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Electric Forces and Electric Fields
21
(c) Outside the spherical dome,
2
e
kq
E
r
=
. Thus, at
4.0 m
r
=
,
()
( )
92
2
4
2
8.99
10 N m
C
2.0
10
C
C
4.0 m
E
−
×⋅
×
==
5
1.1
10 N
×
15.35
For a uniformly charged sphere, the field is strongest at the surface.
Thus,
max
max
2
e
E
R
=
,
or
( )
( )
2
6
2
3
max
max
2
2.0 m
3.0
10 N C
1.3
10
C
8.99
C
e
RE
q
k
−
×
=
×
15.36
If the weight of the drop is balanced by the electric force, then
mg
or the
mass of the drop must be
q E
eE
( )
( )
19
4
16
2
1.6
10
C
3
51
0
k
g
9.8 m s
eE
m
g
−
−
××
≈
×
But,
3
4
3
mV
r
ρρ
π
and the radius of the drop is
13
3
4
m
πρ
r
=
16
7
3
35 10 kg
5.2
10
m
or
~ 1 m
48
5
8
k
gm
rr
µ
−
−
×
×
15.37
(a)

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