Since the repulsive electrical force neutralizes the attractive gravitational
force, the magnitudes of the two forces are equal:
e
m
2
2
Electrical
Gravitational
force,
force,
Equation 18.1
Equation 4.3
GM M
k q q
r
r
=
±²³²´
±²³²´
Solving this equation for the magnitude
q
of the charge on either body, we find
(
)(
)
2
11
24
22
2
13
e
m
2
9
2
N m
6.67
10
5.98
10
kg
7.35
10
kg
kg
5.71
10
C
N m
8.99
10
C
GM M
q
k
−
⎛
⎞
⋅
×
×
×
⎜
⎟
⎝
⎠
=
=
=
×
⋅
×
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11.
SSM
WWW
REASONING
Initially, the two spheres are neutral.
Since negative
charge is removed from the sphere which loses electrons, it then carries a net positive
charge.
Furthermore, the neutral sphere to which the electrons are added is then negatively
charged.
Once the charge is transferred, there exists an electrostatic force on each of the
two spheres, the magnitude of which is given by Coulomb's law (Equation 18.1),
2
1
2
/
F
k q
q
r
=
.
SOLUTION
a.
Since each electron carries a charge of
19
1.60
10
C
−
−
×
, the amount of negative charge
removed from the first sphere is
(
)
19
13
6
1.60
10
C
3.0
10
electrons
4.8
10
C
1 electron
−
−
⎛
⎞
×
×
=
×
⎜
⎟
⎜
⎟
⎝
⎠
Thus, the first sphere carries a charge +4.8
×
10
–6
C, while the second sphere carries a
charge

4.8
×
10
–6
C.
The magnitude of the electrostatic force that acts on each sphere is,
therefore,
(
)(
)
(
)
2
9
2
2
6
1
2
2
2
8.99
10
N
m
/C
4.8
10
C
0.83 N
0.50 m
k q
q
F
r
−
×
⋅
×
=
=
=
b.
Since the spheres carry charges of opposite sign, the force is
attractive
.
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