HW 6 Solutions (due online 1 AM, Friday, February 4)
1. Chapter 24 Problem 28
Figure 2442 shows a thin plastic rod of length
L
= 14.3 cm and uniform positive charge
Q
=
52.4 fC lying on an
x
axis. With
V
= 0 at infinity, find the electric potential at point
P
1
on the
axis, at distance
d
= 3.76 cm from one end of the rod.
Solution: Consider an infinitesimal segment of the rod, located between
x
and
x + dx
. It has length
dx
and contains charge
dq =
dx
, where
=
Q
/
L
is the linear charge density of the rod. Its distance from
P
1
is
d
+
x
and the potential it creates at
P
1
is
00
11
.
44
dq
dx
dV
d x
d x
To find the total potential at
P
1
, we integrate over the length of the rod and obtain:
0
0
0
0
0
9
2
2
15
3
ln(
)
ln 1
4
4
4
(8.99 10 N m
C )(56.1 10
C)
0.12 m
ln 1
7.39 10 V.
0.12 m
0.025 m
L
L
dx
Q
L
V
d x
d x
L
d
2. Chapter 24 Problem 34
Two large parallel metal plates are 2.2 cm apart and have charges of equal magnitude but opposite signs
on their facing surfaces. Take the potential of the negative plate to be zero. If the potential halfway
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 Spring '08
 Hickman
 Charge, Electric Potential, Electrostatics, Electric charge, linear charge density, uniform positive charge

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