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.
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 Fall '07
 Hudson
 Electric charge, EY, 3 radians, Vmany pointcharges

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