P22_049.PDF
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Chapter 22 - 22.49
49. In experiment 1, sphere
C
first touches sphere
A
, and they divided up their total charge (
Q/
2plus
Q
)
equally between them. Thus, sphere
A
and sphere
C
each acquired charge 3
Q/
4. Then, sphere
C
touches
B
and those spheres split up their total charge (3
Q/
4plus
−
Q/
4) so that
B
ends up with charge equal
to
Q/
4. The force of repulsion between
A
and
B
is therefore
F
1
=
k
3
4
4
d
2
at the end of experiment 1. Now, in experiment 2, sphere
C
first touches
B
which leaves each of them
with charge
Q/
8. When
C
next touches
A
, sphere
A
is left with charge 9
Q/
16. Consequently, the force
of repulsion between
A
and
B
is
9
16
8
d
2
F
2
=
k
at the end of experiment 2. The ratio is
F
1
=
16
8
4
4
=0
.
375
.
F
2
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