solution to quiz1.tex
1. 1
→
Φ
E
= 3
.
0
×
10
6
Nm
2
/C
2
→
Φ
E
= 0
hint:
Φ
E
≡
E A
cos
θ
, where
θ
is the angle between the direction of the ﬁeld and the direction normal
to the area.
2. stay the same
hint:
From Gauß’s theorem, the number of ﬁeld lines through a closed surface is proportional the
enclosed charge, which is a constant for this problem.
3. 2
.
25
×
10

9
N/m
hint:
According to Hook’s law,

F

=
κx
where
κ
is the spring constant. On the other hand,
F
is just
the Coulomb attraction between the two charges.
4. 5
×
10
5
N
hint:
The number of charges is
n
= 1
gram/m
p
where
m
p
is the proton mass, so the resulting
Coulomb force is
F
=
k
(
ne
)
2
/
(2
R
E
)
2
.
5.
E
a
=
kq/r
2
a
,
E
b
= 0,
E
c
=
kq/r
2
c
hint:
There will be a total charge of
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 Winter '07
 BRIANKEATING
 Electric charge, 1 gram, Hook, 0.85 m

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