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Physics 2220
Spring 2014
Paolo Gondolo
FINAL EXAM
PLEASE FILL IN THE INFORMATION BELOW
Name (printed):
Name (signed):
Student ID Number
Discussion Instructor:
U __ __ __ __ __ __ __
Anthony
KC
Matt
Paul
Peter
Important!
You are not required to answer all questions in this exam. You will receive points
toward your exam points for every question correctly answered. Partial credit is
available, however a minimum amount of work and explanation must be shown to
receive any credit (for example, a mere list of equations with no explanation of their
connection to the problem will not receive credit).
Seat #
Physics 2220
Spring 2014
Paolo Gondolo
Data: Use these constants (where it states, for example, 1 ft, the 1 is exact for significant figure purposes).
1 ft = 12 in (exact)
1 m = 3.28 ft
1 mile = 5280 ft (exact)

x


x 2  a 2 dx 
1
3
 x2  a2 
3
1 hour = 3600 sec = 60 min (exact)
1 day = 24 hr (exact)
gearth = 9.80 m/s2 = 32.2 ft/s2
2
2
gmoon = 1.67 m/s = 5.48 ft/s






dx

x2  a2

3

x
a2 x2  a2
1 year = 365.25 days
  ax
e
dx


1 kg = 0.0685 slug
1 N = 0.225 pound
1 horsepower = 550 ft⋅pounds/s (exact)
24
Mearth = 5.98 × 10 kg
Rearth = 6.38 × 103 km






Msun = 1.99 × 1030 kg





Rsun = 6.96 × 108 m
22
Mmoon = 7.35 × 10 kg
3
1
  eax
a
xdx
 x2  a2 
3/2
xdx
a2  x2

1
x2  a2
  a2  x2
Rmoon = 1.74 × 10 km
G = 6.67 × 10-11 N⋅m2/kg2
k = 8.99 × 109 N⋅m2/C2





εo = 8.85 × 10-12 C2/(N·m2)
eelectron charge = -1.60 × 10-19 C
melectron = 9.11 × 10-31 kg





μo = 4π × 10-7 T⋅m/A (exact)
N(Avogadro's No.) = 6.02 × 1023 atoms/gm⋅mole
26
= 6.02 × 10 atoms/kg⋅mole
cos(a ± b) = cos a cos b ∓ a sin b
 n  x  x 2  a 2 


x2  a2
1  a  x 2  a 2
  n
2
2
a 
x
x x a

dx
x2  a2





x
x
 sin 1   , or  cos 1  
a
a
a2  x2
xdx
 x2  a2
dx
sin(a ± b) = sin a cos b ± sin b
mproton = 1.67 × 10−27 kg
h = 6.64 × 10-34 J
π = 3.14
8
c = 3.00 × 10 m/s









1 Tesla = 10,000 gauss (exact)
ρ(H2O) = 1000 kg/m3
dx









dx
1
 n  a  bx 
a  bx b
dx
 a  bx 2

1
b  a  bx 
Physics
Physics2220
2220
Fall 2009Spring 2014
Name: __________________________________
Unid: ___________________________________
Discussion TA: ___________________________
Final Exam
Paolo Gondolo
1
Show all work!! Report all numbers to three (3) significant figures.
A Van de Graaff generator is a device for generating a large electric potential by building up charge on a hollow metal
sphere. A typical classroom-demonstration model has a diameter of 30 cm.
(a)
(b)
[10 pts.] How much charge is needed on the sphere for its potential to be 500 kV?
[10 pts.] What is the electric field strength just inside and just outside the surface of the sphere when it is charged
to 500 kV?
Physics
Physics2220
2220 Fall 2009
Spring 2014
Name: __________________________________
Unid: ___________________________________
Discussion TA: ___________________________
Final Exam
Paolo Gondolo
2
Show all work!! Report all numbers to three (3) significant figures.
A proton (charge 1.602 × 10-19 C) is fired with a speed of 1.0 × 106 m/s through the 10 μF parallel-plate capacitor shown
in the figure. The voltage across the plates of the capacitor is 50 kV, and the distance between the plates is 10 cm.
(a)
(b)
(c)
[10 pts.] Find the magnitude of the electric field between the
capacitor’s plates.
[10 pts.] Find the electric force on the proton inside the capacitor.
[10 pts.] What magnetic field, both magnitude and direction, must
be applied to allow the proton to pass through the capacitor with no
change in speed or direction?
Physics
Physics2220
220
Fall 2009Spring 2014
Name: __________________________________
Unid: ___________________________________
Discussion TA: ___________________________
Final Exam
Show all work!! Report all numbers to three (3) significant figures.
The switch in the circuit shown in the figure has been closed for a long time.
(a)
(b)
[10 pts.] What is the current in each leg of the circuit?
[10 pts.] When the switch is opened, the current in the inductor drops by a
factor of 2 in 8 μs. What is the value of the inductance?
Paolo Gondolo
3
Physics
Physics2220
220
Fall 2009Spring 2014
Name: __________________________________
Unid: ___________________________________
Discussion TA: ___________________________
Final Exam
Show all work!! Report all numbers to three (3) significant figures.
The figure is a cross section through three long wires with linear mass density 50.0 g/cm.
They each carry the same current I in the directions shown. The lower wires are 4.00 cm
apart and are attached to a table. The upper wire “floats” so as to form an equilateral triangle
with the lower wires.
(a)
(b)
[10 pts.] What current I allows the upper wire to “float”?
[10 pts.] What are the magnitude and direction of the magnetic field vector due to
the lower wires at the location of the upper wire?
Paolo Gondolo
4
Physics
Physics2220
220
Fall 2009Spring 2014
Name: __________________________________
Unid: ___________________________________
Discussion TA: ___________________________
Final Exam
Paolo Gondolo
5
Show all work!! Report all numbers to three (3) significant figures.
A method to measure inductance is to connect the inductor in series with a known capacitance C, a known resistance R, an
AC ammeter, and a variable-frequency signal generator. The frequency of the signal generator is varied and the emf rms
is kept constant until the current I is maximum.
(a)
(b)
[10 pts.] If C = 10 μF, rms = 10 V, R = 100 Ω, and I is maximum at the frequency f = 800 Hz, what is the
inductance L?
[10 pts.] What is the electric power dissipated in the circuit when I is maximum?
Physics2220
220 Fall 2009
Physics
Spring 2014
Name: __________________________________
Unid: ___________________________________
Discussion TA: ___________________________
Final Exam
Paolo Gondolo
6
Show all work!! Report all numbers to three (3) significant figures.
An object located 100 cm from a concave spherical mirror forms a real image 75 cm from the mirror.
(a)
[10 pts.] Find the focal length of the concave mirror (including its sign).
The mirror is now turned around so that its convex side faces the object. The mirror is moved so that the image is now
35 cm behind the mirror.
(b)
(c)
[10 pts.] How far was the mirror moved? Was it moved toward or away from the object?
[10 pts.] Sketch a principal ray diagram for the object and the convex mirror after it is moved. Be as accurate as
you can.
Physics
Physics2220
220
Fall 2009Spring 2014
Name: __________________________________
Unid: ___________________________________
Discussion TA: ___________________________
Final Exam
Paolo Gondolo
7
Show all work!! Report all numbers to three (3) significant figures.
A positive charge +Q = 4.0 nC is located at x = -a, where a = 0.20 m.
(a)
(b)
[10 pts.] A second equal positive charge +Q is brought from infinity to x = +a. What is the change of electric
potential energy of the second charge?
[10 pts.] With the two equal positive point charges at x = -a and x = +a, a third charge –Q is brought from
infinity to the origin. What is the change of electric potential energy of the third charge?
Physics
Physics2220
220
Fall 2009Spring 2014
Name: __________________________________
Unid: ___________________________________
Discussion TA: ___________________________
Final Exam
Show all work!! Report all numbers to three (3) significant figures.
A 10 cm by 5 cm rectangular loop with resistance 2.5 Ω is pulled through a
20 cm by 20 cm region of uniform magnetic field B = 1.7 T (see figure) with
constant speed v = 2.4 cm/s. The front of the loop enters the region of the
magnetic field at time t = 0.
(a)
(b)
[10 pts.] Find and graph the magnetic flux through the moving loop
as a function of time from t = 0 to t = 16 s (let a flux out of the page
be positive).
[10 pts.] Find and graph the induced current in the moving loop as a
function of time from t = 0 to t = 16 s (let a counterclockwise current be
positive).
Paolo Gondolo
8
Physics
Physics2220
220
Fall 2009Spring 2014
Name: __________________________________
Unid: ___________________________________
Discussion TA: ___________________________
Final Exam
Show all work!! Report all numbers to three (3) significant figures.
[10 pts.] The figure is a graph of the light intensity on a screen
behind a double slit. The slit spacing is 0.20 mm and the screen is
2.0 m behind the slits. What is the wavelength (in nm) of the light?
Paolo Gondolo
9
Physics
Physics2220
220
Fall 2009Spring 2014
Name: __________________________________
Unid: ___________________________________
Discussion TA: ___________________________
Final Exam
Paolo Gondolo
10
Show all work!! Report all numbers to three (3) significant figures.
A laser beam of small but finite radius r passes through a thin diverging lens with a focal length of -10 cm. The laser
beam’s axis is on the principal axis of the lens.
(a)
(b)
[10 pts.] At what distance past the lens has the laser beam’s intensity decreased by a factor of 4?
[10 pts.] At what distance past the lens has the laser beam’s electric field strength decreased by a factor of 4?
Physics
Physics2220
220
Fall 2009Spring 2014
Name: __________________________________
Unid: ___________________________________
Discussion TA: ___________________________
Final Exam
Paolo Gondolo
11
Show all work!! Report all numbers to three (3) significant figures.
The figure shows a circular current loop near a wire, carrying currents of 0.20 A and 2.0 A, respectively, in the directions
indicated.
(a)
(b)
[10 pts.] What is the magnitude and direction of the torque on the
current loop?
[10 pts.] What is the loop’s orientation that minimizes the loop
energy in the magnetic field of the wire? Specify the
counterclockwise angle from the upward vertical (dashed line in
the figure).
Physics
Physics2220
220
Fall 2009Spring 2014
Name: __________________________________
Unid: ___________________________________
Discussion TA: ___________________________
Final Exam
Paolo Gondolo
12
Show all work!! Report all numbers to three (3) significant figures.
[10 pts.] A charge of 2 μC is 20 cm above the center of a square of side length 40 cm. Find the electric flux through the
square. (Hint: Do not integrate.)
Ph~sics
Name:
Unid:
2220
..
Paolo Condolo
Sp.-in:,: 2014
,AA,.;
'1 /V "
'-fY'
~
/
------------------------------yb o e7 .. j
Discussion T A: ·
1
Final Exam
Show all work!! Report all numbers to three (3) significant figures.
A Van de Graaff generator is a device for generating a large electric potential by building up charge on a hollow metal
sphere. A typical classroom-demonstration model has a diameter o~30 cr11.
(a}
(b)
[10 pts.} How much charge is needed on the sphere for its potential to be 500 kV?
[I 0 pts.] What is the electric field strength just inside and just outside the surface of the sphere when it is charged
to 500 kV?
v
f
=
v
- I~
Q
=
~
0 - 4,, L
f
v.:
• 10
'
Cl S
J>h~ sin
22211
Spring 21114
Paolo Condolo
Name:
2
Final Exam
Unid: - - - - - - - - - - - - - - - - Discussion TA: _ _ _ _ _ _ _ _ _ __
Show all work!! Report all numbers to three (3) significant figures.
19
C) is fired with a speed of 1.0 x 106 m/s through the 10 J-lF parallel-plate capacitor shown
in the figure. The voltage across the plates of the capacitor is 50 kV, and the distance between the plates is 10 em.
A proton (charge 1.602 x 10'
[ 10 pts.} Find the magnitude of the electric field between the
(a)
capacitor's plates.
[ 10 pts.] Find the electric force on the proton inside the capacitor.
[ 10 pts.} What magnetic field, both magnitude and direction, must
be applied to allow the proton to pass through the capacitor with no
change in speed or direction?
(b)
(c)
q
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Name: _
___1_:_.:::_ _ _ _ _ _ __
Final Exam
Unid: - - - - - - - - - - Discussion TA: - - - - - - - -
Slaow all work!! Reoort all numbers to three (3) significant figures.
12 v
The switch in the circuit shown in the figure has been closed for a long time.
(a)
(b)
[10 pts.] What is the current in each leg of the circuit?
[10 pts.] When the switch is opened, the current in the inductor drops by a
factor of2 in 8 J.IS. What is the value ofthe inductance?
(a-) Afte-r
ll-
'""'(5 . f-r..-e.- ~
~tdy -> ~;:: D
S·i'-"~~ po~t..,•a..R
A\i = L ~
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t..
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Name:
~~'0
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Pa.
11
Paolo Condolo
201-l
I
Unid: - - - - - - - - - - - - Discussion TA: . . . . ~--------
4
Final Exam
Slacm all work!! Reoort all numbers to three (3) significant figures.
The figure is a cross section through three long wires with linear mass density 50.0 g/cm.
They each carry the same current I in the directions shown. The lower wires are 4.00 em r,. l(c-.
apart and are attached to a table. The upper wire "floats" so as to form an equilateral triangle
with the lower wires.
(a)
(b)
[10 pts.] What current I allows the upper wire to "float"?
[1 0 pts.] What are the magnitude and direction of the magnetic field vector due to
the lower wires at the location of the upper wire?
b)
/
r,
I,
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Ph~ sics
2211
Paolo Gondolo
Spring 21114
Name: ___f_~~fc~r___________________
Discussion T A:
5
Final Exam
Unid: ---------------------------
---------------------
Show all work!! Report all numbers to three (3) significant figures.
A method to measure inductance is to connect the inductor in series with a known capacitance C, a known resistance R, an
AC ammeter, and a variable-frequency signal generator. The frequency of the signal generator is varied and the emf Enns
is kept constant until the current I is maximum.
[I 0 pts.] If C = I 0 j..lF, Erms = I 0 V, R = 100 Q, and I is maximum at the frequency f = 800 Hz, what is the
inductance L?
[10 pts.] What is the electric power dissipated in the circuit when I is maximum?
(a)
(b)
c
(o..)
z,l
/..,p,.lahce.'
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R. +
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(b)
p=
P=
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L=~.'lb
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(?.nf)~
rnH
e~e.Hs. I/CHs = EteHS
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Ph~ sks
Name:
220
Spring 2014
Paolo Gondolo
________________
----~r~~~r
Unid: ----------------------------Discussion T A:
6
Final Exam
-----------------------
Show all work!! Report all numbers to three (3) significant figures.
An object located 100 em from a concave spherical mirror forms a real image 75 em from the mirror.
[10 pts.} Find the focal length of the concave mirror (including its sign).
(a)
The mirror is now turned around so that its convex side faces the object. The mirror is moved so that the image is now
35 em behind the mirror.
(b)
(c)
[ 10 pts.} How far was the mirror moved? Was it moved toward or away from the object?
[10 pts.] Sketch a principal ray diagram for the object and the convex mirror after it is moved. Be as accurate as
you can.
..l
J.:::.
t-
i.
fY
~-
--·-
----
tr.:. 100
f
(...l't'\1
i
:::.+-=15 c.~
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=- 35 c.nv
-+
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loo o-.
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IOO+ "T 5'
(b)
-
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Ph~ sics
220
Spring 2014
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Paolo (;ondolo
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Name:---------~~~----~~--~-~--------
Unid: ----------------------------Discussion T A: -·-~--+-''-'-"'-<-':....;"'-'-'"'=-;;,___________
7
Final Exam
Show all work!! Report all numbers to three (3) significant figures.
A positive charge +Q = 4.0 nC is located at x = -a, where a= 0.20 m.
(a)
(b)
[ 10 pts.} A second equal positive charge +Q is brought from infinity to x =+a. What is the change of electric
potential energy of the second charge?
[ 10 pts.} With the two equal positive point charges at x = -a and x = +a, a third charge -Q is brought from
infinity to the origin. What is the change of electric potential energy of the third charge?
a. () ::
::
- Q
'hr €.
+Q
-Q
+Q
-a
0
a
Name:
kC.....
Unid:
·
Kf.\(
Discussion TA: - - - - - - - - - -
8
Final Exam
Slao!f all work!! Reoort all numbers to three (3) significant figures.
A 10 em by 5 em rectangular loop with resistance 2.5 n is pulled through a
20 em by 20 em region of uniform magnetic field B = 1.7 T (see figure) with
constant speed v =2.4 em/s. The front of the loop enters the region of the
magnetic field at time t = 0.
(a)
(b)
[1 0 pts.] Find and graph the magnetic flux through the ,moving loop
as a function oftime from t = 0 tot= 16 s (let a flux out of the page
be positive).
[1 0 pts.] Find and graph the induced current in the moving loop as a
function of time from t = 0 tot= 16 s (let a counterclockwise current be
positive).
"'
..,
20cm
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•
saii.
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Name:
{t£N
9
Final Exam
Unid: - - - - - - - - - - - Discussion TA:
~----------
SilO!! all work!! Beport all numbers to three (3) significant figures.
Intensity (mW/m2)
{ 10 pts.] The figure is a graph of the light intensity on a screen
behind a double slit. The slit spacing is 0.20 mm and the screen is
2.0 m behind the slits. What is the wavelength (in nm) of the light?
.
12
,1-.
~10\/
-5
(o, ~~PAAJ\. o, Z.o ~to
z.,olY\-
&A-1.
\
J
Ph~sil's
2211
Paolo Gondolo
Spring 2014
fVI.., f-}__
Name:
Unid: _ _ _ _ _ _ _ _ _ _ _ _ __
10
Final Exam
Discussion TA: _ _ _ _ _ _ _ _ _ __
Show all work!! Report all numbers to three (3) significant figures.
A laser beam of small but finite radius r passes through a thin diverging lens with a focal length of -10 em. The laser
beam's axis is on the principal axis ofthe lens.
(a)
(b)
[I 0 pts.] At what distance past the lens has the laser beam's intensity decreased by a factor of 4?
(d c 1"\
[I 0 pts.] At what distance past the lens has the laser beam's electric field strength decreased by a factor of 4?
13 e... "' ;"u.m .'Yl_j "-' ,
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Unid: ----4==-\L~E~'----
Name:
Discussion TA: ~---------
SilO!! all work!!
11
Final Exam
Reoort all numben to three (3) significant figures.
The figure shows a circular current loop near a wire, carrying currents of0.20 A and 2.0 A, respectively, in the directions
indicated.
(a)
(b)
~
- -------1!1
·~
[10 pts.] What is the magnitude and direction ofthe torque on the
current ·loop?
[10 pts.} What is the loop's orientation that minimizes the loop
energy in the magnetic field of the wire? Specify the
counterclockwise angle from the upward vertical (dashed line in
the figure).
~
2.0cm
_
j2.0mm
®--Wire
2.0A
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12
Final Exam
Sian all work.!! Beoort all numbers to three (3) significant figures.
[10 pts.] A charge of2 J.LC is 20 em above the center of a square of side length 40 em. Find the electric flux through the
square. (Hint: Do not integrate.)
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