#### Answer

(a) $I = 0.80~A$
(b) $J = 7.1\times 10^7~A/m^2$

#### Work Step by Step

(a) We can find the current $I$:
$I = J~A$
$I = J~\pi~r^2$
$I = (4.5\times 10^5~A/m^2)~(\pi)~(0.75\times 10^{-3}~m)^2$
$I = 0.80~A$
(b) We can find the current density in the filament:
$J = \frac{I}{A}$
$J = \frac{I}{\pi~r^2}$
$J = \frac{0.80~A}{(\pi)~(0.06\times 10^{-3}~m)^2}$
$J = 7.1\times 10^7~A/m^2$