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6. (a) By Eq. 2418, the change in potential is the negative of the
“area”
under the curve.
Thus, using the areaofatriangle formula, we have
VE
d
s
x
−=
−
⋅=
=
z
10
1
2
22
0
0
2
G
G
b
gb
g
which yields
V
= 30 V.
(b) For any region within 0
3
<< − ⋅
z
xE
d
s
m,
G
G
is positive, but for any region for which
x
> 3 m it is negative. Therefore,
V = V
max
occurs at
x
= 3 m.
d
s
x
−
=
z
10
1
2
32
0
0
3
G
G
b
g
which yields
V
max
= 40 V.
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 Spring '10
 Rebello,NobelS

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