Physics 8.02
Exam One
Fall 2002
PLEASE DETACH THIS SHEET
AND USE AT YOUR CONVENIENCE
Some (possibly useful) Relations:
F
=
1
4
πε
o
q
1
q
2
r
2
E
=
q
4
o
r
2
ˆ
r
observer
to
source
from
points
r
ˆ
2
0
1
ˆ
4
V
dq
r
=
∫
Er
G
∫
=
⋅
surface
closed
o
inside
Q
ε
dA
E
outside
to
inside
from
points
dA
∫
⋅
−
=
−
=
∆
b
a
a
b
b
to
a
from
moving
V
V
V
ds
E
0
=
⋅
∫
path
closed
ds
E
V
point charge
=
q
4
o
r
∑
=
−
=
N
i
i
o
i
q
V
1
4
r
r
charges
point
many
j
i
q
q
U
ij
j
i
o
j
i
≠
−
=
∑∑
,
4
2
1
r
r
E
x
=

∂
V
∂
x
,
E
y
=

∂
V
∂
y
,
E
z
=

∂
V
∂
z
C
≡
Q
∆
V
U =
1
2
C
∆
V
2
=
Q
2
2C
d
A
o
plate
parallel
κ
=
C
Circumferences, Areas, Volumes:
1) The area of a circle of radius
r
is
π
r
2
Its circumference is
2
r
2) The surface area of a sphere of radius
r
is
4
r
2
Its volume is
3
3
4
r
3) The area of the sides of a cylinder of
radius
r
and height
h
is
2
rh
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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Part I
 Concept Questions (25 Points)
Circle your choice for the correct answer to the five concept questions below. Each
question is worth five points.
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
nonuniform electric field. 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
CORRECT
4.
no noticeable electric force and no noticeable electric torque
B:
When you place a positively charged particle in an electric field, does it move from
1.
higher to lower electric potential and lower to higher potential energy
2. higher to lower electric potential and higher to lower potential energy
CORRECT
3.
lower to higher electric potential and lower to higher potential energy
4.
lower to higher electric potential and higher to lower potential energy
C:
A
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 Fall '07
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