42.
(a) Since P = i
2
R = J
2
A
2
R, the current density is
J
=
1
A
P
R
=
1
A
P
ρL/A
=
P
ρLA
=
1.0 W
π(3.5
× 10
−5
Ω
·m)(2.0 × 10
−2
m)(5.0
× 10
−3
m)
2
= 1.3
× 10
5
A/m
2
.
(b) From P = iV = J AV w e get
V =
P
AJ
=
P
πr
2
J
=
1.0 W
π(5.0
× 10
−3
m)
2
(1.3
× 10
5
A/m
2
)
= 9.4
× 10
−2
V .