P25_043.PDF
(
65 KB
)
Pobierz
Chapter 25 - 25.43
43. We use the conservation of energy principle. The initial potential energy is
U
i
=
q
2
/
4
πε
0
r
1
, the initial
kinetic energy is
K
i
= 0, the final potential energy is
U
f
=
q
2
/
4
πε
0
r
2
, and the final kinetic energy is
K
f
=
2
mv
2
,where
v
is the final speed of the particle. Conservation of energy yields
q
2
4
πε
0
r
1
=
4
πε
0
r
2
+
1
q
2
2
mv
2
.
The solution for
v
is
v
=
2
q
2
4
πε
0
m
1
r
1
−
1
r
2
(8
.
99
=
×
10
9
N
·
m
2
/
C
2
)(2)(3
.
1
×
10
−
6
C)
2
1
0
.
90
10
−
3
m
−
1
20
×
10
−
6
kg
×
2
.
5
×
10
−
3
m
=2
.
5
×
10
3
m
/
s
.
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