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Physics 8.02
Exam One
Fall 2004
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
==
Er
G
r
G
ˆ
points
source q
observer
r
r
r=
from
to
G
2
0
1
ˆ
4
V
dq
r
=
∫
G
free, inside
closedsurface
o
Q
d
κ
ε
⋅=
∫∫
EA
G
G
w
pointsfrom inside to outside
d
A
G
moving from
to
b
ab
b
a
a
VV
V
∆
=−=
− ⋅
∫
Es
G
G
d
closedpath
0
d
∫
G
G
v
point charge
4
o
q
V
r
=
many point charges
1
4
N
i
i
oi
q
V
=
=
−
∑
G
K
all pairs
0
4
ij
U
=
−
∑
GG
2
vol
1
2
o
UE
⎛⎞
=
⎜⎟
⎝⎠
∫∫∫
x
d
V
V
=−∇
E
G
or
E
x
=

∂
V
∂
x
,
E
y
=

∂
V
∂
y
,
E
z
=

∂
V
∂
z
Q
C
V
=
∆
2
2
1
()
22
Q
UC
V
C
∆
1
parallel
CC
2
C
=
+
12
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 Document 8.02 Fall 2004
Name_____________________
Problem 1 (25 Points)
Circle your choice for the correct answer to the five questions below.
A:
Consider an electric dipole immersed in a uniform electric field. Which of the
following statements regarding the force
F
G
and the torque
τ
G
is strictly true regardless of
the orientation of the dipole:
1.
and
.
0
≠
F
G
0
≠
τ
G
2.
and
.
0
=
F
G
0
≠
τ
G
3.
and
.
0
≠
F
G
0
=
τ
G
4.
and
.
0
=
F
G
0
=
τ
G
5.
but
may or may not be zero.
0
=
F
G
τ
G
6.
may or may not be zero but
F
G
0
=
τ
G
.
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This test prep was uploaded on 04/07/2008 for the course 8 8.02 taught by Professor Hudson during the Fall '07 term at MIT.
 Fall '07
 Hudson

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