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Physics 8.02
Exam One Solutions
Fall 2007
Please Remove this Tear Sheet from Your Exam
23
ˆ
44
oo
qq
rr
πε
==
Er
G
r
G
ˆ
points
source q
observer
r
r
r=
from
to
G
insidefree
o
closed surface
Q
κ
ε
⋅=
∫∫
EdA
G
G
w
points from inside to outside
dA
G
q
=
FE
GG
∫
⋅
−
=
−
=
Δ
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
WU
q
V
=Δ = Δ
point charge
4
o
q
V
r
=
∑
−
=
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
r
V
E
r
∂
=−
∂
for spherical symmetry
Q
C
V
=
Δ
U =
1
2
C
Δ
V
2
=
Q
2
2C
1
parallel
CC
=+
Circumferences, Areas, Volumes:
Circle of radius
r
:
Area =
π
r
2
Circumference =
2
π
r
Sphere of radius
r
Surface Area =
4
r
2
Volume =
3
4
3
r
Cylinder of radius
r
and height
h
Side surface area =
2
r h
End cap surface area =
2
r
2
Volume =
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
Some potentially useful numbers
2
9
2
0
1N
91
0
4C
e
k
×
m
Breakdown of air
E ~ 3 x 10
6
V/m
2
C
12
series
C
=
+
Speed of light
c = 3 x 10
8
m/s
Electron charge
e = 1.6 x 10
19
C
Avagadro’s number N
A
= 6.02 x 10
23
mol
1
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page
2 of 12
Problem 1:
Five Short Questions.
Circle your choice for the correct answer.
Question A (4 points out of 20 points):
Two charges 4Q and Q lie on the yaxis, with the 4Q charge
above
the Q charge.
Below are four possible “grass seed” representations of the electric field of the two
charges.
Which of these representations is most nearly right for the two charges in this
problem?
(1)
(2)
(3)
(4)
Since charges are the same sign the field lines must “fight” (can’t go from one into other)
and the top one is stronger so should “win.”
8.02 Exam #1 Solutions
Fall 2007
MIT PHYSICS DEPARTMENT
page
3 of 12
Question B (4 points out of 20 points):
Two charges lie on the yaxis.
A representation
of
the equipotentials
of the electric potential of these
two charges is shown at left.
The “streaks” in this
representation are parallel to the equipotential
curves.
Which one of the following statements
about the sign and magnitude of the charges is
true?
Compared to the bottom charge, the top charge…
1.
has the opposite sign and is smaller in magnitude
2.
has the opposite sign and is larger in magnitude
3.
has the same sign and is smaller in magnitude
4.
has the same sign and is larger in magnitude
Equipotentials circle around the two charges individually, showing they are of opposite
sign.
The bottom one exerts its effects over a larger area and is hence stronger.
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This homework help 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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