Name: _______________________________________________________________________
Exam #3
Physics I
Fall 2006
If you would like to get credit for having taken this exam, we need
your name (printed clearly) at the top and section number below.
Your name should be at the top of every page.
Section #
_____ 1
_____ 2
_____ 3
_____ 5
_____ 6
_____ 7
_____ 8
_____ 9
_____ 10
M/R 8-10 (Bedrosian)
M/R 10-12 (Bedrosian)
M/R 12-2 (Zhang)
M/R 2-4 (Schroeder)
T/F 10-12 (Wetzel)
T/F 12-2 (Wetzel)
T/F 2-4 (Eah)
M/R 4-6 (Bedrosian)
T/F 12-2 (Eah)
Questions
A
Value
24
B-1
20
B-2
28
C
28
Total
100
Score
You may not unstaple this exam.
Only work written on the same page as the question will be graded.
Cheating on this exam will result in an F in the course.
1
Name: _______________________________________________________________________
On this exam, please neglect any relativistic and/or quantum mechanical effects. If you don’t
know what those are, don’t worry, we are neglecting them! On all multiple-choice questions,
choose the best answer(s) in the context of what we have learned in Physics I.
On graphing and numerical questions (Parts B and C), show all work to receive credit.
Part A – Multiple Choice – 24 Points Total
Write your choice(s) on the line to the left of the question number.
Questions on this page are worth 4 points each.
_______1.
A)
B)
C)
D)
An electron is moving in a static, uniform magnetic field. The only force on the
electron is the magnetic force. Which of the following quantities must remain
constant? Pick all that apply or put "0" for none of them.
The electron's speed.
The electron's velocity.
The electron's momentum.
The electron's kinetic energy.
Questions 2 and 3 will use the following directions as answers. Pick the letter of the direction
arrow that best answers each respective question. (Please don't draw an arrow!)
A)
B)
C)
D)
↑
↓
→
←
_______2.
E)
F)
G)
H)




In the figure below, what is the direction of the electric field at the X due to the two
point charges, one –Q and one +Q?
-Q
_______3.
+Q
In the figure below, what is the direction of the electric field at the X due to the two
point charges, both +Q?
+Q
+Q
2
Name: _______________________________________________________________________
Each question on this page is worth 2 points.
Questions 4-9 involve finding points on the line connecting two point charges where either the
electric field or the electric potential is zero. The line has been broken into three regions – A, B,
and C – as we did in class. If there is a zero point somewhere in a region, select the appropriate
letter. Pick all regions that apply. If there are no points, put "0" for your answer. Points at
"infinity" don't count since we define the electric potential to be zero at infinity and the electric
field is always zero infinitely far from all charges.
Region A
Region B
-e
Region C
+2e
Figure Q4-Q5
_______4.
In Figure Q4-Q5, in which region(s) of the line is the electric field zero at a point?
_______5.
In Figure Q4-Q5, in which region(s) of the line is the electric potential zero at a
point?
Region A
Region B
+e
Region C
+e
Figure Q6-Q7
_______6.
In Figure Q6-Q7, in which region(s) of the line is the electric field zero at a point?
_______7.
In Figure Q6-Q7, in which region(s) of the line is the electric potential zero at a
point?
Region A
Region B
-e
Region C
+e
Figure Q8-Q9
_______8.
In Figure Q8-Q9, in which region(s) of the line is the electric field zero at a point?
_______9.
In Figure Q8-Q9, in which region(s) of the line is the electric potential zero at a
point?
3
Name: _______________________________________________________________________
B-1 – Graphing – 20 Points
An electron moving in the +X direction experiences an electric force shown in the graph below.
(The maximum value is +3.2  10–17 N.)
Plot the electric field (X component) and electric potential corresponding to the force.
Assume the electric potential begins at zero at X = 0 cm.
Make sure to include the following features – they should be clearly shown on your graphs:
1. Clearly labeled vertical axis with values and units.
2. General shapes of the curves, noting any points where the curvature or slope changes.
Show all work.
Fx (10^-17 N)
3.2
1.6
x (cm)
0
10
-1.6
Ex (
20
30
)
x (cm)
0
10
20
30
0
V (
)
x (cm)
0
10
20
30
4
Name: _______________________________________________________________________
B-2 – Graphing – 28 Points
In the figure below, Regions A and B are squares with side lengths = 10.0 cm.
A beam consisting of helium nucleii (charge = +2e and mass = 6.64  10–27 kg) enters into
Region A at the tip of the arrow as shown, halfway along a side, with a velocity of 7.00  10+5
m/s in the +X direction. There is a uniform electric field of 1.00  10+5 N/C in the +X direction
and no magnetic field in Region A. In Region B, the electric field is zero and the magnetic field
is uniform with the value 0.500 T in the –Z direction (into the page).
Plot the path of the beam of helium nucleii as it travels through region A, into region B, and
finally exits region B. Ignore the interactions of the individual helium nucleii with each other.
Show all work. Your plot should clearly show the shape of the path in each region (straight line,
parabola, circle, etc.) and exactly where the particle exits each region.
Y
X
10 cm
10 cm
10 cm
Region A
Region B
5
Name: _______________________________________________________________________
Problem C (28 Points) – Electric Field and Electric Potential
Find the electric field and electric potential at the location marked “X” due to the three point
charges as shown in the figure below. The point charges and “X” are on the corners of a square
0.10 m on a side. Note: 1.00 nC = 1.00 × 10–9 C.
Assume that the electric potential is defined to be zero at infinity.
+1.00 nC
-2.00 nC
0.10 m
Y
0.10 m
X
0.10 m
0.10 m
+1.00 nC
Electric Field X Component:
_________________________________ units ________
Electric Field Y Component:
_________________________________ units ________
Electric Potential:
_________________________________ units ________
6
Name: _______________________________________________________________________
Formula Sheet for Homework and Exams – Page 1 of 2


U    Fcons  dx
1.
v  v 0  a t  t 0 
23.
2.
x  x 0  v 0 ( t  t 0 )  12 a ( t  t 0 ) 2
24.
U g  m g (y  y 0 )
3.
x  x 0  12 ( v0  v)( t  t 0 )
25.
U s  12 k ( x  x 0 ) 2
4.
x  x 0  v( t  t 0 )  12 a ( t  t 0 ) 2
26.
27.
28.
 K   U  Wnoncons
s  r
v tangential   r
29.
a tangential   r
6.
v 2  v 02  2a x  x 0 
 

 F  Fnet  m a
7.
T
8.
a centripetal 
5.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
2r
v
v2
 2 r
r
a radial  a centripetal


p  mv

 
dp
F

F


net
dt



J   Fnet dt   p


P   pi


dP
  Fext
dt
30.
  0  t  t 0 
31.
   0  0 ( t  t 0 )  12 ( t  t 0 ) 2
32.
   0  12 (0  )( t  t 0 )
33.
   0  ( t  t 0 )  12 ( t  t 0 ) 2
 2  02  2   0 
   
35a. a  b  a b sin( )
 
a  b  a y b z  a z b y î 
35b.
a z b x  a x b z  ĵ  a x b y  a y b x k̂
34.

36.
37.
M   mi
38.
1
1
x cm   m i x i y cm   m i y i
M
M


P  M v cm
   
a  b  a b cos()  a x b x  a y b y  a z b z
 
W  Fd
 
W   F  dx
21.
K  12 m v 2  12 m (v x  v y )
22.
K f  K i  Wnet
2
39.
40.
41.
42.
43.
2
I   m i ri


2
K rot  12 I  2
 
W     d
  
  r F

 dL

  I  d t
  
l  r p


L  l i


L  I
44x. m1 v1, x ,before  m 2 v 2, x ,before  m1 v1, x ,after  m 2 v 2, x ,after
44y. m1 v1, y ,before  m 2 v 2, y ,before  m1 v1, y ,after  m 2 v 2, y,after
44z. m1 v1,z ,before  m 2 v 2,z ,before  m1 v1,z ,after  m 2 v 2,z ,after
45a. v1,f 
m1  m 2
2 m2
v1,i 
v 2 ,i
m1  m 2
m1  m 2
45b.
7
v 2,f 
2 m1
m  m1
v1,i  2
v 2 ,i
m1  m 2
m1  m 2

Formula Sheet for Homework and Exams – Page 2 of 2
46a.
46b.
47a.
47b.
48a.
48b.
49.

m m
| F | G 1 2 2
r

m m
F  G 1 2 2 r̂
r

1 | q1 || q 2 |
| F |
4  0
r2

1 q1 q 2
F
(r̂ )
4  0 r 2

1 | qi |
| Ei |
4   0 ri 2

1 qi
E
(r̂i )
4   0 ri 2


F  qE
50.
51.
52.
1 qi
4   0 ri
U  qV
 
V    E  dx
V
V
x
V
53y. E y  
y
V
53z. E z  
z

 
54. F  q v  B
mv
55. r 
qB
53x. E x  
Useful Constants
(You can use the approximate values on exams.)
Universal Gravitation Constant
G  6.67310 11 N m 2 kg 2  6.67 10 11
Electrostatic Force Constant
1
 8.987551788 10 9 N m 2 C  2  9.0 10 9
4  0
Magnetic Constant
 0  4  10 7 H m 1  1.26 10 6
Speed of Light in Vacuum
c  2.99792458 10 8 m s 1  3.0 10 8
Charge of a Proton
e  1.602176462 10 19 C  1.6 10 19
Electron-Volt Conversion Constant
1eV  1.602176462 10 19 J  1.6 10 19
Mass of a Proton
m p  1.6726215810 27 kg  1.67 10 27
Mass of an Electron
m e  9.10938188 10 31 kg  9.110 31
8