Answer
$J = 1.3\times 10^5~A/m^2$
Work Step by Step
We can find the resistance:
$R = \frac{\rho~L}{A}$
$R = \frac{\rho~L}{\pi~r^2}$
$R = \frac{(3.5\times 10^{-5}~\Omega\cdot m)(2.0\times 10^{-2}~m)}{(\pi)(5.0\times 10^{-3}~m)^2}$
$R = 8.9\times 10^{-3}~\Omega$
We can find the current:
$P = i^2~R$
$i^2 = \frac{P}{R}$
$i = \sqrt{\frac{P}{R}}$
$i = \sqrt{\frac{1.0~W}{8.9\times 10^{-3}~\Omega}}$
$i = 10.6~A$
We can find the magnitude of the current density:
$J = \frac{i}{A}$
$J = \frac{i}{\pi~r^2}$
$J = \frac{10.6~A}{(\pi)~(5.0\times 10^{-3}~m)^2}$
$J = 1.3\times 10^5~A/m^2$
