Electrical Energy and Capacitance
47
16.18
Outside the spherical charge distribution, the potential is the same as for a point charge
at the center of the sphere,
e
VkQ
r
=
()
, where
Thus,
9
1.00
10
C
Q
−
=×
11
ee
f
i
ek Q
rr
=
−
−
PE
q
V
∆=
∆
and from conservation of energy
( ) ( )
e
PE
−
∆
KE
,
or
2
0
2
fi
mv
ekQ
−=
−−
−
1
This gives
2
e
ef
i
kQe
mrr
=−
v
, or
( )
2
1
9
2
Nm
2 8.99
10
10
C
C
9.
0.020 0 m
0.030 0 m
v
⋅
×
99
31
1.00
10
C
1.60
11
10
kg
−
××
×
6
7.25
10 m s
v
16.19
From conservation of energy,
( ) ( )
f
i
KE
PE
KE
PE
+=
+
, which gives
2
1
00
2
e
i
f
kQq
r
α
+
or
( )( )
22
27
92
2
e
e
f
ii
ke
e
r
αα
==
2
2
91
9
2
14
2
27
7
28
.
9
9 1
0
1
5
8 1
.
6
0 1
0 C
C
2.74
10
m
6.64
10
kg
2.00
f
r
−
−
−
⋅
×
16.20
By definition, the work required to move a charge from one point to any other point on
an equipotential surface is zero. From the definition of work,
( )
cos
WF
s
θ
=
⋅
, the work
is zero only if
or
0
s
=
cos
0
F
=
. The displacement
s
cannot be assumed to be zero in all
cases. Thus, one must require that

This is the end of the preview. Sign up
to
access the rest of the document.