P24_044.PDF

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Chapter 24 - 24.44
44. The field is zero for 0
≤
r
≤
a as a result of Eq. 24-16. Since q enc (for a
≤
r
≤
b ) is related to the volume
by
q enc = ρ 4 πr 3
3
4 πa 3
3
−
then
4 πε 0 r 2 4 πr 3
4 πa 3
3
=
r 3
a 3
1
4 πε 0
q enc
r 2
ρ
ρ
3 ε 0
−
E =
=
3 −
r 2
for a
≤
r
≤
b .Andfor r
≥
b we have E = q total / 4 πε 0 r 2 or
E =
ρ
3 ε 0
b 3
−
a 3
r
≥
b.
r 2
This is plotted below for r inmetersfrom0to0 . 30 m. The peak value of the electric field, reached at
r = b =0 . 20 m, is 6 . 6
×
10 3 N/C.
6000
4000
2000
0
0.1
r
0.2
0.3
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