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Physics 8.02
Exam One Solutions
Fall 2003
PLEASE DETACH THIS SHEET
AND USE AT YOUR CONVENIENCE
Some (possibly useful) Relations:
F
=
1
4
πε
o
q
1
q
2
r
2
23
ˆ
44
oo
qq
rr
==
Err
G
G
ˆ
points
source
observer
r
r
r=
from
to
G
2
0
1
ˆ
4
V
dq
r
=
∫
Er
G
inside
o
closed surface
Q
ε
⋅=
∫∫
EdA
G
G
w
outside
to
inside
from
points
A
d
G
∫
⋅
−
=
−
=
∆
b
a
a
b
b
to
a
from
moving
V
V
V
s
d
E
G
G
0
=
⋅
∫
path
closed
s
d
E
G
G
V
point charge
=
q
4
o
r
∑
=
−
=
N
i
i
o
i
q
V
1
4
r
r
K
G
charges
point
many
∑
−
=
pairs
all
j
i
o
j
i
q
q
U
r
r
G
G
4
2
1
2
ov
o
l
UE
d
V
=
∫∫∫
x
E
x
=

∂
V
∂
x
,
E
y
=

∂
V
∂
y
,
E
z
=

∂
V
∂
z
Q
C
V
=
∆
U =
1
2
C
∆
V
2
=
Q
2
2C
o
parallel plate
A
C
d
κε
=
12
parallel
CC
C
=
+
series
C
=
+
Circumferences, Areas, Volumes:
1) The area of a circle of radius
r
is
π
r
2
Its circumference is
2
π
r
2) The surface area of a sphere of radius
r
is
4
r
2
Its volume is
3
4
3
r
3) The area of the sides of a cylinder of
radius
r
and height
h
is
2
r h
Its volume is
r
2
h
Definition of trig functions
sin is opposite/hypotenuse;
cos is adjacent/hypotenuse;
tangent is opposite over adjacent;
Properties of
30, 45,
and 60 degrees
(
π
/6,
π
/4, and
π
/3 radians)
:
sin(
π
/6) = cos(
π
/3) = 1/2,
sin(
π
/3) = cos(
π
/6) =
2
/
3;
sin(
π
/4) = cos(
π
/4) =
2
/
1
;
Integrals that may be useful
a
b
dr
b
a
−
=
∫
)
/
ln(
1
a
b
dr
r
b
a
=
∫
−
=
∫
b
a
dr
r
b
a
1
1
1
2
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View Full Document8.02 Spring 2003
Name_____________________
Page
2
Problem 1 (25 Points)
Circle your choice for the correct answer to the five questions below.
A:
An electric dipole, consisting of two equal and opposite point charges at the ends of a
insulating rod, sits in the electric field of a stationary positive point charge, as shown.
The dipole is free to move.
The dipole will
1.
rotate clockwise and move to the left
2.
rotate counterclockwise and move to the right
3.
rotate clockwise and move to the right
4.
rotate counterclockwise and move to the left
CORRECT
5.
rotate clockwise but otherwise not move
6. rotate counterclockwise but otherwise not move
B:
A parallel plate capacitor is connected to a battery and charged to a charge
Q
.
The
battery is left in the circuit.
A slab of material with dielectric constant
κ
in inserted
between the plates.
Which one of the following statements is true?
1. The charge
Q
on the capacitor plates increases and the voltage difference between
the plates increases
2. The charge
Q
on the capacitor plates decreases and the voltage difference between
the plates decreases
3.
The charge
Q
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 Fall '07
 Hudson

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