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Physics 8.02
Exam One
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
o
parallel plate
A
C
d
κε
=
23
ˆ
44
oo
qq
rr
==
Er
G
r
G
1
parallel
CC
2
C
=
+
12
series
=
+
C
ˆ
points
source
observer
r
r
r=
from
to
G
Circumferences, Areas, Volumes:
1)
The area of a circle of radius
r
is
π
r
2
Its circumference is
2
π
r
2
0
1
ˆ
4
V
dq
r
=
∫
G
2)
The surface area of a sphere of radius
r
is
4
r
2
inside
o
closed surface
Q
ε
⋅=
∫∫
EdA
G
G
w
G
Its volume is
3
4
3
r
outside
to
inside
from
points
A
d
∫
⋅
−
=
−
=
∆
b
a
a
b
b
to
a
from
moving
V
V
V
s
d
E
G
G
G
G
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
0
=
⋅
∫
path
closed
s
d
E
Definition of trig functions
V
point charge
=
q
4
o
r
sin is opposite/hypotenuse;
cos is adjacent/hypotenuse;
∑
=
−
=
N
i
i
o
i
q
V
1
4
r
r
K
G
charges
point
many
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,
∑
−
=
pairs
all
j
i
o
j
i
q
q
U
r
r
G
G
4
sin(
π
/3) = cos(
π
/6) =
2
/
3;
sin(
π
/4) = cos(
π
/4) =
2
/
1
;
2
1
2
ov
UE
=
∫∫∫
x
o
l
d
V
Integrals that may be useful
a
b
dr
b
a
−
=
∫
E
x
=

∂
V
∂
x
,
E
y
=

∂
V
∂
y
,
E
z
=

∂
V
∂
z
)
/
ln(
1
a
b
dr
r
b
a
=
∫
Q
C
V
=
∆
U =
1
2
C
∆
V
2
=
Q
2
2C
−
=
∫
b
a
dr
r
b
a
1
1
1
2
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View Full Document8.02 Spring 2003
Name_____________________
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
5.
rotate clockwise but otherwise not move
6.
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 Fall '07
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