This preview shows page 1. Sign up to view the full content.
23.52:
From Problem 22.51, the electric field of a sphere with radius
R
and
q
distributed
uniformly over its volume is
for
4
and
for
4
2
0
3
0
R
r
r
πε
q
E
R
r
R
πε
qr
E
≥
=
≤
=
∫
=

b
a
b
a
b
Edr
V
V
Take
.
at infinity and
.
0
=
∞
V
Let point
a
be a distance
R
r
<
from
the center of the sphere.
∫
∫

=
+
=
∞
R
r
R
r
R
r
R
πε
q
dr
r
πε
q
dr
R
πε
qr
V
2
2
0
2
0
3
0
3
8
4
4
Set
e
q
2
+
=
to get
r
V
for the sphere. The work done by the attractive force of the sphere
when one electron is removed from
is
to
∞
=
d
r


=

=
2
2
0
2
sphere
3
8
2
R
d
R
πε
e
eV
W
r
The total work done by the attractive force of the sphere when both electrons are
removed is twice this,
.
2
sphere
W
The work done by the repulsive force of the two electrons
is
)
2
(
4
0
2
d
πε
e
W
ee
=
The total work done by the electrical forces is
.
2
sphere
ee
W
W
+
The
energy required to remove the two electrons is the negative of this,
This is the end of the preview. Sign up
to
access the rest of the document.