Physics 8.02
Exam One
Spring 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
Quadratic formula:
0
2
=
+
+
c
bx
ax
a
ac
b
b
x
2
4
2
−
±
−
=
r
E
ˆ
4
2
r
q
o
πε
=
G
Circumferences, Areas, Volumes:
observer
to
source
from
points
r
ˆ
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
πε
=
∫
E
r
G
2)
The surface area of a sphere of radius
r
is
4
π
r
2
∫
=
⋅
surface
closed
o
inside
Q
ε
A
d
E
G
G
G
Its volume is
3
3
4
r
π
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
π
rh
Its volume is
π
r
2
h
0
=
⋅
∫
path
closed
s
d
E
Definition of trig functions
V
point charge
=
q
4
πε
o
r
sin is opposite/hypotenuse;
cos is adjacent/hypotenuse;
∑
=
−
=
N
i
i
o
i
q
V
1
4
r
r
K
G
πε
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
πε
4
sin(
π
/3) = cos(
π
/6) =
2
/
3
;
sin(
π
/4) = cos(
π
/4) =
2
/
1
;
E
x
=

∂
V
∂
x
,
E
y
=

∂
V
∂
y
,
E
z
=

∂
V
∂
z
Integrals that may be useful
a
b
dr
b
a
−
=
∫
C
≡
Q
∆
V
)
/
ln(
1
a
b
dr
r
b
a
=
∫
U =
1
2
C
∆
V
2
=
Q
2
2C
−
=
∫
b
a
dr
r
b
a
1
1
1
2
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8.02 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, is free to rotate about a pivot point in the center. The rod is placed in a
uniform
electric field
E
that is perpendicular to the axis of the rod
. The dipole will
experience
1.
a noticeable electric force and no noticeable electric torque
2.
no noticeable electric force and a noticeable electric torque
3.
a noticeable electric force and a noticeable electric torque
4.
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 Fall '07
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