large
electric ﬁeld, near a negatively charged rod as shown. . Assume that both of the spheres are initially uncharged. Then one of the two spheres is displaced slightly so that the two spheres I
touch each other brieﬂy. Assume that neither touches the rod, and I
that their relative positions always are as shown. t Which of following are possible values for the resulting charge on)
each sphere, #1 and #2, respectively, after the sequence of events described? I3
0 nC o nC 123. In laboratory, the EMF produced within a small coil (by a sinusoidal magnetic ﬁeld within a
solenoid) can be measured with an AC voltmeter. This EMF can be measured for coils of various
design, such as those whose main features are listed in the table below. Other conditions being
equal, how would your expect the reading of the voltmeter when using coil #6 (in place within the
solenoid) to be related to the reading observed when using coil #1? Coil # of nuns Diameter EMF
.
(RMS)
— 1 o _
1'5! 05 — 100
A) The readings with #6 should be about twice that obtained with #1.
B) The readings with #1 and #6 should be approximately the same.
C) The readings with #6 should be about 4 times that obtained with #1.
D) The readings with #6 should be about 1/4 that obtained with #1.
E) The readings with #6 should be about 1/2 that obtained with #1. 124. A laser beam strikes a Plexiglas block (such as you used in lab) that is lying on a table. Which of the paths shown is a possible path for the beam? (Choose E if none of the paths shown is
appropriate.) 125. In the Polarization lab, you measured the
intensity of the light (in lux) transmitted
through two polarizers, as a function of the
angle of rotation of one of the polarizers. Data
from such an experiment is shown at the right.
For these data, which of the following
theoretical forms best represents the data. A) 200 cos (6) B) 200 cos2 (6) C) 160 cos: (6) + 40 D) 80 cos (6) + 40 E) None of the above represents the data
very well. Intensity (lux) o 90 180 270 360
Theta (degrees) 126. You have an incandescent light bulb and you
would like to determine the energy it consumes
for various applied potential differences. You
have available DC power supplies (PS) and high
quality volmieters (V) and ammeters (A). Which
instruments would you place in the positions
shown in the ﬁgure to make the necessary
measurements? I!
E E. None of the above arrangements will
give the required information 127. In laboratory, the EMF ~ ' f ti .
produced Within a small ggggragr SDlEHOld (15 cm long) v/les‘imcsg :rrrilagfoi
coil (located within a sDigital
solenoid powered by the IIIII— can: or
voltmeter sine ﬁmction output of a
function generator
operating at 5000 Hz)
was measured with an
AC voltmeter, a typical
result is shown in the
table below for one of
the coils. (inches) ' ) lfthe signal from the small coil was connected instead to an oscilloscope (rather than to an AC
voltmeter), which of the following best describes the waveform that would be observed? (Assume
that the 0 volt level is centered in the middle of the screen, and that the scope is operated in the
“sweep” or “triggered” mode, with the horizontal axis corresponding to time.) A) A sine ﬁmction, with its vertical peaks at i 0.30 volts. B) A horizontal line, displaced upward from 0 at +0.30 volts.
C) A horizontal line, displaced upward from O at +0.42 volts.
D) A horizontal line, at the middle of the screen. E) A sine function, with its vertical peaks at i 0.42 volts. 128. 129. 130. As you read this exam, which of the following best describes some aspect of the light reaching
your eye from the page? A)
B) C)
D) E) Light is emitted by the page. Light from various places suffers diffuse reﬂection from the page, a process in which the
angle of reﬂection equals the angle of incidence. Light from various places suffers diffuse reﬂection from the page, a process in which the
direction of the reﬂected light has little relation to the direction of the incident rays. Light from various places suffers specular reﬂection from the page, a process which is
described by Snell’s Law. Light from various places suffers specular reﬂection from the page, a process in which the
angle of reﬂection equals the angle of incidence. Assume that you are focusing your eyes on an upright Q! Cyclone. If someone could look inside
your eyeball, what would they see when they examined the retina of your eye? A)
B)
C)
D)
E) a little upsidedown picture of Cy on your retina;
a little rightside—up picture of Cy on your retina; _ nothing, because the image of C31 is virtual. However, you see an upsidedown Cy, nothing, because the image of Cy is virtual. However, you see a right—sideup Cy;
None of the above descriptions is correct. In laboratory, you had access to a precision vertical adjustable slit. Assume there is a laser beam
passing through the slit, and that you can see a bright spot (with a diameter of a few m) where this
beam impinges on a distant wall. Which of the following best describes how that spot is affected as
you slowly close the slit. A)
B)
C)
D) E) The spot remains about the same size, but gradually gets dimmer. The spot gradually gets smaller in the vertical dimension, eventually disappearing entirely.
The spot gradually gets smaller in the horizontal dimension, eventually disappearing entirely.
The spot gradually gets dimer, and horizontally wider, with considerable spatial variation in
intensity. No matter how slowly you close the slit, the spot suddenly disappears, because it is laser light. PHYSICS 222
SUMMER 2009 — FINAL
FORMULA SHEETS versi‘m 4'5 n1 sin 91=n2 sin 62 sin 9c=gl
%+§=%=% m=—%
%=E§‘l(g—l—ﬁ> %+é=%
m=S§I 1114:25—fm‘
dsin6=mA asin91=/\
asin61=1.22A dsin6=mA
9min=ﬁ I 11:5
ITRANS = % INCIDENT ITRANS. = IINCIDENT 0052 9
tan 93: :1 T: :vz ET
Aﬁﬁ dsin9=rnA I=Im(§"§;—“’)2
I=4Iocoszﬁ asin6=mA a=7r7asin9
= 17d sin a sin 6 = 1.22 g ' I=Im (0032 5) (ﬂue?
dsin6=mA 2dsin6=mA a=7r7asi116
Aghw = Ndiosﬁ = ¥ Sin 6
h=6.63><10'34Js E=hf c=fA
hf=KEmax+© AA=#(1—cos¢) A=§
%:‘¥+8’gim [E—U<x>]w=0 hf=AE wn<x)=Asin(% x) = —#q,% =ﬁiﬁ=w 5:511; ’ 1eV=1.60x1019J L= e<2+1>n 11:11125 . [Jar—$13
“Olaf—mm; S=mh ug=ﬁ=9274x1044m
sz=msﬁ #szz—st/JJB AMIN=%
Am T = 0.2898 ><”1o2 m  K K13max = eVS . N = NoeAt
7.m=lnT2 §¥=(%>oe"\t AxApx Z h/27r c=3.oox1o' ms"
=5,53x10*" Js ‘
sg= 5.351042 Flm
p0: 410(10'7 Him
5:1.sox10'“ C
m,=9.11x1o~’" kg
m,=1.57x1o'27 kg
1ev=1 .sox1 0'“J I?“ = ;—%3r pomt charges
4st r
 I?“
E = —
9m
 1 q .. .
E = —2r pom! charges
471:5, r
ﬁg . d2 = L
a, .
E = E— above conducting surface
so
with charge density 0'
f _ 1
AU = —j 95  d1
1
AU = qAV
. f  
AV = j E  J!
'U = 1 g‘qz point charges
471:1:n r _ V  1 2 point charge —47r£.,r
_(_§Z§Z_§Z _ ax, ay 62
$5: d2 (Resistors & Inductors in series) Ran = R1+R2+R3 Len = L1+Lz~+ La (Resistors & Inductors in Parallel)
1 1 1 1 c=2
V
A5,, C = —d— parallel plate capacitor 1
U=— V
2Q 1 u :35”? energy density .dQ 1=—=n9lAvd ’ ,IIRC 9(I)=Qn(1e ) em = 902"“
0+1)" =1+nx+ n(n1)12/Z‘+...
sin(a) + sin(b) = 1 1
25in— a+b cos (1—17 2( ) 2( )
VolumeSphere = 47v3 / 3 mafacem'gaSphere = 47V2 '
areaCirde = 7172 ' circmnfermceCircle = 2er bl:t\/b2 —4ac a?+bz+c=0,z=
1 2a .2 .§ = A3 cos(€) 
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can C1 OZ 03
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to second with ﬁngers,
thumb direction of product b) thumb in direction of
current, curl tip of your
ﬁngers, the curl points in
direction of Bﬁeid c) integrate around line integral
in direction of ﬁngers, thumb
is direction of normal vector
for flux ﬁ=q§x§
R B = [J—0 center of loop, radius a 2a .8 = ﬂout center of circnlararc
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45 i d] = pain”,
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igdihﬂé
1 d1
£=(ix§) l
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M=ﬂ2321=3ﬁ¢12
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  do
3111: _E.
f #050 d1
 — do
i3 d1=Fofon+ﬂolxmm
. do; ‘
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(I 0 d1 5 = Emsinchwt)
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B V/‘u5o
1 2 1 2
u=—E +—B
2 DE 2%
§=irxé
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J4SPLAA
2/1»
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surfaceArea .R
f‘E =(n dsinQ sphericalmirror l)(l1—)thinlens
rl r2 =M m=0,1,l.. two—slit 1mm
(2st = m m=l,2,..
shaglcrslit diﬁiacﬁm mm ' sin6=122— )1
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L __1_ Ug=éLi2
0’ ’Jﬁ
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_l 2
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mac
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k b 2
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m 2m
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“( )=ﬂi
2“ 22 e = ~d¢B/dt
8=IE'ds =—Ldi/dt
L=NéB __1:
1 IL R
E
n— (l—e't/TL) _
R tan ¢ =XL Xc
Tc: RC
VL= ILXL
H5: 32/2110
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dt dt i=i'
LC V=,/V,f +(VL—VC)2 =J(IR)2+(IXL—IXC)2 =1,/R1+(XL—XC)2 =Iz;i=ivi; di2
encl’ £1=—M ;’ £2 = 2 _k,
, ;UB=lLi2;u,=lB—;i=5(1—e L);i=1
l 2 2/10 R JQ2—q2;i=Icosax;v=Vcos(ax+¢);XL=wL=2fo;XC l c 1 1 l R
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(0C 27rfC "M £2 N2
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v=—;l=
n 20 n n . _ .  _  . _”b ._ 2.
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