P27_045.PDF

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Chapter 27 - 27.45
45. (a) Since the area of a hemisphere is 2 πr 2 then the magnitude of the current density vector is
J
= i
A =
I
2 πr 2
.
(b) Eq. 27-11 yields
E
= ρ
J
= ρI/ 2 πr 2 .
(c) Eq. 25-18 leads to
r
r
ρI
2 πr 2
dr = ρI
2 π
1
r −
1
b
.
E
∆ V = V r −
V b =
−
·
dr =
−
b
b
(d) Using the given values, we obtain
J
=
2 π (10) 2 =0 . 16 A/m 2 .
100
(e) Also,
E
= 16 V/m (or 16 N/C).
(f) With b =0 . 010 m, the voltage is ∆ V =
−
1 . 6
×
10 5 V.
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