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12. Eq. 236 (Gauss’ law) gives
ε
ο
Φ =
q
enc
.
(a) Thus, the value
52
2.0 10 N m /C
Φ=
×
⋅
for small
r
leads to
12
2
2
5
2
6
6
central
0
(8.85 10
C /N m )(2.0 10 N m /C)
1.77 10 C
1.8 10 C
q
ε
−−
−
=Φ
=
×
⋅
×
⋅
=
×
≈ ×
.
(b) The next value that
Φ
takes is
4.0 10 N m /C
Φ=−
×
⋅
, which implies
6
enc
3.54 10 C.
q
−
=−
×
But we have already accounted for some of that charge in part (a), so
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 Fall '10
 AC

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