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Physics 8.02
Exam One Solutions
Spring 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
inside
o
closed surface
Q
κ
ε
⋅=
∫∫
EdA
G
G
w
outside
to
inside
from
points
A
d
G
∫
⋅
−
=
−
=
∆
b
a
a
b
b
to
a
from
moving
V
V
V
s
d
E
G
G
0
=
⋅
∫
path
closed
s
d
E
G
G
point charge
4
o
q
V
r
=
many point charges
1
4
N
i
i
oi
q
V
=
=
−
∑
G
K
∑
−
=
pairs
all
j
i
o
j
i
q
q
U
r
r
G
G
4
2
1
2
ov
UE
⎡⎤
=
⎢⎥
⎣⎦
∫∫∫
x
o
l
d
V
E
x
=

∂
V
∂
x
,
E
y
=

∂
V
∂
y
,
E
z
=

∂
V
∂
z
Q
C
V
=
∆
U =
1
2
C
∆
V
2
=
Q
2
2C
o
parallel plate
A
C
d
κε
=
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 Document8.02 Spring 2004
Name_____________________
Problem 1 (25 Points)
Circle your choice for the correct answer to the five questions below.
A:
We have two electric dipoles.
Each dipole consists of two equal and opposite point
charges at the ends of an insulating rod of length
d
.
The dipoles sit along the
x
axis a
distance
r
apart, oriented as shown below.
Their separation
r >> d.
The dipole
ON THE
LEFT
:
1. will feel a force to the
left and a torque trying to make it rotate clockwise
2. will feel a force to the
left and a torque trying to make it rotate counterclockwise
3. will feel a force to the
left and no torque
CORRECT
4. will feel a force to the
right and a torque trying to make it rotate clockwise.
5. will feel a force to the
right and a torque trying to make it rotate counterclockwise
6. will feel a force to the
right and no torque
7. will feel no force and a torque trying to make it rotate counterclockwise.
8. will feel no force and a torque trying to make it rotate counterclockwise
9. will feel no force and no torque
B:
A parallel plate capacitor is filled with a slab of material with dielectric constant
κ
.
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 Fall '07
 Hudson

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