Answer
(a) $J = 1.7\times 10^7~A/m^2$
(b) $i_e = 5.3\times 10^{18}~electrons/s$
Work Step by Step
(a) We can find the current density in the filament:
$J = \frac{I}{A}$
$J = \frac{I}{\pi~r^2}$
$J = \frac{0.85~A}{(\pi)~(0.125\times 10^{-3}~m)^2}$
$J = 1.7\times 10^7~A/m^2$
(b) We can find the electron current:
$i_e = \frac{I}{e}$
$i_e = \frac{0.85~C/s}{1.6\times 10^{-19}~C/electron}$
$i_e = 5.3\times 10^{18}~electrons/s$
